**Interferometer Instantaneous Frequency Identifier**

M. T. de Melo, B. G. M. de Oliveira, Ignacio Llamas-Garro and Moises Espinosa-Espinosa

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/52623

**1. Introduction**

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[19] Wang, L. C., Lin, Y. C. and Lin, P. H. (2006). "Dynamic Mobile RFID-based Supply Chain Control and Management System in Construction." International Journal of Advanced Engineering Informatics - Special Issue on RFID Applications in Engineer‐

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282 Radio Frequency Identification from System to Applications

Computing in Civil Engineering, ASCE, 16(1), 23-38.

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Civil and Infrastructure Engineering, Vol. 20, pp.242-264.

132(9), 680-688.

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mation in Construction, 18(5), 677-691.

299-314.

12(1), 477-490.

dio Frequency Identification Systems, Prentice Hall PTR.

The rapid development of radar, communication and weapons guidance systems generates an urgent need for microwave receivers to detect possible threats at the earliest stage of a military mission. The microwave receivers used to intercept the RF signals must be able to meet these challenges. Thus, microwave receivers have become an important research area because of their applications to electronic warfare (EW) [1].

The instantaneous frequency measurement (IFM) receiver has been mostly incorporated in advanced EW systems. As to perform the fundamental function, which is to detect threat signals and provide information to the aircrafts, ships, missiles or ground forces, the IFM re‐ ceiver offers high probability of intercept over wide instantaneous RF bandwidths, high dy‐ namic ranges, moderately good sensitivity, high frequency measurement accuracy, real time frequency measurement and relatively low cost.

IFM started out as a simple technique to extract digital RF carrier frequency over a wide in‐ stantaneous bandwidth mainly for pulsed RF inputs. It is been gradually developed to a re‐ sourceful system for real time encoding of the RF input frequency, amplitude, pulse width, angle of arrival (AOA) and time of arrival (TOA) for both pulsed and continuous wave (CW) RF inputs. For many electronic support measures (ESM) applications, the carrier fre‐ quency is considered to be one of the most important radar parameters, since it is employed in many tasks: sorting, even in dense signal environments; emitter identification and classifi‐ cation; and correlation of similar emitter reports from different stations or over long time in‐ tervals, to allow emitter location [2,3].

An IFM receiver is an important component in many signal detection systems. Though nu‐ merous improvements have been made to the design of these systems over the years, the basic principle of operation remains relatively unchanged, in that the frequency of an in‐

coming signal is converted into a voltage proportional to the frequency. Microwave interfer‐ ometers are usually base circuits of the IFM systems. These interferometers most often consist of directional couplers, power combiners/dividers and delay lines [4-8]. As a good example, a coplanar interferometer based on interdigital delay line with different finger lengths, will be presented. Another example of interferometers, but now, implemented with micro strip multi-band-stop filters to obtain signals similar to those supplied by the interfer‐ ometers was published recently and will be presented here as well [9,10].

*S*1*(t)* and *S*2*(t)* are the signals after passing the delay τ1 and τ2, respectively. Then the output *s(t)* is given by the addition of (2) and (3), and after some trigonometric manipulations that

From (4), one can see that the frequency interval between two consecutive maxima or mini‐

2,1 <sup>1</sup> *<sup>f</sup>* , tD =

where *Δτ*2,1 =*τ*<sup>2</sup> −*τ*1 is the delay difference between the two branches of the interferometer.

max <sup>1</sup> . <sup>4</sup> *<sup>R</sup>*

t

1 max min 2 , *<sup>n</sup>*

1 min <sup>1</sup> . <sup>2</sup> *<sup>R</sup> <sup>n</sup> <sup>f</sup>* t

 t

Fig. 2 shows the architecture of a traditional instantaneous frequency measurement subsys‐ tem (IFMS), where delay lines are used to implement five interferometers as discrimination

Each discriminator provides one bit of the output binary word that is assigned to a certain sub-band of frequency [1]. Wilkinson power dividers are used at the input and output of each interferometer [3]. The output of each discriminator is connected to a detector. The 1 bit A/D converter receives the signal from the amplifier, and attributes "0" or "1" to the output to form the digital word for each frequency sub-band. These values depend on the power level of the received signal. A limiting amplifier is used in IFM input to control the signal gain, to increase sensitivity, and clean up the signal within the band of interest [1], [7].

 wt t


<sup>D</sup> (5)

Interferometer Instantaneous Frequency Identifier

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285

<sup>=</sup> <sup>D</sup> (6)


<sup>+</sup> <sup>=</sup> <sup>D</sup> (8)

12 21 2() () ( ) sin . 2 2

*t s t cos* <sup>æ</sup> w wt t

Still from (5), it is noticed that from *Δ f* max one gets *Δτ*min and vice-versa.

