**1. Introduction**

One of the most important blocks in the electronic systems is undoubtedly the oscillator block. The oscillator converts a direct current (DC) generated by power supply into an alternating current (AC) signal. The design of this block involves many trade-offs between phase noise, oscillation frequency range, power consumption, layout size, etc. Oscillators are employed in many applications such as phase-locked loops (PLL), frequency dividers/multipliers, clock recovery, frequency synthesizers, etc. Nowadays, the demand for compact and portable systems has increased. Hence, the oscillators, amplifiers, mixers, power amplifiers, etc. may be integrated on a chip. For example, FM radio, Bluetooth, GPRS, Wi-Fi, NFC, and GPS are integrated into modern mobile systems. According to the application, the oscillators are classified as the free-running oscillators and injected oscillators. Free-running oscillators have been extremely studied in many electronic engineering books and articles so far [1–6]. In the free-running oscillators, there is no external signal injected into the oscillator. In the injected oscillators, an external periodic signal mentioned as an injection signal is injected to the oscillator, which may be deliberately applied by the designers to make an injected oscillator, or any injection signals are accidentally injected to the oscillator which may be generated from other blocks such as power

amplifiers and other oscillators. By injected oscillators, designers can implement many high-performance blocks such as quadrature oscillators and frequency dividers/multipliers, frequency synthesizers without a frequency-locked loop, which are useful in the fast frequency locking-loop systems. Thus, the cost of fabrication is cheaper than a frequency-locked loop. There are many devices operating with different center frequencies. As a result, several oscillators and other devices are placed together for implementing a system called system on chip (SOC). However, when the oscillators are integrated with other devices on the chip, various signals with different center frequencies may leak through the substrate, parasitic elements, or packaging and be injected into the oscillator. Hence, the performance of the oscillators is changed which can be suitable or not dependent on their functionality. When an oscillator is injected with an injection signal, the pulling and locking phenomena occur. Thus, pulling and locking phenomena are important parameters for designers. between the external signal and free-running oscillator are not suitable for locking, the oscillator is perturbed, and the output signal is modulated called pulling phenomenon. In the pulling case, the output spectrum of the injected oscillators has some spurious tones along with the effective oscillation frequency of the external signal. While the strength of the external signal and frequency difference between the external signal and free-running oscillator are suitable, the oscillator is locked, and the frequency of the output signal is locked to the first, sub- or super-harmonic of the oscillation frequency of the external signal called locking phenomenon. The range of the oscillation frequency of the external signal causes a locking phenomenon called the locking range. In **Figures 1** and **2**, these phenomena are simply

At first, a free-running oscillator is chosen. Next, the oscillation frequency, the output voltage oscillation amplitude, and the current oscillation amplitude are obtained. Second, the given oscillator is injected with the external signal, which is modeled by a current source and in parallel with the output nodes. Third, the results of the injected oscillator are revealed under locking and pulling phenomena. The free-running oscillator, implemented by a three-stage differential ring oscillator, is depicted in **Figure 1a** along with the delay cell in **Figure 1b**. In the time

and frequency domain, the output voltage of the oscillator is presented in **Figure 1c** and **d**. According to **Figure 1b** and **c**, there is no frequency or phase modulation on the output voltage. It has a center frequency (257 MHz). In addition, the output voltage amplitude is constant (0.481 V), and the oscillation current (*Iosc*)

is equal to 0.18 mA. In fact, there is not any amplitude modulation (AM).

tor is equal to the oscillation frequency of the injected signal.

**3. Review of the previously significantly published papers**

The pulling and locking phenomena have been investigated in previously published papers [2, 8–60]. According to the output waveform, oscillators may be categorized as nonharmonic oscillators, for example, LC oscillators and harmonic oscillators such as ring oscillators. For the nonharmonic oscillators, the output waveform has a center frequency near the resonance frequency of the LC tank. Consequently, the output waveform is almost sinusoidal. For harmonic oscillators, since the output waveform is not sinusoidal, the higher harmonics effect on the output waveform. In fact, nonharmonic oscillators have an LC tank block

near locking range as portrayed in **Figure 2**.

