Source : Phase-Locked Loops: Design, Simulation, and Applications, Sixth 1 Edition Ronald E. Best Introduction to PLLs Operating Principles of the PLL The phase-locked loop (PLL) helps keep parts of our world orderly. If we turn on a television set, a PLL keeps heads at the top of the screen and feet at the bottom. In color television, another PLL makes sure green remains green and red remains red (even if politicians claim the reverse is true).
A PLL is a circuit that causes a particular system to track with another one. More precisely, a PLL is a circuit synchronizing an output signal (generated by an oscillator) with a reference or input signal in frequency as well as in phase. In the synchronized— often called “locked”—state, the phase error between the oscillator’s output signal and the reference signal is zero, or it remains constant. If a phase error builds up, a control mechanism acts on the oscillator in such a way that the phase error is again reduced to a minimum.
In such a control system, the phase of the output signal is actually locked to the phase of the reference signal. This is why it is referred to as a phase-locked loop. The operating principle of the PLL is explained by the example of the linear PLL (LPLL). As will be pointed out in Sec.3, other types of PLLs exist—for example, digital PLLs (DPLLs), all-digital PLLs (ADPLLs), and software PLLs (SPLLs).
The PLL block diagram is shown in Fig.1a and consists of three basic functional blocks: ■ A voltage-controlled oscillator (VCO) ■ A phase detector (PD) ■ A loop filter (LF) In this simple example, there is no down scaler between the output of VCO [u2(t)] and the lower input of the phase detector [ω2]. Systems using down scalers are discussed in the following chapters. In some PLL circuits, a current-controlled oscillator (CCO) is used instead of the VCO. In this case, the output signal of the phase detector is a controlled Printed from Digital Engineering Library @ McGraw-Hill (www.
Copyright ©2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTRODUCTION TO PLLS Ronald E.1 (a) Block diagram of the PLL.
(b) Transfer function of the VCO. (uf = control voltage; ω2 = angular frequency of the output signal.) (c) Transfer function of the PD. ( = average value of the phase-detector output signal; θe = phase error.) current source rather than a voltage source. However, the operating principle remains the same.
The signals of interest within the PLL circuit are defined as follows: ■ The reference (or input) signal u1(t) ■ The angular frequency ω1 of the reference signal ■ The output signal u2(t) of the VCO ■ The angular frequency ω2 of the output signal ■ The output signal ud(t) of the phase detector ■ The output signal uf(t) of the loop filter ■ The phase error θe, defined as the phase difference between signals u1(t) and u2(t) INTRODUCTION TO PLLS Ronald E. Best 3 Let us now look at the operation of the three functional blocks in Fig. The VCO oscillates at an angular frequency ω2, which is determined by the output signal uf of the loop filter. The angular frequency ω2 is given by (1.1) where ω0 is the center (angular) frequency of the VCO and K0 is the VCO gain in rad s−1 V−1.1) is plotted graphically in Fig.
Because rad (radian) is a dimensionless quantity, we will drop it mostly in this text. (Note, however, that any phase variables used in this book will have to be measured in radians and not in degrees!) Therefore, in the equations a phase shift of 180° must always be specified as a value of π. The PD (also referred to as a phase comparator) compares the phase of the output signal with the phase of the reference signal and develops an output signal ud(t), which is approximately proportional to the phase error θe, at least within a limited range of the latter (1.2) Here, Kd represents the gain of the PD. The physical unit of Kd is V/rad.1c is a graphical representation of Eq.
The output signal ud(t) of the PD consists of a DC component and a superimposed AC component. The latter is undesired; hence, it is canceled by the loop filter. In most cases, a first-order low-pass filter is used. Let us now see how the three building blocks work together.
First, we assume the angular frequency of the input signal u1(t) is equal to the center frequency ω0. The VCO then operates at its center frequency ω0. As we see, the phase error θe is zero. If θe is zero, the output signal ud of the PD must also be zero.
Consequently, the output signal of the loop filter uf will also be zero. This is the condition that permits the VCO to operate at its center frequency. If the phase error θe were not zero initially, the PD would develop a nonzero output signal ud. After some delay, the loop filter would also produce a finite signal uf.
This would cause the VCO to change its operating frequency in such a way that the phase error finally vanishes. Assume now that the frequency of the input signal is changed suddenly at time t0 by the amount Δω. As shown in Fig.2, the phase of the input signal then starts leading the phase of the output signal. A phase error is built up and increases with time.
The PD develops a signal ud(t), which also increases with time. With a delay given by the loop filter, uf(t) will also rise. This causes the VCO to increase its frequency. The phase error becomes smaller now, and after some settling time the VCO will oscillate at a frequency that is exactly the frequency of the input signal.
