**2. Biomedical sensors**

### **2.1. Biomedical sensor classification**

Many different kinds of sensors can be used in biomedical application. According to the sensing principle in biomedical application, biomedical sensors can be classified into physical sensors and chemical sensors, seen in table 1.

It's possible to categorize all sensors as being physical or chemical. In the case of physical sensors, quantities such as geometric, mechanical, thermal, and hydraulic variables are measured. In biomedical applications these variables can include things such as muscle displacement, blood pressure, core body temperature, blood flow, cerebrospinal fluid pres‐ sure, and bone growth velocity. Two types of physical sensors deserve special mention with regard to their biomedical application: sensors of electrical phenomena in the body, usually known as electrodes, play a special role as a result of their diagnostic therapeutic applications. The most familiar of these are sensors used to pick up the electrocardiogram, an electrical signal produced by the heart. The other type of physical sensor that finds many applications in biology and medicine is optical sensor. These sensors can utilize light to collect information, and, in the case of fiber optic sensors, light is the signal transmission medium as well.

The second major classification of sensing device is chemical sensors. In this case sensors are concerned with the chemical quantities such as identifying the presence of chemical composite, detecting the concentration of various chemical species, and monitoring the chemical activities in the body for diagnostic and therapeutic application. A wide variety of chemical sensors are classified in many ways. Chemical sensors are used to detect chemical components being measured and chemical composition measured in the gas phase. Electrochemical sensors are utilized to measure chemical concentration, or more precisely, activities based on chemical reactions that interact with electrical systems. Photometric chemical sensors are optical devices that detect chemical concentrations based on changes in light transmission, reflection or color. Other types of physical chemical sensors such as the mass spectrometer utilize various physical methods to detect and quantify chemicals associated with biologic systems.


**Table 1.** Classifications of biomedical sensor

Although bioanalytic sensors are essentially chemical sensors, they are often classified as a separate major sensor category. These devices incorporate biologic recognition reaction such as enzyme-substrate to identify complex biochemical molecules. The use of biologic reactions gives bioanalytic sensors high sensitivity and specificity in identifying and quantifying biochemical substances.

## **2.2. Oxygen and carbon dioxide sensor for blood**

Measurements of arterial blood gas (pO2 and pCO2) and pH are frequently performed by on critical patients in both the operating rooms and intensive care unit. They are selected and used by the physician to adjust mechanical ventilation or administer pharmacological agents. Such measurement could provide information about the respiratory and metabolic imbalance in the body and reflect the change of blood oxygen increment and carbon dioxide(CO2) elimination.

Noninvasive sensors for measuring O2 and CO2 in arterial blood are based on the discovery that gases such as O2 and CO2 can easily diffuse from body skin. Diffusion occurs due to a partial pressure difference between the blood in the superficial layers of the skin and the outermost surface of the skin. Such idea has been used to develop two types of noninvasive electrochemical sensors pO2 and pCO2. The discovery that blood changes its color depending on the percent of oxygen has led to the development of several optical methods to measure the oxygen saturation in blood.

#### *2.2.1. Oxygen sensor for blood*

The second major classification of sensing device is chemical sensors. In this case sensors are concerned with the chemical quantities such as identifying the presence of chemical composite, detecting the concentration of various chemical species, and monitoring the chemical activities in the body for diagnostic and therapeutic application. A wide variety of chemical sensors are classified in many ways. Chemical sensors are used to detect chemical components being measured and chemical composition measured in the gas phase. Electrochemical sensors are utilized to measure chemical concentration, or more precisely, activities based on chemical reactions that interact with electrical systems. Photometric chemical sensors are optical devices that detect chemical concentrations based on changes in light transmission, reflection or color. Other types of physical chemical sensors such as the mass spectrometer utilize various physical

> Geometric Mechanical Thermal Hydraulic Electric Optical

Gas

Electrochemical Photometric

Metal plate

Enzyme Protein Antigen Antibody Ligand Cell DNA

Microelectrode

Other physical chemical methods

Body surface biopotential electrode

Intracavitary and intratissue electrode

methods to detect and quantify chemicals associated with biologic systems.

**Class of sensor Biomedical sensor**

Physical sensors

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Chemical sensors

Biopotential electrodes

Bioanalytic (or biosensor)

**Table 1.** Classifications of biomedical sensor

The method for measuring blood oxygenation is very great important in assessing the circulatory and respiratory condition of a patient. The blood from the lungs to the tissues in two distinct states transports oxygen. Under normal physiological conditions, approximately 2% of the total amount of oxygen carried by the blood is dissolved in the plasma. This amount is proportional to the blood pO2.. The 98% remain is carried inside the erythrocytes in a loose reversible chemical combination with hemoglobin (Hb) as oxyhemoglobin (HbO2). Thus, there are two methods for measuring the blood oxygenation: either using polarographic pO2 sensor or measuring oxygen saturation (the relative amount of hemoglobin dioxide HbO2 in the blood) by means of an optical oximeter.

A pO2 sensor, also widely known as a Clark electrode, is used to measure the partial pressure of O2 gas in a sample of air or blood. This sensor is categorized as an amperometric sensor and requires an external polarization bias source. The measurement is based on the principle of polarography as illustrated in figure 4. The electrode utilizes the ability of oxygen O2 molecules to react chemically with H2O in the presence of electrons to produce hydroxyl (OH- ) ions. This electrochemical reaction, called an oxidation/reduction or redox reaction, generates a small current and requires an externally applied constant polarizing voltage source of about 0.6V.

Oxygen is reduced (consumed) at the surface of a noble metal (such as platinum or gold) cathode (this electrode is connected to the negative side of voltage source) according to the following the chemical reaction:

$$\text{O}\_2 + 2\text{H}\_2\text{O} + 4e \leftharpoons 4\text{OH}^-$$

In this reduction reaction, one O2 molecule takes four electrons and reacts with two water molecules, generating four hydroxyl ions. The resulting OH ions migrate and react with a reference Ag/AgCl anode (this electrode is connected to the positive side of voltage source), causing a two-step oxidation reaction as follows:

$$\begin{aligned} Ag &\rightharpoonup Ag^\cdot + e \\\\ Ag^\cdot + Cl^- &\rightharpoonup AgCl \end{aligned}$$

**Figure 4.** Sensing principle of Clark-type pO2 sensor

In this oxidation reaction, silver from the anode electrode is firstly oxidized to silver ions, and electrons are liberated to the anode. These silver ions are immediately combined with chloride ions to form a kind of compound precipitant silver chloride *AgCl* which precipitates on the surface of anode. The transient current between the anode and the cathode in the external circuit produced by this reaction is directly proportional to the number of O2 molecules constantly reduced on the surface of the cathode. The electrodes in the polarographic cell are immersed in an electrolyte solution of potassium chloride and surrounded by an O2-permeable or polypropylene membrane that permits gases to diffuse slowly into electrode. Thus, by measuring the change in current between the cathode and the anode, the amount of oxygen that is dissolved in the solution can be determined.

#### *2.2.2. Carbon dioxide sensor for blood*

*<sup>O</sup>*<sup>2</sup> + 2*H*2*<sup>O</sup>* + 4*e*↔4*OH* <sup>−</sup>

In this reduction reaction, one O2 molecule takes four electrons and reacts with two water

reference Ag/AgCl anode (this electrode is connected to the positive side of voltage source),

*Ag* ↔*Ag* <sup>+</sup> + *e*

*Ag* <sup>+</sup> + *Cl* −↔*AgCl* ↓

In this oxidation reaction, silver from the anode electrode is firstly oxidized to silver ions, and electrons are liberated to the anode. These silver ions are immediately combined with chloride ions to form a kind of compound precipitant silver chloride *AgCl* which precipitates on the surface of anode. The transient current between the anode and the cathode in the external circuit produced by this reaction is directly proportional to the number of O2 molecules constantly reduced on the surface of the cathode. The electrodes in the polarographic cell are immersed in an electrolyte solution of potassium chloride and surrounded by an O2-permeable or polypropylene membrane that permits gases to diffuse slowly into electrode. Thus, by

ions migrate and react with a

molecules, generating four hydroxyl ions. The resulting OH-

causing a two-step oxidation reaction as follows:

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**Figure 4.** Sensing principle of Clark-type pO2 sensor

Electrodes for measuring partial pressure of carbon dioxide CO2 in blood are based on measuring the pH as illustrated in figure 5. The measurement is based on the observation that it forms a weakly dissociated carbonic acid (H2CO3) that subsequently forms free hydrogen and bicarbonate ions when CO2 is dissolved in water according to the following reaction:

> *CO*<sup>2</sup> <sup>+</sup> *<sup>H</sup>*2*<sup>O</sup>* <sup>↔</sup>*H*2*CO*3↔*<sup>H</sup>* <sup>+</sup> <sup>+</sup> *HCO*<sup>3</sup> −

As a result of this chemical reaction, the pH of the solution is changed. This change generates a potential between the glass pH and a reference electrode that is proportional to the negative logarithm of the concentration of the carbon dioxide pCO2 in the plasma.