**89**

tion signal, which its current (*Iinj*) and oscillation frequency (*Finj*) are equal to *Iosc*/20 and 260 MHz, respectively. Assuming locking conditions are covered, the oscillation frequency of the injected oscillator is the same as the injected signal as shown in **Figure 2b** and **c**. **Figure 2b** and **c** displays the output voltage of the injected oscillator under locking phenomenon in the time and frequency domain, respectively. **Figure 2b** and **c** illustrates the output voltage of the injected oscillator locked in *Finj*. It is clear that there is not any modulation on the output voltage at the time and frequency domain. Then, the oscillation frequency of the injected oscilla-

**Figure 2a** shows the given three-stage differential ring oscillator under an injec-

**Figure 2d**–**g** illustrates the output voltage of the injected oscillator in the pulling phenomenon when *Iinj* = *Iosc*/20 and *Finj* is equal to 262.5 and 265 MHz. It is obvious that there are modulations on the output voltage at the time and frequency domain. The injected oscillator produces amplitude and frequency (or phase) modulation in the output voltage. According to **Figure 2d** and **f**, the center frequency of the oscillator is pulled to the frequency of the external signal. Furthermore, the beat frequency, instance variation of oscillation frequency, is reduced when *Finj* becomes

presented in the time domain and frequency domain.

*Review of Injected Oscillators*

*DOI: http://dx.doi.org/10.5772/intechopen.91687*

The injected locked oscillators designed by engineers are classified into three classes. While the oscillation frequency of the injection signal is near to the free-running oscillator, the first-harmonic injection locking takes place. When the oscillation frequency of the injection signal is near to the sub-/super-harmonic of the oscillation frequency of the free-running oscillator, frequency dividers/multipliers are realized. These phenomena occur since the nonlinear performance of the injected oscillators. So, the size of the layout and complexity of designing frequency dividers/multipliers are lower than the frequency-locked loop because they do not employ many blocks in the frequency-locked loop such as filters, charge pomp, and frequency detector [7]. Consequently, power consumption is reduced. Furthermore, they are fast and may be applied to the high-speed or high clock data recovery and fast-locking systems. At last, the phase noise of the injected oscillator is different from the free-running oscillator and is dependent on the phase noise of the injection signal. Therefore, while the injection signal is generated by an oscillator which owns excellent phase noise, the injected oscillator will have a better phase noise [7, 8]. This chapter tries to disclose all subtleties and challenges encountered during the design of injected oscillators.

The presented chapter aims to investigate the injected oscillators. A summary of the injected oscillator specifications regarding locking and pulling phenomena, previously significantly published papers about the first harmonic injection oscillator, frequency dividers and enhancing locking range are presented. Section 2 covers with introducing pulling and locking phenomena in the first-harmonic injection locking oscillator. Then, a free-running oscillator is implemented for exploring the pulling and locking phenomena by various injection signals. Section 3 will be dedicated to the pulling and locking formula, and beat frequency equation is discussed for injected oscillators for nonharmonic (LC) and harmonic (ring) oscillators. Section 4 will treat the implementation of injected locked frequency dividers and increase the locking range. First, a block of the injection-locked frequency dividers/multiplier is displayed. In a literature overview, two classes of realization will be recognized: the conventional LC-injection-locked frequency dividers where the injection signal is applied to the oscillator by the tail current source or a transistor connected to the output nodes. Furthermore, the previously important published papers are reviewed. Finally, some structures and techniques employed in order to extend the locking range of frequency dividers are exhibited from previously significant published papers. Section 5 will conclude with the main contributions of the presented chapter.

#### **2. Pulling and clocking phenomena**

When an oscillator is injected with an external signal, two phenomena occur for the oscillator. Once the strength of the external signal and frequency difference

#### *Review of Injected Oscillators DOI: http://dx.doi.org/10.5772/intechopen.91687*

amplifiers and other oscillators. By injected oscillators, designers can implement many high-performance blocks such as quadrature oscillators and frequency

*Modulation in Electronics and Telecommunications*

dividers/multipliers, frequency synthesizers without a frequency-locked loop, which are useful in the fast frequency locking-loop systems. Thus, the cost of fabrication is cheaper than a frequency-locked loop. There are many devices operating with different center frequencies. As a result, several oscillators and other devices are placed together for implementing a system called system on chip (SOC). However, when the oscillators are integrated with other devices on the chip, various signals with different center frequencies may leak through the substrate, parasitic elements, or packaging and be injected into the oscillator. Hence, the performance of the oscillators is changed which can be suitable or not dependent on their functionality. When an oscillator is injected with an injection signal, the pulling and locking phenomena occur. Thus, pulling and locking phenomena are important parameters for designers. The injected locked oscillators designed by engineers are classified into three classes. While the oscillation frequency of the injection signal is near to the free-running oscillator, the first-harmonic injection locking takes place. When the oscillation frequency of the injection signal is near to the sub-/super-harmonic of the oscillation frequency of the free-running oscillator, frequency dividers/multipliers are realized. These phenomena occur since the nonlinear performance of the injected oscillators. So, the size of the layout and complexity of designing frequency dividers/multipliers are lower than the frequency-locked loop because they do not employ many blocks in the frequency-locked loop such as filters, charge pomp, and frequency detector [7]. Consequently, power consumption is reduced. Furthermore, they are fast and may be applied to the high-speed or high clock data recovery and fast-locking systems. At last, the phase noise of the injected oscillator is different from the free-running oscillator and is dependent on the phase noise of the injection signal. Therefore, while the injection signal is generated by an oscillator which owns excellent phase noise, the injected oscillator will have a better phase noise [7, 8]. This chapter tries to disclose all subtleties and challenges encountered during the design of injected oscillators.

