UNIT-4
Lecture-1
Log, –Anti Log Amplifiers, Analog Multipliers
and their applications
Nonlinear Op-Amp Circuits
• Most typical applications require op amp and its components
to act linearly
– I-V characteristics of passive devices such as resistors,
capacitors should be described by linear equation (Ohm’s
Law)
– For op amp, linear operation means input and output
voltages are related by a constant proportionality (Av
should be constant)
• Some application require op amps to behave in nonlinear
manner (logarithmic and antilogarithmic amplifiers)
Logarithmic Amplifier
• Output voltage is proportional to the logarithm of input voltage
• A device that behaves nonlinearly (logarithmically) should be used to
control gain of op amp
– Semiconductor diode
• Forward transfer characteristics of silicon diodes are closely described
by Shockley’s equation
IF = Ise(VF/ηVT)
– Is is diode saturation (leakage) current
– e is base of natural logarithms (e = 2.71828)
– VF is forward voltage drop across diode
– VT is thermal equivalent voltage for diode (26 mV at 20°C)
– η is emission coefficient or ideality factor (2 for currents of same
magnitude as IS to 1 for higher values of IF)
Basic Log Amp operation
D1
• I1 = Vin/R1
R1 IF • IF = - I1
-
I1
• IF = - Vin/R1
Vo
Vin + • V0= -VF = -ηVT ln(IF/IS)
RL
• V0= -ηVT ln[Vin/(R1IS)]
• rD = 26 mV / IF
• IF < 1 mA (log amps)
• At higher current levels (IF > 1 mA) diodes begin to behave
somewhat linearly
Logarithmic Amplifier
• Linear graph: voltage gain is very high for low input voltages and
very low for high input voltages
• Semilogarithmic graph: straight line proves logarithmic nature of
amplifier’s transfer characteristic
• Transfer characteristics of log amps are usually expressed in terms of
slope of V0 versus Vin plot in milivolts per decode
• η affects slope of transfer curve; IS determines the y intercept
Operational Amplifiers and Linear
Integrated Circuits: Theory and Applications
Additional Log Amp Variations
Q1
IC IE
R1 IC = IESe (VBE/VT)
-
I1
Vo = VBE - IES is emitter
Vin saturation current
+
RL
- VBE is drop across
base-emitter junction
• Often a transistor is used as logging element in log amp (transdiode
configuration)
• Transistor logging elements allow operation of log amp over wider current
ranges (greater dynamic range)
Antilogarithmic Amplifier
• Output of an antilog amp is proportional to the antilog of the
input voltage
• with diode logging element
– V0 = -RFISe(Vin/VT)
• With transdiode logging element
– V0 = -RFIESe(Vin/VT)
• As with log amp, it is necessary to know saturation currents
and to tightly control junction temperature
Antilogarithmic Amplifier
RF
IE Q1 I1 IF
-
Vo
Vi +
n RL
R1
(α = 1) I1 = IC = IE
D1 IF
-
I1
V + Vo
i RL
n
Logarithmic Amplifier Applications
• Logarithmic amplifiers are used in several areas
– Log and antilog amps to form analog multipliers
– Analog signal processing
• Analog Multipliers
– ln xy = ln x + ln y
– ln (x/y) = ln x – ln y
D1
Analog Multipliers
R R
- R R
Vx + D3
-
- Vo
D2 +
+
R RL
- R
+
Vy
One-quadrant multiplier: inputs must
both be of same polarity
Analog Multipliers
Four quadrants
of operation
General symbol
Two-quadrant multiplier: one input should have positive voltages, other
input could have positive or negative voltages
Four-quadrant multiplier: any combinations of polarities on their inputs
Analog Multipliers
Implementation of mathematical operations
Square root Circuit
Squaring Circuit
Signal Processing
• Many transducers produce output voltages that vary nonlinearly with
physical quantity being measured (thermistor)
• Often It is desirable to linearize outputs of such devices; logarithmic amps
and analog multipliers can be used for such purposes
• Linearization of a signal using circuit with complementary transfer
characteristics