Depending on the type of loop filter used, the final phase error will have been reduced to zero or to a finite value. The VCO now operates at a frequency which is greater than its center frequency ω0 by an amount Δω. This will force the signal uf(t) to settle at a final INTRODUCTION TO PLLS Ronald E.2 Transient response of a PLL onto a step variation of the reference frequency. (b) Output signal u2(t) of the VCO.
(c) Signals and θe (t) as a function of time. (d) Angular frequency ω2 of the VCO and loop filter output signal uf(t) as a function of time. value of uf = Δω/K0. If the center frequency of the input signal is frequency-modulated by an arbitrary low-frequency signal, then the output signal of the loop filter is the demodulated signal.
The PLL can consequently be used as an FM detector. As we shall see later, it can be further applied as an AM or PM detector. One of the most intriguing capabilities of the PLL is its ability to suppress noise superimposed on its input signal. Let us suppose that the input signal of the PLL is buried in noise.
The PD tries to measure the phase error between input and output signals. The noise at the input causes the zero crossings of the input signal u1(t) to be advanced or delayed in a stochastic manner. This causes the PD output signal ud(t) to jitter around an average value. If the corner frequency of the loop filter is low enough, almost no noise will be noticeable in the signal uf(t), and the VCO will operate in such a way that the phase of the signal Printed from Digital Engineering Library @ McGraw-Hill (www.
Copyright ©2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTRODUCTION TO PLLS Ronald E.
Therefore, we can state that the PLL is able to detect a signal that is buried in noise. These simplified considerations have shown that the PLL is nothing but a servo system that controls the phase of the output signal u2(t). As shown in Fig.2, the PLL was always able to track the phase of the output signal to the phase of the reference signal; this system was locked at all times. This is not necessarily the case, however, because a larger frequency step applied to the input signal could cause the system to “unlock.” The control mechanism inherent in the PLL will then try to become locked again, but will the system indeed lock again? We shall deal with this problem in the following chapters.
Basically two kinds of problems must be considered: ■ The PLL is initially locked. Under what conditions will the PLL remain locked? ■ The PLL is initially unlocked. Under what conditions will the PLL become locked? If we try to answer these questions, we notice that different PLLs behave quite differently in this regard. We find there are some fundamentally different types of PLLs.
We will identify these various types in Sec. Historical Background The French engineer Henri de Bellescize is considered to be the inventor of the PLL. His very first implementation goes back to the year 1932. De Bellescize published his vacuum tube circuit in the French journal L’Onde Electrique.22 The actual schematic is given in Fig.3 and will probably look familiar only to a Figure 1.3 De Bellescize’s PLL circuit of the year 1932.
INTRODUCTION TO PLLS Ronald E. Best 6 few veterans who started their career with building ham radios from electron tubes. The tube on the right side of the figure in combination with the LC tank circuit forms an oscillator, and as we will recognize soon, it is even a voltage-controlled oscillator. The output signal of the oscillator [labeled H and corresponding to u2(t) in Fig.1a] is capacitively coupled to the grid of the tube on the left.
The reference signal [labeled S and corresponding to u1(t) in Fig.1a] is also fed via another capacitor to that grid. Because the grid voltage–anode current characteristic of electron tubes is nonlinear, the anode current contains a product term that is, a signal proportional to S · H or u1(t) · u2(t). As will be shown in Sec.1, the circuit around the left tube is a multiplier type phase detector. When the circuit is locked, this product is a measure of phase error—in other words, of the phase difference between the signals S and H.
The parallel RC circuit in the anode is the loop filter. The voltage drop across that filter is therefore proportional to the phase error. That voltage applied to the anode of the right tube is now the difference of the battery voltage (e) and the voltage drop across resistor R—that is, the phase error modulates the anode voltage of the oscillator. Because the frequency generated by the oscillator is an almost linear function of anode voltage, the oscillator is a VCO indeed! This brilliant invention was widely ignored by most engineers for about 20 years.
One of the first large-scale industrial applications of the PLL (back in the 1950s) was the color subcarrier recovery in color TV receivers. PLL-like circuits were also used in TV for line and frame synchronization. Somewhat later frequency synthesizers built from PLLs were used to generate a raster of frequencies in the local oscillator of FM receivers. The real breakthrough of the PLL came with desktop computers and with the PC, where PLLs are used for many types of data synchronization—for instance, reading digital data to and from floppy disks, hard disks, modems, tape drives, and the like.
One of the largest applications today is probably the mobile phone, where the PLL is used again for frequency synthesis. Classification of PLL Types The very first phase-locked loops (PLLs) were built from discrete components, including electron tubes and, later, discrete transistors. All these circuits were linear circuits. The first PLL ICs appeared around 1965 and were also purely analog devices.