**Figure 5.** Sensing principle of a pCO2 electrode

#### **2.3. Heart sound sensor**

The expansion and shrinkage of heart necessarily lead to the vibration of artery that is formed by blood turbulence in vein. When the vibration of artery is transported to the surface of thoracic cavity, heart sound will take place. Heart sound is very valuable for doctor to diagnose many kinds of diseases in our body.

The range of heart sound is from 20Hz to 200Hz. Low limit frequency of heart sound could reach about 4Hz and high frequency limit is greater than 1000Hz. There are many kinds of medical heart sound sensors that are divided into two classifications: air conduction heart sound sensor and direct conduction heart sound sensor. Air conduction heart sound sensor consists of air chamber and common sensor. Such sensor has obvious defects: low sensitivity and easy disturb by surrounding circumstance. Hence, in clinic application, the most sensors applied are direct conduction heart sound sensor.

#### *2.3.1. Piezoelectric heart sound sensor*

The sensing structure of piezoelectric acceleration sensor is illustrated in figure 6. Such sensor is used to measure heart sound. Its structure is very simple, which consists of vibration mass block and piezoelectric crystal. A stress spring is utilized to exert a certain stress on vibration mass block between top shell and mass block. Such method could timely adjust the linear characteristic of sensing component. This sensor's gravity is less than 30g, and is used to detect heart sound and buffeting from body organisms.

**Figure 6.** Sensing structure of piezoelectric acceleration sensor

#### *2.3.2. Fetus heart sound sensor*

Detecting fetus heart sound is very important in clinic application for doctor sometimes needs to grasp the present body status of fetus. PVDF piezoelectric thin film sensor is utilized to be fit for the measurement of fetus's heart sound as illustrated in figure 7. Its piezoelectric coefficient is the following:

$$d\_{31} = (15 \sim 30) \times 10^{-12} \text{C} / \text{N}$$

$$d\_{33} = -(5 \sim 8) \times 10^{-12} \text{C} / \text{N}$$

In this structure, silicon rubber converts the vertical motion of itself into the radial motion of PVDF piezoelectric thin film and then corresponding dynamic charge produced by PVDF thin film is proportional to the externally transient force. The voltage along thickness direction is output. Obviously, its work mode is *d*31 work mode. For both thin film and silicon rubber are very soft, they could well touch the skin of body belly. Then fetus heart sound is gained to judge fetus heart. Design requirement of PVDF heart sound sensor is as follows:


**Figure 7.** Sensing structure of PVDF piezoelectric acceleration sensor

With the development of sensing technology, more and more heart sound sensors are appearing in our life. Although they have different sensing principle, their functions are alike.

#### **2.4. Blood flow sensor**

thoracic cavity, heart sound will take place. Heart sound is very valuable for doctor to diagnose

The range of heart sound is from 20Hz to 200Hz. Low limit frequency of heart sound could reach about 4Hz and high frequency limit is greater than 1000Hz. There are many kinds of medical heart sound sensors that are divided into two classifications: air conduction heart sound sensor and direct conduction heart sound sensor. Air conduction heart sound sensor consists of air chamber and common sensor. Such sensor has obvious defects: low sensitivity and easy disturb by surrounding circumstance. Hence, in clinic application, the most sensors

The sensing structure of piezoelectric acceleration sensor is illustrated in figure 6. Such sensor is used to measure heart sound. Its structure is very simple, which consists of vibration mass block and piezoelectric crystal. A stress spring is utilized to exert a certain stress on vibration mass block between top shell and mass block. Such method could timely adjust the linear characteristic of sensing component. This sensor's gravity is less than 30g, and is used to detect

Detecting fetus heart sound is very important in clinic application for doctor sometimes needs to grasp the present body status of fetus. PVDF piezoelectric thin film sensor is utilized to be fit for the measurement of fetus's heart sound as illustrated in figure 7. Its piezoelectric

many kinds of diseases in our body.

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*2.3.1. Piezoelectric heart sound sensor*

applied are direct conduction heart sound sensor.

heart sound and buffeting from body organisms.

**Figure 6.** Sensing structure of piezoelectric acceleration sensor

*2.3.2. Fetus heart sound sensor*

coefficient is the following:

If oxygen and nutrients are to reach tissues, the flow of blood must be maintained in body. Cardiac output flow is often measured as an index of cardiac performance, blood flow through arterial graft is used to ensure that a graft has been successfully inserted during surgery, or the blood flow in peripheral arteries and veins may be measured to assess vascular diseases. There are usually two kinds of measuring methods: one method is direct measurement, sensor is inserted into the blood pipe to sense transient blood flow; another one is indirect measure‐ ment, sensor is placed outside vein and senses blood flow by the parameter related to the blood flow. Here, an electromagnetic flow sensor as an example is introduced to demonstrate the measurement of blood flow.

**Figure 8.** Sensing principle of electromagnetic flow sensor (a) Relation diagram between electrode and magnetic field intensity; (b) Three dimension diagram

Blood flow through an exposed vessel could be measured by means of electromagnetic flow sensor. Electromagnetic flow sensor can be used in biomedicine and science research studies to measure blood flow in major blood vessels near the heart. Such sensor requires that the tested vein must be peeled off and placed into the magnetic gap of sensor. According to the output voltage of sensor, the mean velocity of vein can be calculated and known. And then in terms of the section area tested of vein, the blood flow could be gained finally. According to above idea, the sensing principle of electromagnetic flow sensor is illustrated in figure 7.

Magnetic field intensity *B* is exerted along the direction vertical to vein, two electrodes are installed at both sides of vein, and then potential between two electrodes could be tested:

$$V = 2aBv\_a$$

Here, *B* is the magnetic induction intensity at the magnetic gap; *a* is the radius of tested vein; *υ<sup>a</sup>* is the mean velocity of vein during given test time; *V* is the output potential between two electrodes EE'.

Practically, this device consists of a clip-on probe that fits snugly around the blood vessel, as illustrated in figure 8. The probe contains electrical coils to produce an electromagnetic field that is transverse to the direction of blood flow. This coil is usually excited by an AC current.

**Figure 9.** Electromagnetic blood flow sensor

the blood flow in peripheral arteries and veins may be measured to assess vascular diseases. There are usually two kinds of measuring methods: one method is direct measurement, sensor is inserted into the blood pipe to sense transient blood flow; another one is indirect measure‐ ment, sensor is placed outside vein and senses blood flow by the parameter related to the blood flow. Here, an electromagnetic flow sensor as an example is introduced to demonstrate the

**Figure 8.** Sensing principle of electromagnetic flow sensor (a) Relation diagram between electrode and magnetic field

Blood flow through an exposed vessel could be measured by means of electromagnetic flow sensor. Electromagnetic flow sensor can be used in biomedicine and science research studies to measure blood flow in major blood vessels near the heart. Such sensor requires that the tested vein must be peeled off and placed into the magnetic gap of sensor. According to the output voltage of sensor, the mean velocity of vein can be calculated and known. And then in terms of the section area tested of vein, the blood flow could be gained finally. According to above idea, the sensing principle of electromagnetic flow sensor is illustrated in figure 7.

