section - Bitsavers

PHASE LOCKED LOOP APPLICATIONSIf n =F 0 in the first term, the loop can lock when wi =(2n + 1) w o ' giving the dc phase detector component2AdVi7T(2n + 1)cos ()ishowing that the loop can lock to odd harmonics of thecenter frequency. The (2n + 1) term in the denominatorshows that the phase detector output is lower for harmoniclock, which explains why the lock range decreases ashigher and higher odd harmonics are used to achieve lock.Note also that the phase detector output during lock is(assuming Ad is constant) also a function of the inputamplitude Vi. Thus, for a given dc phase detector outputVd, an input amplitude decrease must be accompanied bya phase change. Since the loop can remain locked only for0i between 0 and 180 0 , the lower Vi becomes, the morereduced is the lock range.Going to the second term, we note that during lock thelowest possible frequency is Wo + wi = 2wi. A sumfrequency component is always present at the phasedetector output. This component is usually greatlyattenuated by the low pass filter capacitor connected tothe phase detector output. However, when rapid trackingis required (as with high-speed FM detection or FSKfrequencyshift keying), the requirement for a relativelyhigh frequency cutoff in the low pass filter may leave thiscomponent unattenuated to the extent that it interfereswith detection. At the very least, additional filtering maybe required to remove this component. Componentscaused by n -=1= 0 in the second term are both attenuated andof much higher frequency, so they may be neglected.Suppose that we have other frequencies represented byVk present. What is their effect for Vk -=1= O?The third term shows that Vk introduces another differencefrequency component. Obviously, if wk is close to wi, itcan interfere with the locking process since it may forma beat frequency of the same magnitude as the desiredlocking beat frequency. Suppose lock has been achieved,however, so that Wo = wi. In order for lock to bemaintained, the average phase detector output must beconstant. If Wo = wk is relatively low in frequency, thephase ()i must change to compensate for this beatfrequency. Broadly speaking, any signal in addition to thesignal to which the loop is locked causes a phase variation.Usually this is negligible since wk is often far removedfrom wi. However, it has been stated that the phase() i can move on Iy between 0 and 180 0 . Su ppose the phaselimit has been reached and Vk appears. Since it cannot becompensated for, it will drive the loop out of lock. Thisexplains vvhy extraneous signals can result in a decrease inthe lock : ange. If Vk is assumed to be an instantaneousnoise c:· )onent, the same effect occurs. When the fullswing of the loop is being utilized, noise will decrease thelock or tracking range. We can reduce this effect bydecreasing the cutoff frequency of the low pass filter sothat the Wo - wk is attenuated to a greater extent, whichillustrates that noise immunity and out-band frequencyrejection is improved (at the expense of capture range sinceWo - wi is likewise attenuated) when the low pass filtercapacitor is large.The third term can have a dc component when wk is anodd harmonic of the locked frequency so that (2n + 1)(w o - wi) is zero and ()k makes its appearance. This willhave an effect on 0i which will change the 0i versusfrequency wi. This is most noticeable when the waveformof the incoming signal is, for example, a square wave. The()k term will combine with the ()i term so that the phase isa linear function of input frequency. Other waveforms willgive different phase versus frequency functions. When theinput amplitude Vi is large and the loop gain is large, thephase will be close to 90 0 throughout the range of veoswing, so this effect is often unnoticed.The fourth term is of little consequence except that if wkapproaches zero, the phase detector output will have acomponent at the locked frequency Wo at the output. Forexample, a dc offset at the input differential stage willappear as a square wave of fundamental Wo at the phasedetector output. This is usually small and well attenuatedby the low pass filter. Since many out-band signals or noisecomponents may be present, many V k terms may becombining to influence locking and phase during lock.Fortunately, we need only worry about those close to thelocked frequency.The quadrature phase detector action is exactly the sameexcept that its output is proportional to the sine of thephase angle. When the phase () i is 90 0 , the quadraturephase detector output is then at its maximum, whichexplains why it makes a useful lock or amplitude detector.The output of the quadrature phase detector is given by:where Vi is the constant or modulated AM signal and()i ~ 90 0 in most cases so that sine ()i = 1 and7TThis is the demodulation principle of the autodyne receiverand the basis for the 567 tone decoder operation.17