*f*

t

And this way, the resolution *f*r of an *n*-bits subsystem can be rewritten as

As in [1], the frequency resolution is given by

A binary code can be generated if

channels.

sum can be written as

ma of *s(t)* are given by

### **2. Important concepts**

The system is based on frequency mapping, going from analogical signal into digital words. Any frequency value in the operating band of the system corresponds to a unique digital word. In the process, there is no need to adjust or tune any device. The signal is identified instantaneously. The frequency resolution depends on the longest delay and the number of discriminators.

Let us see how the IFMS maps the incoming signal *x(t)* into digital words. First of all, con‐ sider a sinusoidal signal *x(t)* = sin(*ωt*) split into two parts, as shown in Fig. 1.

**Figure 1.** Interferometer used in instantaneous frequency measurement subsystem.

The signals *x*1*(t)* and *x*2*(t)* are then described as

$$\mathbf{x}\_1(t) = \mathbf{x}\_2(t) = \frac{\sin(\alpha t)}{2} \tag{1}$$

Because of different delays *τ*1 and *τ*2, one has

$$s\_1(t) = x\_1(t - \tau\_1) \tag{2}$$

and

$$\mathbf{x}\_2(t) = \mathbf{x}\_2(t - \tau\_2). \tag{3}$$

*S*1*(t)* and *S*2*(t)* are the signals after passing the delay τ1 and τ2, respectively. Then the output *s(t)* is given by the addition of (2) and (3), and after some trigonometric manipulations that sum can be written as

$$s(t) = \sin\left(\frac{2\alpha\vartheta - \alpha(\tau\_1 + \tau\_2)}{2}\right)\cos\left(\frac{\alpha(\tau\_2 - \tau\_1)}{2}\right). \tag{4}$$

From (4), one can see that the frequency interval between two consecutive maxima or mini‐ ma of *s(t)* are given by

$$
\Delta f = \left| \frac{1}{\Delta \tau\_{2,1}} \right|,
\tag{5}
$$

where *Δτ*2,1 =*τ*<sup>2</sup> −*τ*1 is the delay difference between the two branches of the interferometer. Still from (5), it is noticed that from *Δ f* max one gets *Δτ*min and vice-versa.

As in [1], the frequency resolution is given by

$$f\_R = \frac{1}{4\text{ }\Delta\tau\_{\text{max}}}.\tag{6}$$

A binary code can be generated if

coming signal is converted into a voltage proportional to the frequency. Microwave interfer‐ ometers are usually base circuits of the IFM systems. These interferometers most often consist of directional couplers, power combiners/dividers and delay lines [4-8]. As a good example, a coplanar interferometer based on interdigital delay line with different finger lengths, will be presented. Another example of interferometers, but now, implemented with micro strip multi-band-stop filters to obtain signals similar to those supplied by the interfer‐

The system is based on frequency mapping, going from analogical signal into digital words. Any frequency value in the operating band of the system corresponds to a unique digital word. In the process, there is no need to adjust or tune any device. The signal is identified instantaneously. The frequency resolution depends on the longest delay and the number of

Let us see how the IFMS maps the incoming signal *x(t)* into digital words. First of all, con‐

sider a sinusoidal signal *x(t)* = sin(*ωt*) split into two parts, as shown in Fig. 1.

**Figure 1.** Interferometer used in instantaneous frequency measurement subsystem.

1 2

*xt xt*

sin( ) () () <sup>2</sup>

1 11 *st xt* () ( ) = t

2 22 *st xt* ( ) ( ). = t

*t*

= = (1)

(2)

(3)

w

The signals *x*1*(t)* and *x*2*(t)* are then described as

Because of different delays *τ*1 and *τ*2, one has

ometers was published recently and will be presented here as well [9,10].

**2. Important concepts**

284 Radio Frequency Identification from System to Applications

discriminators.

and

$$
\Delta \tau\_{\text{max}} = \mathcal{Z}^{n-1} \Delta \tau\_{\text{min}}.\tag{7}
$$

And this way, the resolution *f*r of an *n*-bits subsystem can be rewritten as

$$\int f\_R = \frac{1}{2^{n+1} \, \Delta \tau\_{\text{min}}}.\tag{8}$$

Fig. 2 shows the architecture of a traditional instantaneous frequency measurement subsys‐ tem (IFMS), where delay lines are used to implement five interferometers as discrimination channels.

