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7. William E. Soyce and Richard C. DiPrima. Elementary Differential Equations and
Boundary Valued Problems. New York: John Wiley & Sons, 1977.
Chapter 15

Sampling Theory and Sampling Mixers

After showing a whole host of equations from the last two chapters, I will try a
graphical approach to the subject of sampling. However, some equations will have
to be shown.
The objectives of this chapter will be the following:

1. To show what sampling is in terms of multiplying a signal
2. To show how sampling can be used for mixing, such as generating an
intermediate-frequency (IF) signal
3. To investigate switch-mode mixers

Sampling Signals as a Form of Muliplication or Mixing

A typical sampling circuit is a switch that is turned on for a short duration that
momentarily passes an input signal to the output terminal of the switch (Figure
1S-lA). In Figure 1S-lA, an input signal such as a direct-current (DC) signal or a
sine-wave signal is "gated" through for a short duration via a sampling signal. Thus
this sampling-switch circuit is sometimes called a chopper modulator, which is a
single balanced mixer circuit. A single balanced mixer means that only one of the
input signals is nulled or removed from the output, but the other input signal

appears at the output. In Figure 1S-lA, the sampling signal that drives the control
signal to the switch does not appear at the output when the input signal is zero.
However, the input signal does leak through to the output terminal. And if the input
signal is a DC signal, the output of the sampling switch is just a series of pulses
where the height or amplitude of each pulse is proportional to the input signal.