Analog multiplier

Combining log amps with adding amps allows one to build analog multipliers and other components of analog computers (for a review, see Faissler, Ch. 30). Here we examine the transfer functions of one such commercial device, AD534.

$\parbox{2.0in}{\raisebox{-1.25in}{\par \hbox{\hskip 0in \vbox to 1.25in{\includegraphics[height=1.25in]{FIGS/fig4.8.ps}\vfill}}}}$ $\parbox{3.0in}{% \vspace{0.25in} AD534 is internally trimmed and does not require external trimmer potentiometers. Its pinout is shown on the left. }$

For multiplication, use the fixed $+10$V supply from the job board as the $X_1$ input and use several fixed voltages from the reference job board as the $Y_1$ input ($+10$V, $-10$V, $-1$V, $+1$V). Connect the $Z_1$ input to the output. Connect the $X_2$, $Y_2$, and $Z_2$ inputs to common. Test the multiplier in all four quadrants by applying voltages of both polarities in the range of $\pm 10$V. The multiplier transfer function should be $\mbox{$V_{\rm out}$}= (V_x\times V_y)/10$. Include in your data set $(X_1,Y_1)$ values of $(+10,0)$, $(0,0)$, and $(0,+10)$.

Offsets modify the multiplier equation:

$$\mbox{$V_{\rm out}$}= \mbox{$V_{\rm out}$}^{(0)} + 0.1 \times... ...[ V_x-V_x^{(0)} \right] \times \left[ V_y - V_y^{(0)} \right]$$

where $V_x^{(0)}$, $V_y^{(0)}$, and $\mbox{$V_{\rm out}$}^{(0)}$ are the $X$, $Y$, and output offsets, respectively. Use your data to evaluate each of the offsets. Explain how magnitude of offset-induced errors changes with $X$ and $Y$ input levels.

To obtain an output voltage proportional to the square of an input voltage, connect both $X_1$ and $Y_1$ inputs to the same voltage source and the $X_2$ and $Y_2$ inputs to common. The $Z_1$ input remains connected to the output. Test the circuit over a $\pm 10$V range of voltages and compare to the expected $\mbox{$V_{\rm out}$}= 0.1 \times \mbox{$V_{\rm in}$}^{2}$.

The ``squared voltage''output can be plotted against the input with the $xy$-mode of the oscilloscope. Substitute the output of the FG set in the sine wave mode as the source in the squaring circuit wired above. Connect the multiplier output to the vertical scope input and the FG output to the horizontal. Use a $10$Hz sine wave signal. Sketch the resulting display.

Now use the dual-trace mode to observe the waveforms of the input and output signals. Sketch a representative display and indicate the position of OV for each waveform.

Explain the relationship of the frequencies and the DC components of the input and output waveforms.