Phase Detectors. Recall that one of the three fundamental elements of a PLL is the phase detector: ref

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1 10/22/2010 Phase Detectors.doc 1/7 Phase Detectors Recall that one of the three fundamental elements of a PLL is the phase detector: ( t ) + phase detector ( t) = f ( t ) ( t ) ( ) ( t ) The phase detector must create a oltage signal ( t ) (the error oltage) that proides and indication of the difference between the two fundamental phase functions ( t ) and ( t ). Recall that when the loop is locked, these two phase functions are ideally equal to each other, so that their difference is zero (i.e., ( t ) ( t ) = 0 when locked). Ideally, the relationship between phase difference = and the error oltage is simple and straight forward: = ( ) =

2 10/22/2010 Phase Detectors.doc 2/7 In other words, the error oltage is directly proportional to the phase difference, with a proportionality constant of. It should be eident to you that has units of olts/radian! From the expression aboe, it appears that the transfer function between the phase error and the error oltage can be plotted as: The reality howeer, is much different. Remember, the phase detector only indirectly knows the phase functions ( t ) and ( t ). The inputs to the phase detector will of course be a oltage signal of some type (e.g., ( t ) = ( t ). cos[ ]

3 10/22/2010 Phase Detectors.doc 3/7 The problem here of course is the phase ambiguity : ( t ) = ( t ) + π = ( t ) + π = ( t) + n π cos cos 2 cos 4 cos 2 Een though we know that: ( t ) ( t ) + 2π ( t ) + 4π ( t) + n2π As a result, we find that real phase detectors exhibit transfer functions more like: 2π π π 2π or: 2π π π 2π or:

4 10/22/2010 Phase Detectors.doc 4/7 2π π π 2π The first of these is known as a π -phase detector, the second a 2π -phase detector, and the last a 4π -phase detector. Q: ut how are phase detectors made? How do they operate? A: The performance and operation of a phase detector depends completely on how the phase function manifests itself in the form of oltage signal. In other words, a phase detector for the signals: ( t ) = cos ( t ) and ( ) cos ( ) t t = must be ery different from the phase detector where:

5 10/22/2010 Phase Detectors.doc 5/7 ( t) = rect ( t ) and ( ) ( ) t rect t = and likewise different still from the phase detector where: ( t) = pulse ( t ) and ( ) ( ) t pulse t =. We will consider phase detectors for the two digital signals of the form ( t) = rect ( t ) and ( t) = pulse ( t ). [ ] [ ] The first thing to know about phase detectors for digital signals is that they are actually delay detectors! To see why, consider two sinusoidal signals whose phase difference is a simple constant c. In other words: A( t) ( ) t = C Note that the two sinusoidal signals must hae identical frequency (do you see why?), and are dissimilar only because of a phase shift c :

6 10/22/2010 Phase Detectors.doc 6/7 Note that this phase shift is really just a time shift of one signal with respect to the other. Note also that the alue of oltage A( t ) at time t = t1 is the same alue as oltage ( t ) at time t = t2. The signal ( t ) is thus a delayed ersion of signal A( t ): Where delay τ is clearly: ( t) = ( t τ ) A τ = t2 t1 Now, the two signals hae the same period T (after all, they hae the same frequency), and so the ratio τ T proides a measure of the delay in terms of one period (e.g. if τ T = 025., then the signal is delayed a quarter of one period). Remember though, that one period likewise represents the time required for the phase function to change by a alue of 2π radians! I.E.,: ( t + T ) ( t ) = 2π Thus, a delay of 025. T corresponds to a phase shift of π = π 2! ( ) More generally, we can conclude that if: ( t) = ( t τ ) A

7 10/22/2010 Phase Detectors.doc 7/7 we can conclude that: ( ) ( ) τ t t = π 2 A T The ratio τ T proides a direct measure of the phase difference! It is this alue (τ T ) that most digital signal phase detectors attempt to proide us.