Magnetic field intensity *B* is exerted along the direction vertical to vein, two electrodes are installed at both sides of vein, and then potential between two electrodes could be tested:

*V* =2*aBva*

Here, *B* is the magnetic induction intensity at the magnetic gap; *a* is the radius of tested vein; *υ<sup>a</sup>* is the mean velocity of vein during given test time; *V* is the output potential between two

Practically, this device consists of a clip-on probe that fits snugly around the blood vessel, as illustrated in figure 8. The probe contains electrical coils to produce an electromagnetic field that is transverse to the direction of blood flow. This coil is usually excited by an AC current.

measurement of blood flow.

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intensity; (b) Three dimension diagram

electrodes EE'.

A pair of very small biopotential electrodes is attached to the housing and rest against the wall of blood vessel to pick up the induced potential. The flow-induced voltage is an AC voltage at the same frequency as the excitation voltage. Utilizing AC method instead of DC excitation could help to remove any offset potential error due to the contact between the vessel wall and the biopotential electrodes.

Certainly, ultrasonic wave could be also used to detect blood flow of artery. In biomedical application, there are four kinds of ultrasonic wave blood flow sensors according to specific sensing principle and methods: (1) pulse time difference; (2) voice beam deflection; (3) phase shift; (4) Doppler frequency shift. Readers could research biomedical engineering handbook to learn more information.

#### **2.5. Respiration sensor**

Respiration measurement often includes two classes: physiological parameter measurement and gas ingredient from respiration system. What sensor the former utilizes is physical sensor, and what sensor the latter employs is chemical sensor and biological sensor. Here, respiration sensor which belongs to the first class is only introduced and explained. The measurement of respiration system is important basis of clinic diagnosis, and it is necessary for patients in the fields of surgery, baby and critically ill patient's monitoring, sports medicine, and medical research. The measurement of respiration system could be classified into three classes of parameters: respiration frequency, respiration flow and lung respiration volume.

In biomedical research or clinic monitoring, respiration frequency of patient needs to be sometimes detected to record the physiological status. Figure 9 illustrates a kind of sensor for respiration frequency based on thermistor sensing principle. Thermistor is mounted to the front-end of binder. When binder clamps the nares, airstreams from body flows through the surface of thermistor. According to the change of thermistor value, the respiration frequency would be measured.

**Figure 10.** Thermistor sensor for respiration frequency (a)structure diagram, (b)measurement diagram

Of course, elastic strain instrument could be also utilized to detect the respiration frequency. Its sensing principle is such: resistance wire is fixed to the surface of elastic plastic pipe. And then mercury or other electrolyte is sealed into the elastic plastic pipe. After elastic plastic pipe is adhered to the front of breast, respiration would lead to the length change of elastic plastic pipe. Such length change causes the change of resistance wire which could show the change of respiration frequency. When resistance wire is introduced into a detecting circuit, the respiration frequency will be sensed and measured.

#### **2.6. Blood pressure sensor**

If blood circulation is to be maintained in the body, tissues are to be perfused with oxygen. Then correct pressure measurement has to be applied in the vascular system. The usual blood pressure methods have: liquid coupling direct measurement, pipe-end sensing measurement, indirect blood pressure sensing measurement. Liquid coupling direct measurement means that the pipe filled with liquid is inserted into the measured part and that the pressure is measured by liquid coupling of pipe end position in the body, which is the simplest method. Pipe-end sensing measurement employs pipe-end sensor to measure blood pressure. Pipe-end sensor which can convert the pressure signal into electronic signal is placed on the measured part. And then the electronic signal measured is transmitted to the external wire. Such method could avoid the distortion of signal of blood pressure. Pipe-end sensing measurement has a lot of advantages, but such method needs to activate the skin and relative sensors have to been placed into the body. Hence indirect blood pressure measurement is noted by people and continuously explored. Blood-pressure meter is a classic example of indirect blood pressure measurement, which is shown in figure 10.

In figure 10, the sensing principle is based on Coriolis sound. Gas is filled into cuff to hold back the arterial blood flow. And then gas in cuff is sent out slowly to monitor whether there appears arterial blood flow at the downstream of arterial blocking point. Here, the employed sensor is common mercury pressure meter. And such method is up to the actual experience of staff.

**Figure 11.** Sensing principle of indirect blood pressure measurement

When coriolis sound is heard, namely when blood flows through artery blood pipe, blood pressure in cuff is shrinking pressure in artery pipe. When blood flows recover normal level, blood pressure in cuff is diastolic pressure of artery. Systole pressure and diastolic pressure are recorded as blood pressure. Such method is not harmful to the skin or organ in the body.

#### **2.7. Electrochemical electrode**

**Figure 10.** Thermistor sensor for respiration frequency (a)structure diagram, (b)measurement diagram

respiration frequency will be sensed and measured.

measurement, which is shown in figure 10.

**2.6. Blood pressure sensor**

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Of course, elastic strain instrument could be also utilized to detect the respiration frequency. Its sensing principle is such: resistance wire is fixed to the surface of elastic plastic pipe. And then mercury or other electrolyte is sealed into the elastic plastic pipe. After elastic plastic pipe is adhered to the front of breast, respiration would lead to the length change of elastic plastic pipe. Such length change causes the change of resistance wire which could show the change of respiration frequency. When resistance wire is introduced into a detecting circuit, the

If blood circulation is to be maintained in the body, tissues are to be perfused with oxygen. Then correct pressure measurement has to be applied in the vascular system. The usual blood pressure methods have: liquid coupling direct measurement, pipe-end sensing measurement, indirect blood pressure sensing measurement. Liquid coupling direct measurement means that the pipe filled with liquid is inserted into the measured part and that the pressure is measured by liquid coupling of pipe end position in the body, which is the simplest method. Pipe-end sensing measurement employs pipe-end sensor to measure blood pressure. Pipe-end sensor which can convert the pressure signal into electronic signal is placed on the measured part. And then the electronic signal measured is transmitted to the external wire. Such method could avoid the distortion of signal of blood pressure. Pipe-end sensing measurement has a lot of advantages, but such method needs to activate the skin and relative sensors have to been placed into the body. Hence indirect blood pressure measurement is noted by people and continuously explored. Blood-pressure meter is a classic example of indirect blood pressure

In figure 10, the sensing principle is based on Coriolis sound. Gas is filled into cuff to hold back the arterial blood flow. And then gas in cuff is sent out slowly to monitor whether there appears arterial blood flow at the downstream of arterial blocking point. Here, the employed sensor is common mercury pressure meter. And such method is up to the actual experience of staff. Biopotential measurements are made using different kinds of specialized electrochemical electrodes. The function of electrodes is to couple the ionic potentials generated inside the body to an electronic instrument. Biopotential electrochemical electrode is classified either as noninvasive (e.g. skin surface) or invasive (e.g. microelectrode, wire electrode) electrodes. When a metal is placed in an electrolyte solution, a charge distribution is created next to the metal/electrolyte solution interface as illustrated in figure 11. The localized charge distribution causes an electronic potential by electrochemical electrode, called half-cell potential, to be developed across the interface between metal electrode and electrolyte solution.

The half-cell potentials of several important metals are listed in table 2. Here, a point needs to be pointed out that hydrogen electrode is considered to be a standard electrode against which the half-cell potentials of other metal electrodes are measured.

**Figure 12.** The charge distribution at a electrolyte/metal interface

Silver and zinc electrodes are immersed in an electrolyte solution. And then we may calculate the potential drop between two electrodes. From table 2, the half-cell potentials for silver and zinc electrodes are 0.799V and -0.763V respectively. Hence, the half-cell potentials between two electrodes are equal to the following value:

$$0.799\text{-(-0.763)} = 1.562\text{V}$$

Typically, utilizing the electrochemical electrodes composed of the same metals could measure the half-cell potentials. Hence, the two half-cell potentials for these electrodes would be equal in magnitude. Some common electrodes are introduced here, which is utilized as a sensor.

#### *2.7.1. ECG electrodes*

A typical flexible biopotential electrode for ECG (electrocardiogram, ECG) recording is composed of certain polymers or elastomers which are made electrically conductive by the addition of a fine carbon or metal powder. These electrodes as illustrated in figure 13a are available with prepasted AgCl gel for quick easy application to the skin using a double-sided peel-off adhesive tape. The most common type of biopotential electrode is the silver/silver chloride electrode (Ag/AgCl), which is formed by electrochemically depositing a very thin layer silver chloride onto the surface of silver electrode as illustrated in figure 13b. These electrodes are recessed and imbedded in foam that has been soaked with an electrolyte paste to provide good electrical contact with the skin. The electrolyte saturated foam is also known to reduce motion artifacts which are produced during stress testing when the layer of the skin moves relative to the surface of the Ag/AgCl electrode. This motion leads to the large inter‐ ference in the recorded biopotential and, in the extreme cases, could severely degrade the measurement.


