1. Phase Lock Loop
EE174 – SJSU
Tan Nguyen

2. OBJECTIVES Introduction to Phase-locked loop (PLL)
Historical Background
Basic PLL System
Phase Detector (PD)
Voltage Controlled Oscillator (VCO)
Loop Filter (LF)

3. Introduction to Phase-locked loop (PLL)
PLL is a circuit that locks the phase of the output to the input.
PLL is a negative feedback control system where fout tracks fin and rising edges of input clock align to rising edges of output clock
PLL is a circuit synchronizing an output signal with a reference or input signal in frequency as well as in phase.
In the synchronized or “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 to reduce the phase error to a minimum so that the phase of the output signal is actually locked to the phase of the reference signal. This is why it is called a phase-locked loop.

4. How Are PLLs Used?

5. Historical Background
The French engineer Henri de Bellescize is considered to be the inventor of the PLL in 1932 using vacuum tubes.
First large-scale industrial applications of the PLL 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.
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.

6. Basic PLL System The basic PLL block diagram consists of:
A phase detector (PD) – type 1 and 2
A voltage-controlled oscillator (VCO)
A loop filter (LF)

7. The signals of interest within the PLL circuit:
■ The reference (or input) signal Φin(t)
■ The angular frequency ωin of the reference signal
■ The output signal Φout(t) of the VCO
■ The angular frequency ωout(t) of the output signal
■ The output signal ve(t) of the phase detector
■ The output signal Vcont(t) of the loop filter

8. Phase Detector
Compares the phase at each input and generates an error signal, ve(t), proportional to the phase difference between the two inputs. KD is the gain of the phase detector (V/rad).
ve(t) = KD [Φout(t) - Φin(t)]
The transfer characteristic of such a phase detector is shown below. Note that in many implementations, the characteristic may be shifted up in voltage (single supply/single ended).

9. Phase Detector
If the phase difference is π/2, then the average or integrated output from the XOR-type phase detector will be zero (or VDD/2 for single supply, digital XOR). The slope of the characteristic in either case is KD.

10. Example:
An analog multiplier or mixer can be used as a phase detector. Recall that the mixer takes the product of two inputs.
ve(t) = A(t)B(t)
where A(t) = A cos(ω0t + φA)
B(t) = B cos(ω0t + φB)
Then, A(t)B(t) = (AB/2)[ cos(2ω0t + φA + φB) + cos(φA - φB)]
Since the two inputs are at the same frequency when the loop is locked, we have one output at twice the input frequency and an output proportional to the cosine of the phase difference. The doubled frequency component must be removed by the low pass loop filter. Any phase difference then shows up as the control voltage to the VCO, a DC or slowly varying AC signal after filtering.

11. VCO
In PLL applications, the VCO is treated as a linear, time-invariant system. Excess phase of the VCO is the system output.
The VCO oscillates at an angular frequency, ωout. Its frequency is set to a nominal ω0 when the control voltage is zero. Frequency is assumed to be linearly proportional to the control voltage with a gain coefficient KO or KVCO (rad/s/v).
ωout = ω0 + KO Vcont
where ω0 is the center (angular) frequency of the VCO and KO is the VCO gain in rad /s V.

12. To obtain an arbitrary output frequency (within the VCO tuning range), a finite Vcont is required. Let’s define φout – φin = φο.
The XOR function produces an output pulse whenever there is a phase misalignment. Suppose that an output frequency ω1 is needed. From the upper right figure, we see that a control voltage V1 will be necessary to produce this output frequency. The phase detector can produce this V1 only by maintaining a phase offset φ0 at its input. In order to minimize the required phase offset or error, the PLL loop gain, KD KO, should be maximized, since

14. Loop Filter
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.
This network has a cutoff (3 dB) frequency ω1 = 1/RC. Thus, the filter transfer function is a simple lowpass:

15. Lock Range
Range of input signal frequencies over which the loop remains locked once it has captured the input signal. This can be limited either by the phase detector or the VCO frequency range.
Limited by PD: 0 < φ < π is the active range where lock can be maintained.
Ve-max = ± KD π/2
When the phase detector output voltage is applied through the loop filter to the VCO,
Δωout – max = ± KV π/2 = ωL (lock range)
where KV = KO KD, the product of the phase detector and VCO gains. This is the frequency range around the free running frequency that the loop can track.
Doesn’t depend on the loop filter
Does depend on DC loop gain

16. Limited by phase detector
Limited by the tuning range of the VCO: Oscillator tuning range is limited by capacitance ratios or current ratios and is finite. In many cases, the VCO can set the maximum lock range.

17. Capture range
Range of input frequencies around the VCO center frequency onto which the loop will lock when starting from an unlocked condition. Sometimes a frequency detector is added to the phase detector to assist in initial acquisition of lock.
Steady-state fosc(fi) characteristic of the basic PLL.

23. How PLL work

29. References: http://www.scribd.com/doc/237983665/PLL
Phase Locked Loops 6/e, 6th Edition by Roland Best