Logarithmic amplifier

Using a non-linear feedback element with an op-amp (e.g. a pn-junction diode) produces startlingly different transfer functions. Logarithmic amplifiers serve as the basis for circuits such as analog multipliers studied in Section 4.6.

$\parbox{2.0in}{\raisebox{-1.25in}{\par \hbox{\hskip 0in \vbox to 1.25in{\includegraphics[height=1.25in]{FIGS/fig4.7.ps}\vfill}}}}$ $\parbox{3.0in}{% Carefully balance a 351 op-amp. Then wire the logarithmic amplifier (log amp), using a signal diode as the feedback element. }$

Measure $V_{\rm out}$ as a function of $V_{\rm in}$ and $R_{\rm in}$:

$V_{\rm in}$	$R_{\rm in}$	$I_{\rm in}$	$V_{\rm out}$
10.0mV	1M$\Omega$
10.0mV	100k$\Omega$
100.0mV	100k$\Omega$
1.0V	100k$\Omega$
10.0V	100k$\Omega$
10.0V	10k$\Omega$

Plot $\log I_{\rm in}$ vs. $V_{\rm out}$.

For all but very small forward bias voltages, the current through a diode varies exponentially with the applied voltage:

$$I \simeq I_i e^{eV/\eta kT}$$

where $\eta$ is an empirical parameter ($\sim 2$ for Si, 1 for Ge diodes), and $I_i$ is the intrinsic current at zero bias.

Apply circuit analysis (Simpson, Sec. 9.7) to your logarithmic amplifier and verify that the same relationship holds for the measured $I_{\rm in}$ and $V_{\rm out}$.

Fit your data to the above equation and determine the parameters $\eta$ and $I_i$ for your diode. Can you tell if this is a Si or a Ge diode?