Pb → Pb2++2e- -0.126

recorded biopotential and, in the extreme cases, could severely degrade the measurement.

**Table 2.** Half-cell Potentials of Important Metals moves relative to the surface of the Ag/AgCl electrode. This motion leads to the large interference in the

Silver and zinc electrodes are immersed in an electrolyte solution. And then we may calculate the potential drop between two electrodes. From table 2, the half-cell potentials for silver and zinc electrodes are 0.799V and -0.763V respectively. Hence, the half-cell potentials between

0.799-(-0.763) =1.562V

Typically, utilizing the electrochemical electrodes composed of the same metals could measure the half-cell potentials. Hence, the two half-cell potentials for these electrodes would be equal in magnitude. Some common electrodes are introduced here, which is utilized as a sensor.

A typical flexible biopotential electrode for ECG (electrocardiogram, ECG) recording is composed of certain polymers or elastomers which are made electrically conductive by the addition of a fine carbon or metal powder. These electrodes as illustrated in figure 13a are available with prepasted AgCl gel for quick easy application to the skin using a double-sided peel-off adhesive tape. The most common type of biopotential electrode is the silver/silver chloride electrode (Ag/AgCl), which is formed by electrochemically depositing a very thin layer silver chloride onto the surface of silver electrode as illustrated in figure 13b. These electrodes are recessed and imbedded in foam that has been soaked with an electrolyte paste to provide good electrical contact with the skin. The electrolyte saturated foam is also known to reduce motion artifacts which are produced during stress testing when the layer of the skin moves relative to the surface of the Ag/AgCl electrode. This motion leads to the large inter‐ ference in the recorded biopotential and, in the extreme cases, could severely degrade the

two electrodes are equal to the following value:

**Figure 12.** The charge distribution at a electrolyte/metal interface

*2.7.1. ECG electrodes*

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measurement.

Figure6.12 Biopotential skin surface ECG electrode

2) EMG electrodes **Figure 13.** Biopotential skin surface ECG electrode

#### Electrochemical electrodes are also used to record electromyography (EMG) signals from different muscles in the body. The body and size of the recorded EMG signals depends on the electrical property of *2.7.2. EMG electrodes*

these electrodes and the recording location. For invasive recordings, proper skin preparation, which normally involves cleaning the skin with alcohol or the application of a small amount of an electrolyte paste, helps to minimize the impedance of the skin-electrode interface and improve the quality of recording signal considerably. The most common electrodes used for the surface EMG recording and nerve conduction studies are circular discs, about 1 cm in diameter, that are made of silver or platinum. For direct Electrochemical electrodes are also used to record electromyography (EMG) signals from different muscles in the body. The body and size of the recorded EMG signals depends on the electrical property of these electrodes and the recording location. For invasive recordings, proper skin preparation, which normally involves cleaning the skin with alcohol or the application of a small amount of an electrolyte paste, helps to minimize the impedance of the

recording of electrical signals from nerves and muscle fibers, a variety of percutaneous needle electrodes are available as illustrated in figure6.13. The most common type of needle electrode is the concentric bipolar electrode as illustrated in figure6.13a. This electrode is made from the thin metallic wires encased inside a larger canola or hypodermic needle. The two wires serve as the recording and reference electrodes.

skin-electrode interface and to improve the quality of recording signal considerably. The most common electrodes used for the surface EMG recording and nerve conduction studies are circular discs, about 1 cm in diameter, that are made of silver or platinum. For direct recording of electrical signals from nerves and muscle fibers, a variety of percutaneous needle electrodes are available as illustrated in figure 14. The most common type of needle electrode is the concentric bipolar electrode as illustrated in figure 14a. This electrode is made from the thin metallic wires encased inside a larger canola or hypodermic needle. The two wires serve as the recording and reference electrodes.

**Figure 14.** Intramuscular biopotential electrode:(a)bipolar electrode, (b)unipolar configuration

Another type of percutaneous EMG electrode is the unipolar needle electrode as illustrated in figure 14b. This electrode is made of a thin wire that is most insulated by a thin layer near the distal tip. Unlike bipolar electrode, this type of electrode requires a second unipolar reference electrode to form a closed electrical circuit. The second recording electrode is normally placed either adjacent to the recording electrode or attached to the surface of our skin.

#### *2.7.3. EEG electrodes*

The most commonly used electrode for recording electroencephalographic (EEG) signals from the brain are cup electrodes and subdermal needle electrodes. Cup electrodes are made of platinum or tin and are approximately 5-10mm in diameter. The cup electrodes are filled with an electrolyte gel and can be attached to the scalp with an adhesive tape.

Recording the biopotentials from the scalp is very difficult because hair and oily skin hold back the good electrical contact. Hence, clinicians sometimes prefer to use subdermal needle electrodes (EEG electrodes) instead of the metal surface electrodes for EEG recording. These electrodes are both fine platinum or stainless-steel needle electrodes about 10mm long by 0.5mm wide, which are inserted under the skin to provide a better electrical contact.

#### *2.7.4. Microelectrodes*

Microelectrodes are biopotential electrodes with ultra-fine tapered tip that can be inserted into biological cells. These electrodes play a very important role in recording action potentials from single cells and are used in neurophysiologic studies to comprehend the course of biological information conversion and transmission in our body. The tip of these electrodes must be very small with respect to the dimensions of the biological cell to avoid cell damage and at the same time sufficiently strong to penetrate the cell wall. The electrode which is applied to microbe studies is called microelectrodes. Generally, there are three types of microelectrodes: (1) glass microelectrodes, (2) metal electrodes, and (3) solid-state microprobes.

For glass microelectrodes, when the tip of such electrodes is inserted into an electrolyte solution, such as the intracellular cytoplasm of a biological cell, ionic current can flow through the fluid junction at the tip of the microelectrode. Such mode could establish a closed electrical circuit between two Ag/AgCl wire electrodes inside the microelectrode and biological cell. For metal electrode, when the tip of such microelectrodes is usually sharpened down to a diameter of a few micrometers by an electrochemical etching process. The wires are then insulated up to its tip.

Solid-state microfabrication techniques commonly used in the production of the integrated circuits can be used to produce microprobes for multichannel recordings of biopotentials or for electrical stimulation of neurons in our brain or spinal cord. Most of solid-state micro‐ electrodes are microsensor actually. Such probe consists of a precisely micromachined silicon substrate with four exposed recording sites. One of main advantages of microfabrication techniques is the ability to mass produce very small and highly sophisticated microsensors with highly reproducible electrical and physical properties.

#### **2.8. Enzyme sensor and microbial sensor**

skin-electrode interface and to improve the quality of recording signal considerably. The most common electrodes used for the surface EMG recording and nerve conduction studies are circular discs, about 1 cm in diameter, that are made of silver or platinum. For direct recording of electrical signals from nerves and muscle fibers, a variety of percutaneous needle electrodes are available as illustrated in figure 14. The most common type of needle electrode is the concentric bipolar electrode as illustrated in figure 14a. This electrode is made from the thin metallic wires encased inside a larger canola or hypodermic needle. The two wires serve as

**Figure 14.** Intramuscular biopotential electrode:(a)bipolar electrode, (b)unipolar configuration

either adjacent to the recording electrode or attached to the surface of our skin.

an electrolyte gel and can be attached to the scalp with an adhesive tape.