Each discriminator provides one bit of the output binary word that is assigned to a certain sub-band of frequency [1]. Wilkinson power dividers are used at the input and output of each interferometer [3]. The output of each discriminator is connected to a detector. The 1 bit A/D converter receives the signal from the amplifier, and attributes "0" or "1" to the output to form the digital word for each frequency sub-band. These values depend on the power level of the received signal. A limiting amplifier is used in IFM input to control the signal gain, to increase sensitivity, and clean up the signal within the band of interest [1], [7].

The *ABCD* matrix of a lossless transmission line section of length *L*, line impedance *Z*0 and

cos( ) sin( ) (1 / ) sin( ) cos( ) *j*

b

From the above equation one can relate *Z*0 to only *B* and *C* elements. If we use the conver‐ sion from *ABCD* matrix to *S*-parameters and assume the source and load reference impe‐

 b

*C D Z LL* (9)

Interferometer Instantaneous Frequency Identifier

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287

1/2

*<sup>C</sup>* (10)

æ ö ç ÷ è ø (11)

 b

*0*

*j* b

*0 A B L L Z*

<sup>=</sup> é ù é ù ê ú ê ú ë û ë û

( )( ) ( )( )

+ +- = = - - <sup>é</sup> <sup>ù</sup> <sup>ê</sup> <sup>ú</sup> <sup>ê</sup> <sup>ú</sup> <sup>ë</sup> <sup>û</sup> *<sup>0</sup>*

*B Z Z* 1 1 <sup>2</sup> 11 22 12 21 1 1 11 22 12 21 *S S SS S S SS*

Note that the *ABCD* matrix is not for a unit cell of the line, it represents the entire transmis‐

Group delay is the measurement of signal transmission time through a test device. It is de‐ fined as the derivative of the phase characteristic with respect to frequency. Assuming linear phase change *ϕ21(2)ϕ21(1)* over a specified frequency aperture *f(2)f(1)*, the group delay can, in

> 1 (2) (1) 21 21 2 (2) (1) *<sup>g</sup> f f* f

p

other parameters fixed. The devices were fabricated, measured and simulated.


t

**3.1.Intedigitalinterferometer. design and measurement**

 f

The structure shown in figure 3 was etched on only one side of an RT/duroid 6010 with rela‐ tive permittivity ε<sup>r</sup> = 10.8, dielectric thickness h = 0.64 mm, conductor thickness t =35*μ*m, w = 0.3 mm, s = 0.3 mm and L = 99 mm. In order to find the line impedance and delay the simu‐ lation was carried out varying the finger length ℓ from 0.6 to 4.2 mm and keeping all the

The simulation used sonnet software in order to find the magnitude and phase of the S-pa‐ rameters, assuming a lossless conductor. Afterwards, equations 10 and 11 were used to find Z0 and τg, respectively. In the experimental procedure each device was connected with co‐ axial connectors to a HP8720A network analyzer. After carrying out a proper calibration, the devices were then measured. This way, the group delay measurement was implemented, and figure 4 summarizes the group delay results from both measurement and simulation for a frequency range of 0.5-3 GHz. As the finger length increases the lumped capacitance per unit length increases. It slows down the group velocity leading to an increase in the group delay. The longer the finger length, compared to the finger width, the closer it is to a purely

phase constant *β* is given by

dance as *Z*, we then have [12]

practice, be obtained approximately by

sion line.

capacitive element.

**Figure 2.** Architecture of a traditional IFM subsystem.

#### **3. Coplanar interdigital delay Line for IFM systems**

The schematic drawing of the interdigital delay is shown in figure 3. The particular line con‐ sists of 164 interdigital fingers of equal length ℓ, finger width w, finger spacing *s* and total length *L*. *d* is the unit cell length representing the periodicity of the transmission line. If *d*<< λ, an amount of lumped capacitance per unit length C0/d is added to the shunt capacitance *C*.

**Figure 3.** Coplanar interdigital delay line under test.

For the structure shown in figure 3 the phase velocity and the characteristic impedance *Z*0, become: [(*C* + 2*C*0*/d*) *L*S ]-1/2 and [*L*S /( *C* + 2 *C*0*/d* )]1/2, respectively. Here, *L*<sup>S</sup> is the series induc‐ tance [11]. Due to the fringing electric fields about the fingers, the amount by which the ca‐ pacitance per unit length increases is greater than the corresponding amount by which the inductance per unit length decreases. In order to exploit the fringing electric fields produced by the fingers, one needs to increase the finger length and keep the finger width fixed.

