This document discusses the design and implementation of an operational amplifier (op-amp) as a logarithmic amplifier. It begins by defining the transfer function of a logarithmic amplifier and describing how op-amps can be used to approximate this function. Next, it discusses the classic diode feedback configuration and provides the key equations. Applications of logarithmic amplifiers are then outlined. The document concludes by presenting the circuit diagram and output waveform of a logarithmic amplifier implemented with a trans-diode configuration in MATLAB.

1. ELECTRONIC CIRCUITS AND
SIMULATION LAB MINI-PROJECT
15EEE287
OPAMP AS LOGARITHMIC AMPLIFIER
PREPARED BY:
S M SHREYAS

2. INTRODUCTION
A log amplifier is an amplifier for which the output voltage Vout is K times
the natural log of the input voltage Vin. This can be expressed as
Vout=k ln((Vin)/(Vref))
where Vref is the normalization constant in volts and K is the scale factor.
The logarithm amplifier gives an output voltage which is proportional to the
logarithm of applied input voltage To design a logarithm amplifier circuit, high
performance op-amps likeLM1458, LM771, LM714 are commonly used and a
compensated logarithm amplifier may include more than one. The term log
amp, as it is generally understood in communications technology, refers to a
device which calculates the log of an input signal's envelope. First of all, no
amplifier can produce a logarithmic transfer function over a dynamic range
which includes an input signal level of zero, since log 0 = -∞. All logarithmic
amplifiers must therefore specify a signal range over which they will "log".
The classic log amp discussed in most introductory texts exploits the I-V
characteristics of a diode junction, and consists of a diode feedback on an
inverting operational amplifier. This approach works well (over a dynamic
range of >4 decades) at low speeds (less than 1 MHz), if the circuit is properly
temperature-compensated. At higher speeds the performance is woeful, and
other schemes⁽¹⁾ to approximate a logarithmic transfer are used.

3. LOGARITHMIC AMPLIFIER APPLICATIONS
Logarithmic amplifiers are used in many ways, such as:
1. To perform mathematical operations like multiplication, division and
exponentiation.
2. To calculate the dB value of a given quantity.
3. As a True RMS converter.
TRANS-DIODE CONFIGURATION:
A necessary condition for successful operation of a log amplifier is that the
input voltage, Vin, is always positive. This may be ensured by using
a rectifier and filter to condition the input signal before applying it to the
log amp input. As Vin is positive, Voutis obliged to be negative (since the op
amp is in the inverting configuration) and is large enough to forward
bias the emitter-base junction of the BJT keeping it in the active mode of
operation. Can be expressed as
V be=V out
V be= V t*ln((Ic)/(Is))
where V s is the saturation current of the emitter-base diode and V t is
the thermal voltage. Due to the virtual ground at the op amp differential
input,
I c=(Vc/R)
Vout= -Vtln((Vin)/(Vso*R))
The output voltage is expressed as the natural log of the input voltage. Both
the saturation current (Is) and the thermal voltage (Vt) are temperature
dependent, hence, temperature compensating circuits may be required.

4. CIRCUIT DIAGRAM:

5. OUTPUT WAVFORM:
MATLAB CODE:
Is= 10e-15
Vin= (0.001:0.001:10);
R=1e3
Vt=0.0259
Plot (Vin, Vt*log(Vin/(R*Is)))
Xlabel(‘Vin’)
Ylabel(‘Vout_inverted’)
Title(‘log amp’)
Grid on

6. OUTPUT WAVEFORM:

7. CONCLUSION:
In summary, DC log amp ICs have evolved into small, easy-to-use, cost-
effective circuits nicely suited for certain analog designs. The logarithmic
function conveniently compresses wide dynamic range signals and linearizes
sensors with (semi-)exponential transfer functions. Calibration procedures
can enhance log-amp performance, but are not necessary in all applications.