Another type of percutaneous EMG electrode is the unipolar needle electrode as illustrated in figure 14b. This electrode is made of a thin wire that is most insulated by a thin layer near the distal tip. Unlike bipolar electrode, this type of electrode requires a second unipolar reference electrode to form a closed electrical circuit. The second recording electrode is normally placed

The most commonly used electrode for recording electroencephalographic (EEG) signals from the brain are cup electrodes and subdermal needle electrodes. Cup electrodes are made of platinum or tin and are approximately 5-10mm in diameter. The cup electrodes are filled with

Recording the biopotentials from the scalp is very difficult because hair and oily skin hold back the good electrical contact. Hence, clinicians sometimes prefer to use subdermal needle electrodes (EEG electrodes) instead of the metal surface electrodes for EEG recording. These electrodes are both fine platinum or stainless-steel needle electrodes about 10mm long by

Microelectrodes are biopotential electrodes with ultra-fine tapered tip that can be inserted into biological cells. These electrodes play a very important role in recording action potentials from

0.5mm wide, which are inserted under the skin to provide a better electrical contact.

the recording and reference electrodes.

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*2.7.3. EEG electrodes*

*2.7.4. Microelectrodes*

Enzyme constitutes a group of more than 2000 proteins having so-called biocatalytic proper‐ ties. These properties give the enzymes the unique and powerful ability to accelerate chemical reactions inside biological cells. Most enzymes react only with specific substrates even though they can be contained in a complicated mixture with other substances. It is important that soluble enzymes are very sensitive both to temperature and pH variations, and they can be inactivated by many chemical inhibitors. For practical biosensor applications, these enzymes are normally immobilized by insolubilizing the free enzymes via entrapment into an inert and stable matrix such as starch gel, silicon rubber, or polyacrylamide. This process is very important to ensure that the enzymes retains its catalytic properties and can be reusable.

The action of specific enzymes may be utilized to form a range of different biosensors. A typical example of enzyme-based sensor is a glucose sensor that uses the enzyme glucose oxidase. Glucose plays an important role in metabolic process. Currently, available glucose sensors are based on an immobilized enzyme, such as glucose oxidase, which acts as a catalyst. Glucose is detected by electromechanically measuring either the amount of gluconic acid or hydrogen peroxide (H2O2) produced or by measuring the percent of oxygen consumed according to the following chemical reaction:

> *Glu*cos*e* + *O*<sup>2</sup> + *H*2*O* ↔ *glu*cos*e oxidase gluconic acide H*2*O*<sup>2</sup>

A glucose sensor is similar to a *pO*2 sensor and is shown in figure 15. Glucose and oxygen enter through outer membrane to interact with glucose oxidase enzyme. The remaining oxygen penetrates through the second oxygen-permeable membrane and is measured by the oxygen electrode.

**Figure 15.** Sensing principle of glucose sensor

Biocatalytic enzyme-based sensors generally consist of an electrochemical gas-sensitive converter or an ion-selective electrode with an enzyme immobilized in or on a membrane that serve as the biological mediator. The analyte diffuses from the bulk sample solution into the biocatalytic layer where an enzymatic reaction takes place. The electroactive product that is formed (or consumed) is usually detected by an ion-selective electrode. A membrane separates the basic sensor from the enzyme if a new gas is produced (such as CO2 or NH3) or consumed (such as O2). Although the concentration of the bulk substrate drops continuously, the rate of consumption is usually negligible. The decrease is detected only when the test volume is very small or when the area of enzyme membrane is large enough. Thus this electrochemical analysis is nondestructive, and the sample is reused. Measurements are usually performed at a constant pH and temperature either in a stirred medium solution or in a flow through solution. In order to control biochemical process including some enzyme sensors, a number of microbial sensors have been continuously developed and applied to various environment, agriculture, food and pharmaceutical.

Microbial sensors typically involve the assimilation of organic compounds by microorganisms, followed by a change in respiration activity(metabolism) or the production of specific electro‐ chemically active metabolites, such as CO2, H2, or NH3, that are secreted by the microorganism.

A microbial sensor is composed of immobilized microorganisms that serve as specific recog‐ nition elements and an electrochemical or optical sensing device that is used to convert the biochemical signal into electronic signal that can be processed. The operation of a microbial sensor can be described by the following five-step process:


A glucose sensor is similar to a *pO*2 sensor and is shown in figure 15. Glucose and oxygen enter through outer membrane to interact with glucose oxidase enzyme. The remaining oxygen penetrates through the second oxygen-permeable membrane and is measured by the oxygen

Biocatalytic enzyme-based sensors generally consist of an electrochemical gas-sensitive converter or an ion-selective electrode with an enzyme immobilized in or on a membrane that serve as the biological mediator. The analyte diffuses from the bulk sample solution into the biocatalytic layer where an enzymatic reaction takes place. The electroactive product that is formed (or consumed) is usually detected by an ion-selective electrode. A membrane separates the basic sensor from the enzyme if a new gas is produced (such as CO2 or NH3) or consumed (such as O2). Although the concentration of the bulk substrate drops continuously, the rate of consumption is usually negligible. The decrease is detected only when the test volume is very small or when the area of enzyme membrane is large enough. Thus this electrochemical analysis is nondestructive, and the sample is reused. Measurements are usually performed at a constant pH and temperature either in a stirred medium solution or in a flow through solution. In order to control biochemical process including some enzyme sensors, a number

electrode.

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**Figure 15.** Sensing principle of glucose sensor


Here, an example of a microbial sensor is given to demonstrate the detecting course of microbial sensor including ammonia (NH3) and nitrogen dioxide (NO2) sensors that utilize the nitrifying bacteria as the biological sensing component. A NH3 biosensor can be constructed on the base of nitrifying bacteria that uses ammonia (NH3) as a source of energy and oxidizes ammonia as follows:

$$\text{N} \,\text{H}\_3 + \text{1.5O}\_2 \overset{\text{Niitrosomous}}{=} \text{NO}\_2 + \text{H}\_2\text{O} + \text{H}^+$$

This oxidation process proceeds at high rate, and the amount of oxygen consumed by the immobilized bacteria can be measured directly by a polarographic oxygen electrode placed behind the bacteria.

Nitric oxide (NO) and NO2 are two principal pollution gases of nitrogen in the atmosphere. The principle of a NO2 biosensor is shown in figure 16. When a sample of NO2 gas diffuses through the gas-permeable membrane, it is oxidized by the nitrosomonas bacteria as follows:

$$2NO\_2 + O\_2 \overset{Nirosomous}{=} NO\_3$$

Similar to an ammonia biosensor, the consumption of oxygen O2 around the membrane is determined by an electrochemical oxygen electrode.

#### **3. Charge, current, voltage, power and energy**

Many biomedical instruments utilize a sensor to convert a signal created by the body into an electrical signal. In medicine, the electrical circuits and electrical components are often utilized to detect the biomedical signal by sensor. After basic electrical components and biomedical sensors are connected together, a bioinstrumentation is then formed. Hence, describing a bioinstrumentation could begin with charge, current, voltage, power and energy. In this section, these basic variables will be introduced and explained.

#### **3.1. Charge and its conversion**

In our life, there are two kinds of charge, negative and positive, and they are carried by the protons and electrons, respectively. The negative charge, *qe*, carried by the electron is the smallest amount of charge that exists and is measured in unit called coulombs(C):

$$q\_e = -1.6 \times 10^{-19} \text{C}$$

The symbol, *q*(*t*), is used to represent the charge that change with time, and the symbol, *Q*, is used for constant charge. The charge carried by a proton is the opposite of a electron.

#### **3.2. Current and voltage**

#### *3.2.1. Current*

Electrical current, *i*(*t*), is defined as the change in the amount of charge that passes through a given point or area in a given time period. Current is measured in amperes (A). By the definition, one ampere equals one coulomb/second (C/s):

$$i(t) = \frac{dq}{dt}$$

and

This oxidation process proceeds at high rate, and the amount of oxygen consumed by the immobilized bacteria can be measured directly by a polarographic oxygen electrode placed

Nitric oxide (NO) and NO2 are two principal pollution gases of nitrogen in the atmosphere. The principle of a NO2 biosensor is shown in figure 16. When a sample of NO2 gas diffuses through the gas-permeable membrane, it is oxidized by the nitrosomonas bacteria as follows:

Similar to an ammonia biosensor, the consumption of oxygen O2 around the membrane is

Many biomedical instruments utilize a sensor to convert a signal created by the body into an electrical signal. In medicine, the electrical circuits and electrical components are often utilized to detect the biomedical signal by sensor. After basic electrical components and biomedical sensors are connected together, a bioinstrumentation is then formed. Hence, describing a bioinstrumentation could begin with charge, current, voltage, power and energy. In this

In our life, there are two kinds of charge, negative and positive, and they are carried by the protons and electrons, respectively. The negative charge, *qe*, carried by the electron is the

*qe* <sup>=</sup> <sup>−</sup>1.6×10−19*<sup>C</sup>*

The symbol, *q*(*t*), is used to represent the charge that change with time, and the symbol, *Q*, is

Electrical current, *i*(*t*), is defined as the change in the amount of charge that passes through a given point or area in a given time period. Current is measured in amperes (A). By the

> *<sup>i</sup>*(*t*)= *dq dt*

used for constant charge. The charge carried by a proton is the opposite of a electron.

smallest amount of charge that exists and is measured in unit called coulombs(C):

*N O*<sup>3</sup>

<sup>2</sup>*N O*<sup>2</sup> <sup>+</sup> *<sup>O</sup>*<sup>2</sup> <sup>=</sup> *Nitrosomonas*

determined by an electrochemical oxygen electrode.