The presented chapter aims to investigate the injected oscillators. A summary of the injected oscillator specifications regarding locking and pulling phenomena, previously significantly published papers about the first harmonic injection oscillator, frequency dividers and enhancing locking range are presented. Section 2 covers with introducing pulling and locking phenomena in the first-harmonic injection locking oscillator. Then, a free-running oscillator is implemented for exploring the pulling and locking phenomena by various injection signals. Section 3 will be dedicated to the pulling and locking formula, and beat frequency equation is discussed for injected oscillators for nonharmonic (LC) and harmonic (ring) oscillators. Section 4 will treat the implementation of injected locked frequency dividers and increase the locking range. First, a block of the injection-locked frequency dividers/multiplier is displayed. In a literature overview, two classes of realization will be recognized: the conventional LC-injection-locked frequency dividers where the injection signal is applied to the oscillator by the tail current source or a transistor connected to the output nodes. Furthermore, the previously important published papers are reviewed. Finally, some structures and techniques employed in order to extend the locking range of frequency dividers are exhibited from previously significant published papers. Section 5 will

When an oscillator is injected with an external signal, two phenomena occur for the oscillator. Once the strength of the external signal and frequency difference

conclude with the main contributions of the presented chapter.

**2. Pulling and clocking phenomena**

**88**

between the external signal and free-running oscillator are not suitable for locking, the oscillator is perturbed, and the output signal is modulated called pulling phenomenon. In the pulling case, the output spectrum of the injected oscillators has some spurious tones along with the effective oscillation frequency of the external signal. While the strength of the external signal and frequency difference between the external signal and free-running oscillator are suitable, the oscillator is locked, and the frequency of the output signal is locked to the first, sub- or super-harmonic of the oscillation frequency of the external signal called locking phenomenon. The range of the oscillation frequency of the external signal causes a locking phenomenon called the locking range. In **Figures 1** and **2**, these phenomena are simply presented in the time domain and frequency domain.

At first, a free-running oscillator is chosen. Next, the oscillation frequency, the output voltage oscillation amplitude, and the current oscillation amplitude are obtained. Second, the given oscillator is injected with the external signal, which is modeled by a current source and in parallel with the output nodes. Third, the results of the injected oscillator are revealed under locking and pulling phenomena.

The free-running oscillator, implemented by a three-stage differential ring oscillator, is depicted in **Figure 1a** along with the delay cell in **Figure 1b**. In the time and frequency domain, the output voltage of the oscillator is presented in **Figure 1c** and **d**. According to **Figure 1b** and **c**, there is no frequency or phase modulation on the output voltage. It has a center frequency (257 MHz). In addition, the output voltage amplitude is constant (0.481 V), and the oscillation current (*Iosc*) is equal to 0.18 mA. In fact, there is not any amplitude modulation (AM).

**Figure 2a** shows the given three-stage differential ring oscillator under an injection signal, which its current (*Iinj*) and oscillation frequency (*Finj*) are equal to *Iosc*/20 and 260 MHz, respectively. Assuming locking conditions are covered, the oscillation frequency of the injected oscillator is the same as the injected signal as shown in **Figure 2b** and **c**. **Figure 2b** and **c** displays the output voltage of the injected oscillator under locking phenomenon in the time and frequency domain, respectively. **Figure 2b** and **c** illustrates the output voltage of the injected oscillator locked in *Finj*. It is clear that there is not any modulation on the output voltage at the time and frequency domain. Then, the oscillation frequency of the injected oscillator is equal to the oscillation frequency of the injected signal.

**Figure 2d**–**g** illustrates the output voltage of the injected oscillator in the pulling phenomenon when *Iinj* = *Iosc*/20 and *Finj* is equal to 262.5 and 265 MHz. It is obvious that there are modulations on the output voltage at the time and frequency domain. The injected oscillator produces amplitude and frequency (or phase) modulation in the output voltage. According to **Figure 2d** and **f**, the center frequency of the oscillator is pulled to the frequency of the external signal. Furthermore, the beat frequency, instance variation of oscillation frequency, is reduced when *Finj* becomes near locking range as portrayed in **Figure 2**.
