A phase detector or phase comparator is a frequency mixer, analog multiplier or logic circuit that generates a signal which represents the difference in phase between two signal inputs. The phase detector is an essential element of the phase-locked loop (PLL). Detecting phase difference is important in other applications, such as motor control, radar and telecommunication systems, servo mechanisms, and demodulators.
Types Phase detectors for phase-locked loop circuits may be classified in two types. A Type I detector is designed to be driven by analog signals or square-wave digital signals and produces an output pulse at the difference frequency. The Type I detector always produces an output waveform, which must be filtered to control the phase-locked loop voltage-controlled oscillator (VCO). A type II detector is sensitive only to the relative timing of the edges of the input and reference pulses and produces a constant output proportional to phase difference when both signals are at the same frequency. This output will tend not to produce ripple in the control voltage of the VCO.
Analog phase detector The phase detector needs to compute the phase difference of its two input signals. Let α be the phase of the first input and β be the phase of the second. The actual input signals to the phase detector, however, are not α and β, but rather sinusoids such as sin(α) and cos(β). In general, computing the phase difference would involve computing the arcsine and arccosine of each normalized input (to get an ever-increasing phase) and doing a subtraction. Such an analog calculation is difficult. Fortunately, the calculation can be simplified by using some approximations. Assume that the phase differences will be small (much less than 1 radian, for example). The small-angle approximation for the sine function and the sine angle addition formula yield:
α − β ≈ sin ( α − β ) = sin α cos β − sin β cos α {\displaystyle \alpha -\beta \approx \sin(\alpha -\beta )=\sin \alpha \cos \beta -\sin \beta \cos \alpha }
The expression suggests a quadrature phase detector can be made by summing the outputs of two multipliers. The quadrature signals may be formed with phase shift networks. Two common implementations for multipliers are the double balanced diode mixer, diode ring and the four-quadrant multiplier, Gilbert cell. Instead of using two multipliers, a more common phase detector uses a single multiplier and a different trigonometric identity:
sin α cos β = sin ( α − β ) 2 + sin ( α + β ) 2 ≈ α − β 2 + sin ( α + β ) 2 {\displaystyle \sin \alpha \cos \beta ={\sin(\alpha -\beta ) \over 2}+{\sin(\alpha +\beta ) \over 2}\approx {\alpha -\beta \over 2}+{\sin(\alpha +\beta ) \over 2}}
The first term provides the desired phase difference. The second term is a sinusoid at twice the reference frequency, so it can be filtered out. In the case of general waveforms the phase detector output is described with the phase detector characteristic. A mixer-based detector (e.g., a Schottky diode-based double-balanced mixer) provides "the ultimate in phase noise floor performance" and "in system sensitivity." since it does not create finite pulse widths at the phase detector output. Another advantage of a mixer-based PD is its relative simplicity. Both the quadrature and simple multiplier phase detectors have an output that depends on the input amplitudes as well as the phase difference. In practice, the input amplitudes of input signals are normalized prior to input into the detector to remove the amplitude dependency.
Digital phase detector
A phase detector suitable for square wave signals can be made from an exclusive-OR (XOR) logic gate. When the two signals being compared are completely in-phase, the XOR gate's output will have a constant level of zero. When the two signals differ in phase by 1°, the XOR gate's output will be high for 1/180th of each cycle — the fraction of a cycle during which the two signals differ in value. When the signals differ by 180° — that is, one signal is high when the other is low, and vice versa — the XOR gate's output remains high throughout each cycle. This phase detector requires inputs that are symmetrical square waves, or nearly so. The XOR detector compares well to the analog mixer in that it locks near a 90° phase difference and has a pulse wave output at twice the reference frequency. The output changes duty cycle in proportion to the phase difference. Applying the XOR gate's output to a low-pass filter results in an analog voltage that is proportional to the phase difference between the two signals. The remainder of its characteristics are very similar to the analog mixer for capture range, lock time, reference spurious and low-pass filter requirements. Digital phase detectors can also be based on a sample and hold circuit, a charge pump, or a logic circuit consisting of flip-flops. When a phase detector based on logic gates is used in a PLL, it can quickly force the VCO to synchronize with an input signal, even when the frequency of the input signal differs substantially from the initial frequency of the VCO. Such phase detectors also have other desirable properties, such as better accuracy when there are only small phase differences between the two signals being compared and superior pull-in range.
… excerpt ends here. Continue reading the full article.