**3. Charge, current, voltage, power and energy**

section, these basic variables will be introduced and explained.

definition, one ampere equals one coulomb/second (C/s):

**3.1. Charge and its conversion**

**3.2. Current and voltage**

*3.2.1. Current*

behind the bacteria.

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$$q\_{\parallel}(t) = \int\_{t\_0}^{t} i(\lambda \,) d\lambda \, + q(t\_0)$$

**Figure 17.** A simple circuit illustrating current flowing around a closed loop

In addition to the above definition, current also depends on the direction of flow, as illustrated in figure 17 Current is defined as positive if


**Figure 18.** A sample current waveform and its electrical circuit

Since these two cases cause the same outcome, there is no need to be concerned as to which is responsible for the current. In electrical circuits, current is carried by electrons in metallic inductors.

Consider the waveform in figure 18, with the current entering into terminal1 in the circuit on the right, the current in the time interval 0 to 1.5 second, is positive and enters terminal1. The current in the time interval 1.5 to 3 second, is negative and enters terminal2 with positive value. If there are no current changes in the time interval 0 to 3s, the curve of current will be a line. Then the electrical circuit in figure 18 is constant which is called direct current (DC) indicating that it does not change with time. We denote a time-varying current with lowercase letter, such as *i* or just *i*(*t*).

#### **Kirchhoff's Current Law**

Current can only flow in a closed circuit. Kirchhoff's current law is used to ensure the rela‐ tionship among every branch of circuit at same point. For current is continuous, any a point in circuit can not accumulate charge. Hence, at any time and any node, the sum of the currents which flow same node is equal to the sum of the currents which outflow from same node. This principle is known as Kirchhoff's current law (KCL).

In circuit as illustrated in figure 19, the current at the node, *a*, can be written as:

$$I\_1 + I\_2 = I\_3$$

or, above formula is adjusted into the following equation:

$$I\_1 + I\_2 - I\_3 = 0$$

Namely,

$$\sum I = 0$$

At any time, the algebraic sum of the currents at a node is equal to zero. It should be clear for all currents whether they are all leaving or entering the node.

**Figure 19.** Node of circuit

**Figure 20.** Voltage and current convention

Since these two cases cause the same outcome, there is no need to be concerned as to which is responsible for the current. In electrical circuits, current is carried by electrons in metallic

Consider the waveform in figure 18, with the current entering into terminal1 in the circuit on the right, the current in the time interval 0 to 1.5 second, is positive and enters terminal1. The current in the time interval 1.5 to 3 second, is negative and enters terminal2 with positive value. If there are no current changes in the time interval 0 to 3s, the curve of current will be a line. Then the electrical circuit in figure 18 is constant which is called direct current (DC) indicating that it does not change with time. We denote a time-varying current with lowercase letter, such

Current can only flow in a closed circuit. Kirchhoff's current law is used to ensure the rela‐ tionship among every branch of circuit at same point. For current is continuous, any a point in circuit can not accumulate charge. Hence, at any time and any node, the sum of the currents which flow same node is equal to the sum of the currents which outflow from same node. This

*I*<sup>1</sup> + *I*<sup>2</sup> = *I*<sup>3</sup>

*I*<sup>1</sup> + *I*<sup>2</sup> − *I*<sup>3</sup> =0

∑ *I* =0

At any time, the algebraic sum of the currents at a node is equal to zero. It should be clear for

In circuit as illustrated in figure 19, the current at the node, *a*, can be written as:

inductors.

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as *i* or just *i*(*t*).

Namely,

**Figure 19.** Node of circuit

**Kirchhoff's Current Law**

principle is known as Kirchhoff's current law (KCL).

or, above formula is adjusted into the following equation:

all currents whether they are all leaving or entering the node.

In describing a circuit, we define its characteristics with terms node, branch, path, closed path, and mesh as follows:


Kirchhoff's current law could be also applied to any closed surface surrounding a part of the circuit. It's understood that the closed surface does not intersect any of the circuit elements.

*3.2.2. Voltage*

Voltage represents the work per unit charge associated with moving a charge between two points (A and B in figure 20) and that is given as the following formula:

$$V = \frac{dW}{dt}$$

The unit of measurement for voltage is the volt (V). A constant voltage source is denoted by the letter V, while a time-varying voltage is denoted by the lowercase letter *v*(*t*), or just *v*. In figure 20, the voltage, *υ* between two points (A and B) is the amount of energy required to move a charge from point A to point B.

#### **Kirchhoff's Voltage Law**

Kirchhoff's voltage law is utilized to ensure the voltage relationship at any branch of circuit. Starting from any point of circuit, the sum of potential drop at the closed branch along the clockwise or counterclockwise direction is equal to the sum of potential rise.

**Figure 21.** Circuit loop

In figure 21, the reference direction of electromotive force, current and branch voltage is marked. Cycling one circle along virtual line given in circuit, the following equation could be listed out:

$$\mathcal{U}\_1 + \mathcal{U}\_4 = \mathcal{U}\_2 + \mathcal{U}\_3$$

Above equation could be also written into the following equation:

$$\mathcal{U}\_1 - \mathcal{U}\_2 - \mathcal{U}\_3 + \mathcal{U}\_4 = 0$$

Namely, ∑ *U* =0

According to above voltage equation, the algebraic sum of branch voltage is equal to zero along any a closed branch circuit. If it is stipulated that potential drop is negative, potential rise is positive.

Kirchhoff's laws are applied in electrical circuit analysis to determine unknown voltages and currents. Each unknown variable has its distinct equation. To solve for the unknowns using MATLAB, we create a matrix representation of the set of equations and solve them using the matrix calculation techniques.

#### **3.3. Power and energy**

Power is the rate of energy expenditure given as:

$$p = \frac{dW}{dt} = \frac{dW}{dq}\frac{dq}{dt} = \mu i = i^2 R^2$$

Where, the letter, *p*, is power measured in watts(W), and the letter, *w*, is energy measured in joules(J). Power is usually determined by the product of voltage across a circuit element and the current through it. By convention, we assume that a positive value for power indicates that power is being delivered (or absorbed or consumed) by the circuit element. A negative value for power indicates that power is being extracted or generated by the circuit element which could be considered as a battery.

**Figure 22.** Polarity references for four cases of current and voltage. Cases (a) and (d) result in positive power being consumed by the circuit element. Cases (b) and(c) result in negative power being extracted from the circuit element.

Figure 22 illustrates the four possible cases for a circuit element's voltage and current config‐ uration. According to the convention, if current and voltage are positive, with the arrow and polarity shown in figure 22, energy is absorbed. If either the current arrow or the voltage polarity is reserved, as in (b) and (c), energy is supplied to the circuit. If both the current direction and voltage polarity are reserved together as in figure 22(d), energy is absorbed.

**Figure 23.** Basic symbol for independent source

**Figure 21.** Circuit loop

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Namely, ∑ *U* =0

matrix calculation techniques.