The *ABCD* matrix of a lossless transmission line section of length *L*, line impedance *Z*0 and phase constant *β* is given by

$$
\begin{bmatrix} A & B \\ C & D \end{bmatrix} = \begin{bmatrix} \cos(\beta \, L) & jZ\_0 \sin(\beta \, L) \\ (1 \, / \, Z\_0) / \sin(\beta \, L) & \cos(\beta \, L) \end{bmatrix} \tag{9}
$$

From the above equation one can relate *Z*0 to only *B* and *C* elements. If we use the conver‐ sion from *ABCD* matrix to *S*-parameters and assume the source and load reference impe‐ dance as *Z*, we then have [12]

$$Z\_{O} = \sqrt{\frac{B}{C}} = \left[ Z^2 \frac{\left(1 + S\_{11}\right)\left(1 + S\_{22}\right) - S\_{12}S\_{21}}{\left(1 - S\_{11}\right)\left(1 - S\_{22}\right) - S\_{12}S\_{21}} \right]^{1/2} \tag{10}$$

Note that the *ABCD* matrix is not for a unit cell of the line, it represents the entire transmis‐ sion line.

Group delay is the measurement of signal transmission time through a test device. It is de‐ fined as the derivative of the phase characteristic with respect to frequency. Assuming linear phase change *ϕ21(2)ϕ21(1)* over a specified frequency aperture *f(2)f(1)*, the group delay can, in practice, be obtained approximately by

$$\text{Tr}\,\mathfrak{g} = -\frac{1}{2\pi} \left( \frac{\phi\_{21}(2) - \phi\_{21}(1)}{f(2) - f(1)} \right) \tag{11}$$

#### **3.1.Intedigitalinterferometer. design and measurement**

**Figure 2.** Architecture of a traditional IFM subsystem.

286 Radio Frequency Identification from System to Applications

**Figure 3.** Coplanar interdigital delay line under test.

**3. Coplanar interdigital delay Line for IFM systems**

The schematic drawing of the interdigital delay is shown in figure 3. The particular line con‐ sists of 164 interdigital fingers of equal length ℓ, finger width w, finger spacing *s* and total length *L*. *d* is the unit cell length representing the periodicity of the transmission line. If *d*<< λ, an amount of lumped capacitance per unit length C0/d is added to the shunt capacitance *C*.

For the structure shown in figure 3 the phase velocity and the characteristic impedance *Z*0, become: [(*C* + 2*C*0*/d*) *L*S ]-1/2 and [*L*S /( *C* + 2 *C*0*/d* )]1/2, respectively. Here, *L*<sup>S</sup> is the series induc‐ tance [11]. Due to the fringing electric fields about the fingers, the amount by which the ca‐ pacitance per unit length increases is greater than the corresponding amount by which the inductance per unit length decreases. In order to exploit the fringing electric fields produced by the fingers, one needs to increase the finger length and keep the finger width fixed.

The structure shown in figure 3 was etched on only one side of an RT/duroid 6010 with rela‐ tive permittivity ε<sup>r</sup> = 10.8, dielectric thickness h = 0.64 mm, conductor thickness t =35*μ*m, w = 0.3 mm, s = 0.3 mm and L = 99 mm. In order to find the line impedance and delay the simu‐ lation was carried out varying the finger length ℓ from 0.6 to 4.2 mm and keeping all the other parameters fixed. The devices were fabricated, measured and simulated.

The simulation used sonnet software in order to find the magnitude and phase of the S-pa‐ rameters, assuming a lossless conductor. Afterwards, equations 10 and 11 were used to find Z0 and τg, respectively. In the experimental procedure each device was connected with co‐ axial connectors to a HP8720A network analyzer. After carrying out a proper calibration, the devices were then measured. This way, the group delay measurement was implemented, and figure 4 summarizes the group delay results from both measurement and simulation for a frequency range of 0.5-3 GHz. As the finger length increases the lumped capacitance per unit length increases. It slows down the group velocity leading to an increase in the group delay. The longer the finger length, compared to the finger width, the closer it is to a purely capacitive element.

