Analog multipliers are commonly available as integrated circuits (IC) and are rarely constructed from scratch due to their complexity. Multipliers commonly have 8 pinouts: X1, X2, Y1, Y2, W, Z, +VCC, -VCC. The common AD632 and MPY634 devices consist of one feedback line (W), two ground lines (X2, Y2), two supply lines (+VCC, -VCC) and one amplification factor line (Z); although the configuration might vary from model to model.
Multiplier in signal processing
Analog multipliers allow the engineer to perform amplitude modulation (AM) techniques; that is, the encoding of one signal as the shape of another signal of a different (higher) frequency. In such applications, the multipliers are used for tweaking the gain by controlling the voltage of one input, effectively turning the multiplier into a voltage-controlled amplifier.
While all multipliers are voltage-controlled amplifiers, not all voltage-controlled amplifiers are true analog multipliers.
When used in conjunction with low-pass filters (and integrators in specific), analog multipliers enable phase detection, and in turn, set the foundation for frequency modulation (FM) techniques; ergo, the encoding of one signal as the frequency variation of another signal of a different amplitude.
An important note for modulation setups is that the carrier signal will always be the one with higher frequency in AM circuits while the carrier signal in FM circuits will be the one with lower frequency [citation needed!].
Cascading a multiplier into a low-pass filter results in a phase detector. A phase detector detects the difference in phase between two input signals. When the phase is 90 degree, the output goes to 0 and this information can be used in self-tuning circuits.
Because the output signal can receive amplifications beyond what is suitable for tuning circuits, the output is often scaled down via a voltage divider circuit before it can be used as a control signal.
Beyond self-tuning circuits, phase detectors also find applications in phase-locked loops, demodulators, radars and servo controllers.
Specifically for the second order universal active filter circuit (conglomerate filter) from the last memo, adding a multiplier to the feedback loops of two integrators turns the entire circuit into a Voltage-Controlled Filter (or Voltage-Controlled Phase Generator).
The above circuit synchronizes the outputs of all four filters’ signals to be in-phase with each other and with the input signal, effectively eliminating race conditions and the likes.
In spite of the name, the circuit itself still requires manual adjustment of the voltage divider after the phase detector (before the control signal). The amplitude of the control signal appears to influence the effective frequency band of the tuner; ergo, the range of input frequencies that the tuner can “lock on”.
Only some amplitudes are usable in reality as a minute change to the control signal’s peak-to-peak voltage can cause this effective frequency band to shift to god-knows-where (possibly beyond the measurement limits of the oscilloscope or cut-off thresholds of op-amps in the circuit).
Voltage-controlled oscillator (FM generator)
Like the phase detector, a voltage-controlled oscillator is essential in phase-locked loop‘s construction. Cascading a multiplier into the (inverting) input of an integrator allows the saw-tooth pattern output to vary in frequency (frequency modulated). In voltage-controlled relaxation oscillators, the oscillation is then provided by the Schmitt Trigger via its positive feedback.
While not covered by this course, harmonic oscillators can be made voltage-controllable in a similar fashion. They are constructed from a feedback network with L-C elements / R-C elements/crystal which provide the oscillation, an amplifier to keep the signal leveled. Harmonic oscillators are linear and produce a sinusoidal waveform. Making a harmonic oscillator voltage-controllable (frequency-wise) is as simple as throwing a multiplier before the primary integrative component of its feedback network (the capacitor or op-amp integrator).
However, unlike non-linear relaxation oscillators, it can become difficult to maintain the sinusoidal shape of the output with a multiplier messing up the integrator’s input.
The circuit for a function generator and a voltage-controlled oscillator (FM generator) is basically the same. The difference lies in the input Vc of the multiplier.
A function generator converts AC input signal and modifies it using separate circuits to produce various waveforms.
On the other hand, an oscillator does NOT need AC input to work. It only needs DC supply and uses positive feedback to generate various waveforms.
Assuming the hypothesis in the first section of this memo holds true, placing a multiplier at the outputs (saw-tooth output of the integrator or square output of the Schmitt trigger) and outside of the feedback loops will allow amplitude modulation of the output signal and an external signal [citation needed!].
Bonus: Electronic noise in recursive analog circuits
The transient operation of an oscillator highlights a key difference between analog and digital electronics. In analog electronics, the electrical noise is never completely suppressed and it can be used in kick-starting oscillations.
“When the power supply to the amplifier is first switched on, electronic noise in the circuit provides a non-zero signal to get oscillations started. The noise travels around the loop and is amplified and filtered until very quickly it converges on a sine wave at a single frequency.” — Wikipedia.
This also explains the existence of conglomerate filters and similar recursive circuits that have no apparent starting or ending point.