Power is the rate of energy expenditure given as:

*<sup>p</sup>* <sup>=</sup> *dW*

*dt* <sup>=</sup> *dW dq*

*dq dt* <sup>=</sup>*ui* <sup>=</sup>*<sup>i</sup>* <sup>2</sup>

Where, the letter, *p*, is power measured in watts(W), and the letter, *w*, is energy measured in joules(J). Power is usually determined by the product of voltage across a circuit element and the current through it. By convention, we assume that a positive value for power indicates that power is being delivered (or absorbed or consumed) by the circuit element. A negative value

*R*

**3.3. Power and energy**

positive.

listed out:

In figure 21, the reference direction of electromotive force, current and branch voltage is marked. Cycling one circle along virtual line given in circuit, the following equation could be

*U*<sup>1</sup> + *U*<sup>4</sup> =*U*<sup>2</sup> + *U*<sup>3</sup>

*U*<sup>1</sup> −*U*<sup>2</sup> −*U*<sup>3</sup> + *U*<sup>4</sup> =0

According to above voltage equation, the algebraic sum of branch voltage is equal to zero along any a closed branch circuit. If it is stipulated that potential drop is negative, potential rise is

Kirchhoff's laws are applied in electrical circuit analysis to determine unknown voltages and currents. Each unknown variable has its distinct equation. To solve for the unknowns using MATLAB, we create a matrix representation of the set of equations and solve them using the

Above equation could be also written into the following equation:

A passive circuit element is defined as an element whose power is always positive or zero, which is dissipated as heat (resistance), stored in an electric field (capacitor), or stored in magnetic field (inductor). We define an active circuit element as one whose power is negative and capable of generating energy. Energy is given by the following equation:

*W* =*∫* −*∞ t pdt* negative and capable of generating energy. Energy is given by the following equation: *<sup>t</sup> pdtW*

Figure6.22 Basic symbol for independent source

in magnetic field (inductor). We define an active circuit element as one whose power is

In circuit, the basic source symbol is listed in figure 23. In circuit, the basic source symbol is listed in figure6.22.

#### **4. Resistance, inductors and capacitors 6.4. Resistance, inductors and capacitors**

#### **4.1. Resistance and its combination**

#### *4.1.1. Resistance* **6.4.1 Resistance and its combination**

In figure 24, the direction of current and voltage is the same. According to Ohm's law, the following formula could be given: 1) Resistance In figure6.23, the direction of current and voltage is the same. According to Ohm's law,

**Figure 24.** Resistance and its symbol

∞.

(a)resister component (b) Ideal resister with the Resistance

*<sup>u</sup> <sup>R</sup> u* =*iR*

Figure6.23 Resistance and its symbol *iRu*

The parameter of resistance is gained: *i* This parameter is called resistance which has the property of holding back the current in The parameter of resistance is gained: *<sup>R</sup>* <sup>=</sup> *<sup>u</sup> i*

terms of conductance, ohm's law could be written as:

circuit. And it is denoted with the symbol in figure6.23b. Here, this relationship could be applied at very high voltage and current. Some electrically materials have a very small range of currents and voltages where they exhibit linear behavior. In reality, some material is linear only within a range of values. Outside this range, resistance is not linear. In circuit, we define:(1) having a 0V voltage drop when R=0;(2)having a 0current through resister when R= This parameter is called resistance which has the property of holding back the current in circuit. And it is denoted with the symbol in figure 24b. Here, this relationship could be applied at very high voltage and current. Some electrictronic materials have a very small range of currents and voltages where they exhibit linear behavior. In reality, some material is linear only within a range of values. Outside this range, resistance is not linear. In circuit, we define:(1) having a 0V voltage drop when R=0;(2)having a 0current through resister when R=∞.

Each material has a property called resistivity(ρ) that indicates the resistance of the material. Conductivity is the inverse of resistivity, and conductance (G) is the inverse of Each material has a property called resistivity(ρ) that indicates the resistance of the material. Conductivity is the inverse of resistivity, and conductance (G) is the inverse of resistance.

*Gui*

resistance. Conductance is measured in unit called siemens(S) and has the unit of A/V. In

Conductance is measured in unit called siemens(S) and has the unit of A/V. In terms of conductance, ohm's law could be written as:

$$\dot{\imath} = Gu$$

For formula *u* =*iR*, if current is produced by both sides of this equation and they are integrated, the following equation could be given:

$$\int\_0^t \mu i dt = \int\_0^t i^{-2} R dt$$

This formula demonstrates that electrical energy is all consumed by resister component. And the energy is converted into thermal energy, that's to say, resister is a consuming-energy component.

#### *4.1.2. Series and parallel combination of resistance*

If the same current flows from one resister to another, the two are said to be in series. If these two resisters are connected to the third and the same current flows through all of them, then the three resistors are in series. Consider figure 25 with three resisters in series, an equivalent circuit can be derived through Kirchhoff's Voltage Law as follows:

**Figure 25.** A series circuit

*W* =*∫* −*∞ t pdt*

 *<sup>t</sup> pdtW*

negative and capable of generating energy. Energy is given by the following equation:

Figure6.22 Basic symbol for independent source A passive circuit element is defined as an element whose power is always positive or zero, which is dissipated as heat (resistance), stored in an electric field (capacitor), or stored in magnetic field (inductor). We define an active circuit element as one whose power is

In figure 24, the direction of current and voltage is the same. According to Ohm's law, the

In figure6.23, the direction of current and voltage is the same. According to Ohm's law,

(a)resister component (b) Ideal resister with the Resistance

Figure6.23 Resistance and its symbol *iRu*

*<sup>u</sup> <sup>R</sup>*

*i*

This parameter is called resistance which has the property of holding back the current in circuit. And it is denoted with the symbol in figure6.23b. Here, this relationship could be applied at very high voltage and current. Some electrically materials have a very small range of currents and voltages where they exhibit linear behavior. In reality, some material is linear only within a range of values. Outside this range, resistance is not linear. In circuit, we define:(1) having a 0V voltage drop when R=0;(2)having a 0current through resister when R=

This parameter is called resistance which has the property of holding back the current in circuit. And it is denoted with the symbol in figure 24b. Here, this relationship could be applied at very high voltage and current. Some electrictronic materials have a very small range of currents and voltages where they exhibit linear behavior. In reality, some material is linear only within a range of values. Outside this range, resistance is not linear. In circuit, we define:(1) having a

*u* =*iR*

Each material has a property called resistivity(ρ) that indicates the resistance of the

Each material has a property called resistivity(ρ) that indicates the resistance of the material. Conductivity is the inverse of resistivity, and conductance (G) is the inverse of resistance.

*Gui*

material. Conductivity is the inverse of resistivity, and conductance (G) is the inverse of resistance. Conductance is measured in unit called siemens(S) and has the unit of A/V. In

0V voltage drop when R=0;(2)having a 0current through resister when R=∞.

In circuit, the basic source symbol is listed in figure 23.

**6.4. Resistance, inductors and capacitors** 

In circuit, the basic source symbol is listed in figure6.22.

**4. Resistance, inductors and capacitors**

**4.1. Resistance and its combination**

**6.4.1 Resistance and its combination** 

The parameter of resistance is gained: *i*

The parameter of resistance is gained: *<sup>R</sup>* <sup>=</sup> *<sup>u</sup>*

**Figure 24.** Resistance and its symbol

terms of conductance, ohm's law could be written as:

following formula could be given:

the following formula could be given:

*4.1.1. Resistance*

206 Advances in Bioengineering

1) Resistance

∞.

$$-V\_s + IR\_1 + IR\_2 + IR\_3 = 0$$

Above equation can be also rewritten as:

$$R\_{eq} = R\_1 + R\_2 + R\_3 = \frac{V\_s}{I}$$

Where, the equivalent resistance, *Req*, is the sum of three resister in figure 25 which is called equivalent resistance. In general, if there are *N* resisters in series, their equivalent resistance is equal to the sum of all resistance, namely:

$$\mathcal{R}\_{eq} = \sum\_{i=1}^{N} \mathcal{R}\_i$$

**Figure 26.** A parallel circuit

Two or more resisters are said to be parallel if the same voltage is across each of resisters. Consider the three parallel resisters as illustrated in figure 26, a equivalent circuit for figure 26 is derived through Kirchoff's Current Law as

$$-I + \frac{V\_s}{R\_1} + \frac{V\_s}{R\_2} + \frac{V\_s}{R\_3} = 0$$

Above equivalent resistance can be also rewritten as:

$$R\_{eq} = \frac{V\_s}{I} = \frac{1}{\frac{1}{R\_1} + \frac{1}{R\_2} + \frac{1}{R\_3}}$$

