method is more a function of the phase-lock loop than of the spectrum of the locking signal. Both types of synthesizers are widely used in modern electronic equipment for the generation of frequencies.

The synthesizer has two specifications which determine its usefulness in any application. One is range and the other is resolution. If the instrument has a range of 10 MHz and a resolution of 0.1 Hz, any frequency up to 10 MHz may be generated in steps of 0.1 Hz. The dials or buttons on the front of the instrument display the output frequency. These controls interconnect the various multipliers, mixers, etc. that are necessary to produce the output frequency.

As mentioned previously, the measurement and comparison of odd frequencies is simplified by the use of a frequency synthesizer. As an example, assume that one wishes to determine the frequency of a crystal oscillator. The output frequency may be measured with an electronic counter if one is available. Barring the availability of a counter, a Lissajous pattern may be displayed on an Oscilloscope with some reference frequency; but the pattern on the oscilloscope might br too complex for an accurate interpretation.

On the other hand, if a frequency synthesizer is available, a low-ratio Lissajous pattern may be obtained. Once the pattern is stabilized, the oscillator frequency may be read off the synthesizer dials. If the pattern is other than 1:1, the oscillator frequency may be computed by using the dial value and the pattern ratio. Similarly, phase or frequency stability of odd-frequency oscillators may be determined using a synthesizer in conjunction with phase detectors, oscilloscopes and chart recorders.

The difference frequency is now 10 times what it was initially. This process can be repeated, as shown in figure 4.41, until the noise gets too big. Four such decades seem to be about the limit. This is equivalent to multiplying two 1-MHz signals to 10 GHz. output of the phase error multiplier is now treated the same way as the input would have been, but the greatly amplified frequency difference simplifies and quickens the measurement process. An application of the phase error multiplier is discussed in the sections on Lissajous patterns (4.2.3A) and frequency comparators (4.6).

4.7.3 PHASE DETECTORS

Why use a phase detector? If two oscillators differed by 1 Hz and we compared their frequencies, we'd see a 1 Hz signal. But what if they only differed by 0.001 Hz? A chart record of their difference frequency or "beat note" would take 1000 seconds to trace a cycle. We soon find ourselves dealing with fractions of a cycle. A cycle has 360 electrical degrees. If we measure the phase of the two signals, then we can calibrate our chart or oscilloscope in terms of phase. This is simply a way of looking at fractional hertz--parts of a cycle.

For example: Consider two 1 MHz oscillators that differ in frequency by 1 part in 108. This means that it will take 100 seconds for a cycle of their beat note to occur. On a chart, we would see 1 cycle (equals 1 microsecond at 1 MHz) in 100 seconds. In 10 seconds, only one-tenth of a microsecond change will have occurred. These small changes of phase can be used to calibrate frequency differences. Of course, if the signals we are comparing differ by large amounts, the phase changes very rapidly.

There are two main types of phase detectors--the linear type and the nonlinear type. They are discussed separately in the following paragraphs. linear phase detector gives a linear output as the relative phase of the input signals change. They are often used with phase error multipliers and strip chart recorders. In a previous section, it was noted that linear phase detectors often cannot accept very high frequencies. This is a good reason for combining a phase detector with a phase error multiplier.

A block diagram of a typical linear phase detector is shown in figure 4.42a. Examination shows that the heart of this type of phase detector is a flip-flop. The action, or duty cycle, of the flip-flop determines the output voltage of the detector. An upper frequency limit for the detector occurs because of the flip-flop. If the shaped signals from the two inputs are less than 0.1 microsecond apart, for instance, the flip-flop might not react at all. So the dc voltage to the chart recorder will not be a true time record of the phase difference. In fact, what happens is that the sawtooth output shown in figure 4.42b begins to shrink. The waveform shifts up from zero and down from full-scale. This shrunken response could be calibrated, but it is much more convenient to use the phase detector at a frequency which it can

FLIP FLOP

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handle. This is where a phase error multiplier proves helpful. With the phase error multiplier, one is able to have very sensitive full-scale values of phase shift, say 0.01 microsecond, with inputs in the 100-kHz range.

DC

A nonlinear phase detector is essentially a phase discriminator like that used in FM receivers. The circuit diagram of a typical nonlinear detector is presented in figure 4.43. These detectors are available with cable connectors or in a printed circuit board package. They are very small.

Because the response characteristic is nonlinear, this phase detector is not used extensively with chart recorders. It has, however, one important characteristic--its output voltage can reverse polarity. In other

words, the output is a dc voltage proportional to the sine of the phase difference between the input signals, and the polarity of the output voltage depends on the lead or lag condition of the reference signal with respect to the unknown signal phase.

If the input signals are different in - frequency, the output voltage is periodic like a sine wave and there is no dc component. This ac output can be measured with a frequency counter, or it can be applied to an oscilloscope to form a Lissajous pattern.

There are commercial meters available to make phase measurements. Several of these can Compare signals at very high frequencies directly without the need to use phase error multipliers, etc. By using sampling techniques, comparisons up to 1000 MHz can be made. Read the equipment manuals carefully to note the linearity and accuracy of any instrument so that the results can be correctly understood.

4.7.4 FREQUENCY DIVIDERS

Frequency dividers are special forms of frequency synthesizers. They may be grouped into two general types: analog dividers that use regenerative feedback, and digital dividers that use binary arithmetic together with logic functions provided by bistable circuits.

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A. Analog or Regenerative Dividers

Figure 4.44 shows the block diagram of an analog or regenerative divider. Frequency f is supplied to the input of the divider. After amplification, this signal becomes one of two inputs to a mixer stage. The mixer output at f/10 is multiplied to 9f/10 and then fed back to the other input of the mixer.

The gain of the various stages is very critical. The regenerative divider is actually an oscillatory circuit though not selfoscillating. If the loop gain around the feedback circuit is too high, the unit will continue to divide even with no input. The output frequency in this condition is determined by tuning of the various circuits. If the circuit gain is too low, the unit will not function at all. The proper condition, as one would suppose, is where the unit divides under conditions of input signal but ceases operation when that input signal is removed.

Some commercial units have their gain set so that the dividers are not self-starting. This feature is designed to eliminate the problems of division with no input signal. Also, since the unit isn't self-starting, the output phase should not shift due to momentary loss of input or dc power. Once the divider stops, it remains stopped until a start button is pressed.

B. Digital Dividers

Simple bistable circuits such as flipflops may be combined to perform digital division. Any flip-flop, whether assembled from discrete components or integrated circuits, performs the same basic function. The output assumes two possible states, first one