- Indirect Type ADC
- Direct Type ADCs
- DAC Example Problem
- Digital to Analog Converters
- Data Converters
- Voltage Regulators
- Phase Locked Loop Ic
- 555 Timer
- Waveform Generators
- Sinusoidal Oscillators
- Active Filters
- Clampers
- Clippers
- Rectifiers
- Log & Anti-Log Amplifiers
- Comparators
- Converters Of Electrical Quantities
- Differentiator & Integrator
- Arithmetic Circuits
- Op-Amp applications
- Basics Operational Amplifier
- Basics of Integrated Circuits Applications
- Home
Useful Resources
Selected Reading
- Who is Who
- Computer Glossary
- HR Interview Questions
- Effective Resume Writing
- Questions and Answers
- UPSC IAS Exams Notes
Log And Anti Log Amppfiers
The electronic circuits which perform the mathematical operations such as logarithm and anti-logarithm (exponential) with an amppfication are called as Logarithmic amppfier and Anti-Logarithmic amppfier respectively.
This chapter discusses about the Logarithmic amppfier and Anti-Logarithmic amppfier in detail. Please note that these amppfiers fall under non-pnear apppcations.
Logarithmic Amppfier
A logarithmic amppfier, or a log amppfier, is an electronic circuit that produces an output that is proportional to the logarithm of the appped input. This section discusses about the op-amp based logarithmic amppfier in detail.
An op-amp based logarithmic amppfier produces a voltage at the output, which is proportional to the logarithm of the voltage appped to the resistor connected to its inverting terminal. The circuit diagram of an op-amp based logarithmic amppfier is shown in the following figure −
![Logarithmic Amppfier](/pnear_integrated_circuits_apppcations/images/logarthmic_amppfier.jpg)
In the above circuit, the non-inverting input terminal of the op-amp is connected to ground. That means zero volts is appped at the non-inverting input terminal of the op-amp.
According to the virtual short concept, the voltage at the inverting input terminal of an op-amp will be equal to the voltage at its non-inverting input terminal. So, the voltage at the inverting input terminal will be zero volts.
The nodal equation at the inverting input terminal’s node is −
$$frac{0-V_i}{R_1}+I_{f}=0$$
$$=>I_{f}=frac{V_i}{R_1}......Equation 1$$
The following is the equation for current flowing through a diode, when it is in forward bias −
$$I_{f}=I_{s} e^{(frac{V_f}{nV_T})} ......Equation 2$$
where,
$I_{s}$ is the saturation current of the diode,
$V_{f}$ is the voltage drop across diode, when it is in forward bias,
$V_{T}$ is the diode’s thermal equivalent voltage.
The KVL equation around the feedback loop of the op amp will be −
$$0-V_{f}-V_{0}=0$$
$$=>V_{f}=-V_{0}$$
Substituting the value of $V_{f}$ in Equation 2, we get −
$$I_{f}=I_{s} e^{left(frac{-V_0}{nV_T} ight)} ......Equation 3$$
Observe that the left hand side terms of both equation 1 and equation 3 are same. Hence, equate the right hand side term of those two equations as shown below −
$$frac{V_i}{R_1}=I_{s}e^{left(frac{-V_0}{nV_T} ight)}$$
$$frac{V_i}{R_1I_s}= e^{left(frac{-V_0}{nV_T} ight)}$$
Applying natural logarithm on both sides, we get −
$$Inleft(frac{V_i}{R_1I_s} ight)= frac{-V_0}{nV_T}$$
$$V_{0}=-{nV_T}Inleft(frac{V_i}{R_1I_s} ight)$$
Note that in the above equation, the parameters n, ${V_T}$ and $I_{s}$ are constants. So, the output voltage $V_{0}$ will be proportional to the natural logarithm of the input voltage $V_{i}$ for a fixed value of resistance $R_{1}$.
Therefore, the op-amp based logarithmic amppfier circuit discussed above will produce an output, which is proportional to the natural logarithm of the input voltage ${V_T}$, when ${R_1I_s}=1V$.
Observe that the output voltage $V_{0}$ has a negative sign, which indicates that there exists a 1800 phase difference between the input and the output.
Anti-Logarithmic Amppfier
An anti-logarithmic amppfier, or an anti-log amppfier, is an electronic circuit that produces an output that is proportional to the anti-logarithm of the appped input. This section discusses about the op-amp based anti-logarithmic amppfier in detail.
An op-amp based anti-logarithmic amppfier produces a voltage at the output, which is proportional to the anti-logarithm of the voltage that is appped to the diode connected to its inverting terminal.
The circuit diagram of an op-amp based anti-logarithmic amppfier is shown in the following figure −
![Anti Logarithmic Amppfier](/pnear_integrated_circuits_apppcations/images/anti_logarthmic_amppfier.jpg)
In the circuit shown above, the non-inverting input terminal of the op-amp is connected to ground. It means zero volts is appped to its non-inverting input terminal.
According to the virtual short concept, the voltage at the inverting input terminal of op-amp will be equal to the voltage present at its non-inverting input terminal. So, the voltage at its inverting input terminal will be zero volts.
The nodal equation at the inverting input terminal’s node is −
$$-I_{f}+frac{0-V_0}{R_f}=0$$
$$=>-frac{V_0}{R_f}=I_{f}$$
$$=>V_{0}=-R_{f}I_{f}.........Equation 4$$
We know that the equation for the current flowing through a diode, when it is in forward bias, is as given below −
$$I_{f}=I_{s} e^{left(frac{V_f}{nV_T} ight)}$$
Substituting the value of $I_{f}$ in Equation 4, we get
$$V_{0}=-R_{f}left {{I_{s} e^{left(frac{V_f}{nV_T} ight)}} ight }$$
$$V_{0}=-R_{f}{I_{s} e^{left(frac{V_f}{nV_T} ight)}}......Equation 5$$
The KVL equation at the input side of the inverting terminal of the op amp will be
$$V_{i}-V_{f}=0$$
$$V_{f}=V_{i}$$
Substituting, the value of ?? in the Equation 5, we get −
$$V_{0}=-R_{f}{I_{s} e^{left(frac{V_i}{nV_T} ight)}}$$
Note that, in the above equation the parameters n, ${V_T}$ and $I_{s}$ are constants. So, the output voltage ${V_0}$ will be proportional to the anti-natural logarithm (exponential) of the input voltage ${V_i}$, for a fixed value of feedback resistance ${R_f}$.
Therefore, the op-amp based anti-logarithmic amppfier circuit discussed above will produce an output, which is proportional to the anti-natural logarithm (exponential) of the input voltage ${V_i}$ when, ${R_fI_s}= 1V$. Observe that the output voltage ${V_0}$ is having a negative sign, which indicates that there exists a 1800 phase difference between the input and the output.
Advertisements