The experimental data of Z0 were obtained using a reflection measurement in time domain low pass function of the HP8720A. The same devices were all measured again and the re‐ sults are summarized in figure 5. Looking at the beginning of the curve on the left hand side, the figure 5 seems to agree with the classical coplanar strips formulation, as we found Z0= 99 *Ω* for ℓ=0 [13]. As we expected, Z0 decreased as the finger length increased, due to the rise in 2C0/d, achieving 50*Ω* at ℓ=3.9mm. As the finger length goes from 0.6 mm to 4.2 mm, τ<sup>g</sup> increases about 150% and Z0 decreases about 45%.

without bends or air bridges. The chip resistors used to increase the isolations between the

Interferometer Instantaneous Frequency Identifier

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289

The design has a delay difference of 1.6ns. Two output traces versus frequency from 1.5GHz to 3GHz are presented in figure 7. The theoretical one was obtained using the design equa‐ tions for a single stage of a typical IFM subsystem [14]. The oscillations in the experimental

trace originated from the coaxial connections and the chip resistors bonds.

**Figure 7.** Theoretical interferometer output and measured scattering parameter in dB versus frequency.

The IFMS presented now is based on band-stop filter and is shown in Fig. 8. The advantage of using the new architecture is that one has in each channel only multi band-stop filters in‐

Each word is assigned to only one frequency sub-band to generate a one-step binary code. The response of each multi band-stop filter should be like the one shown in Fig. 9 (a) with discriminators 0, 1, 2, 3 and 4. The discriminator 0 provides the least-significant bit (LSB) and the discriminator 4 provides the most-significant bit (MSB). The form of these responses is suitable to implement the 1 bit A/D converters. Here, let us attribute value 1 if the inser‐

**4. Interferometer based on band-stop filter for IFM**

stead of delay lines and power splitter, as one finds in classical IFMS.

outputs of the power splitter (and the input of the combiner) are not shown below.

**Figure 6.** Uniplanar single stage of the IFM under test, scale 1/1

**Figure 4.** Group delay as a function of finger length at a Frequency range of 0.5-3 GHz.

**Figure 5.** Characteristic Impedance as a function of finger length at a frequency range of 0.5-3 GHz.

These results look promising as far as an IFM application is concerned. Referring to a single stage of a typical IFM, a coplanar unequal output impedance power splitter can be designed to feed two delays with different characteristic impedances. The length of the second delay of each discriminator may be increased to achieve better resolution. The results from figures 4 and 5 may be used together to redesign the coplanar unequal output impedance power splitter to achieve the exact impedance matching. Figure 6 shows a prototype system fabri‐ cated based on results of figures 4 and 5. Coplanar wave guide, coplanar strips, coplanar un‐ equal output impedance power splitter and coplanar interdigital delay line are integrated without bends or air bridges. The chip resistors used to increase the isolations between the outputs of the power splitter (and the input of the combiner) are not shown below.

**Figure 6.** Uniplanar single stage of the IFM under test, scale 1/1

The experimental data of Z0 were obtained using a reflection measurement in time domain low pass function of the HP8720A. The same devices were all measured again and the re‐ sults are summarized in figure 5. Looking at the beginning of the curve on the left hand side, the figure 5 seems to agree with the classical coplanar strips formulation, as we found Z0= 99 *Ω* for ℓ=0 [13]. As we expected, Z0 decreased as the finger length increased, due to the rise in 2C0/d, achieving 50*Ω* at ℓ=3.9mm. As the finger length goes from 0.6 mm to 4.2 mm, τ<sup>g</sup>

> simulation experiment

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 finger length (mm**)**

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 finger length (mm)

These results look promising as far as an IFM application is concerned. Referring to a single stage of a typical IFM, a coplanar unequal output impedance power splitter can be designed to feed two delays with different characteristic impedances. The length of the second delay of each discriminator may be increased to achieve better resolution. The results from figures 4 and 5 may be used together to redesign the coplanar unequal output impedance power splitter to achieve the exact impedance matching. Figure 6 shows a prototype system fabri‐ cated based on results of figures 4 and 5. Coplanar wave guide, coplanar strips, coplanar un‐ equal output impedance power splitter and coplanar interdigital delay line are integrated

simulation experiment

increases about 150% and Z0 decreases about 45%.

288 Radio Frequency Identification from System to Applications

0.5 1 1.5 2 2.5 3 3.5 4

**Figure 4.** Group delay as a function of finger length at a Frequency range of 0.5-3 GHz.

**Figure 5.** Characteristic Impedance as a function of finger length at a frequency range of 0.5-3 GHz.

Z0( )

g. delay (ns)

The design has a delay difference of 1.6ns. Two output traces versus frequency from 1.5GHz to 3GHz are presented in figure 7. The theoretical one was obtained using the design equa‐ tions for a single stage of a typical IFM subsystem [14]. The oscillations in the experimental trace originated from the coaxial connections and the chip resistors bonds.

**Figure 7.** Theoretical interferometer output and measured scattering parameter in dB versus frequency.