In general, if there are *N* resisters in parallel,

$$R\_{eq} = \frac{V\_s}{I} - \frac{1}{\frac{1}{R\_1} + \frac{1}{R\_2} + \dots + \frac{1}{R\_N}}$$

#### **4.2. Capacitor**

Where, the equivalent resistance, *Req*, is the sum of three resister in figure 25 which is called equivalent resistance. In general, if there are *N* resisters in series, their equivalent resistance

> *Req* <sup>=</sup>∑ *i*=1 *N Ri*

Two or more resisters are said to be parallel if the same voltage is across each of resisters. Consider the three parallel resisters as illustrated in figure 26, a equivalent circuit for figure 26

> *<sup>I</sup>* <sup>=</sup> <sup>1</sup> 1 *R*1 + 1 *R*2 + 1 *R*3

*<sup>I</sup>* <sup>=</sup> <sup>1</sup> 1 *R*1 + 1 *R*2

+ ⋯ +

1 *RN*

− *I* + *Vs R*1 + *Vs R*2 + *Vs R*3 =0

*Req* = *Vs*

*Req* = *Vs*

is equal to the sum of all resistance, namely:

208 Advances in Bioengineering

**Figure 26.** A parallel circuit

is derived through Kirchoff's Current Law as

In general, if there are *N* resisters in parallel,

Above equivalent resistance can be also rewritten as:

A capacitor in figure 27 is a device that stores energy in the electrical field by charge separation when appropriately polarized by the voltage. Simple capacitors consist of parallel plates of conducting material that are separated by a gap filled with a dielectric material. Dielectric materials that are air or mica contain a large number of electric dipoles that become polarized in the presence of electric field. The charge separation caused by the polarization of the dielectric is proportional to the external voltage and given by the following equation:

$$q(t) = \mathbf{C}u(t)$$

Where the symbol, *C*, represents the capacitance of element. The unit of measurement for capacitance is the farad or farads (F).

$$1F = 10^6 \mu F = 10^{12} pF$$

When the charge or voltage of capacitor changes, the produced current in circuit is given as:

$$i = \frac{dq}{dt} = C\frac{du}{dt}$$

This equation is given on the base of the same direction of current and voltage; otherwise there should be a negative symbol in this equation.

The capacitance of capacitor is determined by the permittivity of the dielectric, *ε*, that fills the gap between the parallel plate, the size of the gap between the plates, *d*, and the cross-section area of the plates, *A*, as

$$C = \frac{\varepsilon A}{d}$$

When a constant voltage is exerted on the both sides of capacitor and its current is zero, this capacitor is considered as an open circuit or DC circuit. In physical structure, capacitor consists of two conducting surfaces that store charge, separated by a thin insulating material that has a very large resistance.

For the equation *idt* =*Cdu*, if voltage is produced by both sides of this equation, the following equation could be given as:

$$\int\_0^t \mu i dt = \int\_0^u C\mu d\mu = \frac{1}{2}C\mu^{\frac{2}{d}}$$

Above equation demonstrates that the electric energy increases with the increase of voltage on the capacitor, and in the course, the capacitor component acquires electric energy from electric source. Formula <sup>1</sup> <sup>2</sup> *Cu* <sup>2</sup> is the electric energy in the capacitor. When voltage reduces on the capacitor, electric energy reduces. Namely, capacitor releases electric energy to electric source. Hence, capacitor is an energy storage element in circuit.

**Figure 28.** Circuit with inductor

For the equation *idt* =*Cdu*, integrating both sides yields the following formula:

$$\int\_{\mu\_0}^u C du = \int\_{t\_0}^t i dt \text{, or } \mu(t) = \frac{1}{C} \int\_{t\_0}^t i dt + \mu\_0(t\_0)$$

If *t*<sup>0</sup> =0, above equation can be simplified to

$$\mu\_{\mathcal{U}}(t) = \frac{1}{C} \int\_{t\_0}^{t} i dt + \mu\_0(0)$$

and for *t*<sup>0</sup> = −*∞*, above equation reduces to

$$u(t) = \frac{1}{C} \int\_{-\infty}^{t} i dt$$

The initial voltage in above equation, *u*0(*t*0), is usually defined with the same polarity as *u*, which means *u*0(*t*0) is a positive quantity. If the polarity of *u*0(*t*0) is in the opposite direction, then *u*0(*t*0) is negative.

#### **4.3. Inductor**

electric source. Formula <sup>1</sup>

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**Figure 27.** Circuit with a capacitor

**Figure 28.** Circuit with inductor

then *u*0(*t*0) is negative.

*idt*, or *u*(*t*)= <sup>1</sup>

*<sup>C</sup> ∫<sup>t</sup>*<sup>0</sup> *t*

If *t*<sup>0</sup> =0, above equation can be simplified to

and for *t*<sup>0</sup> = −*∞*, above equation reduces to

*idt* + *u*0(*t*0)

*∫u*0 *u Cdu* <sup>=</sup>*∫<sup>t</sup>*<sup>0</sup> *t* <sup>2</sup> *Cu* <sup>2</sup>

source. Hence, capacitor is an energy storage element in circuit.

For the equation *idt* =*Cdu*, integrating both sides yields the following formula:

*<sup>u</sup>*(*t*)= <sup>1</sup> *<sup>C</sup> ∫<sup>t</sup>*<sup>0</sup> *t idt* + *u*<sup>0</sup> (0)

> *<sup>u</sup>*(*t*)= <sup>1</sup> *C ∫* −*∞ t idt*

The initial voltage in above equation, *u*0(*t*0), is usually defined with the same polarity as *u*, which means *u*0(*t*0) is a positive quantity. If the polarity of *u*0(*t*0) is in the opposite direction,

is the electric energy in the capacitor. When voltage reduces on

the capacitor, electric energy reduces. Namely, capacitor releases electric energy to electric

An inductor in figure 28 is a passive element that is to store energy in magnetic field and is made by winding a coil of wire around a core that is a insulator or a ferromagnetic material.

A magnetic field is established when current flows through the coil. The symbol is utilized to represent the inductor in a circuit. The unit of measurement for inductance is the Henry or Henries (H). The relationship between voltage and current for inductor is given by

$$u = L \cdot \frac{di}{dt}$$

The convention for writing the voltage drop across an inductor is similar to that of a resistor.

Physically, current cannot change instantaneously through a inductor since an infinite voltage required. Mathematically, a step change in current through an inductor is possible by applying a voltage. For convenience, when a circuit has just DC currents (or voltages), the inductors can be replaced by short circuits, since voltage drops across the inductors are zero.

After producing current on the both sides of equation, the following expression can be acquired after integration:

$$\int\_0^t \mu \dot{u} dt = \int\_0^t L \, d\dot{u} = \frac{1}{2} L \quad \dot{u}^2$$

Above expression demonstrates that magnetic energy increases with the increase of current through inductor component. In this course, electrical energy could be converted into magnetic energy, namely inductor acquires energy from the source. Formula <sup>1</sup> <sup>2</sup> *L i* <sup>2</sup> is the magnetic energy of inductive element. When current decreases, magnetic energy decreases and then is converted into electric energy, namely inductor releases energy to the source. Hence, inductor is not a dissipative element, but a energy storage element, too.

For the equation *udt* = *Ldi*, integrating both sides yields the following formula:

$$\int\_{t\_0}^{t} \mu(t)dt = \int\_{i(t\_0)}^{i(t)} Ldi\_\prime \text{ or, } i(t) = \frac{1}{\square} \int\_{t\_0}^{t} \mu(t)dt + i(t\_0)$$

If *t*<sup>0</sup> =0, above equation can be simplified to

$$i(t) = \frac{1}{L} \int\_{t\_0}^{t} \mu(t)dt + i(0).$$

and for *t*<sup>0</sup> = −*∞*, above equation reduces to

$$i(t) = \frac{1}{L} \int\_{-\infty}^{t} \mu(t)dt$$

The initial current in above equation, *i*(*t*0), is usually defined with the same polarity as *i*, which means *i*(*t*0) is a positive quantity. If the polarity of the initial current *i*(*t*0) is in the opposite direction, then *i*(*t*0) is negative.
