A square root amplifier is a circuit that takes a signal as input and produces an output that is the square root of the input signal. This type of amplifier is often used in applications where the amplitude of a signal needs to be compressed, such as in audio processing or automatic gain control (AGC) circuits.
Here's how to design a simple square root amplifier using operational amplifiers (op-amps):
1. Basic Principle:
The basic principle behind a square root amplifier is to use a voltage-controlled amplifier (VCA) whose gain is proportional to the square root of the input control voltage. This can be achieved by using a logarithmic amplifier or an exponential amplifier.
2. Logarithmic Amplifier:
One approach is to use an op-amp in a logarithmic configuration. The logarithmic relationship between the input voltage (Vin) and the output voltage (Vout) can be achieved using a diode and a resistor. The logarithmic amplifier's output is proportional to the logarithm of the input voltage.
3. Exponential Amplifier:
To obtain a square root relationship, we can use another op-amp as an exponential amplifier. This can be done by connecting a capacitor and a resistor in the feedback path of the op-amp. The output of the exponential amplifier is proportional to the exponential of the input voltage.
4. Combining Log and Exp Amplifiers:
The final square root amplifier can be obtained by cascading the logarithmic amplifier and the exponential amplifier. The logarithmic amplifier's output is fed into the exponential amplifier's input to generate an output that is proportional to the square root of the input voltage.
5. Circuit Topology:
The following is a simplified circuit diagram of a square root amplifier using op-amps:
[Image of square root amplifier circuit diagram]
In this circuit, the op-amp U1 is configured as a logarithmic amplifier using the diode D1 and resistor R1. The output of U1 is then connected to the input of U2, which is configured as an exponential amplifier using the capacitor C1 and resistor R2.
6. Component Selection:
The component values (diode, resistors, and capacitor) should be chosen based on the desired gain and frequency response of the square root amplifier. Proper biasing of the op-amps may also be required.
7. Output Adjustment:
The output of the square root amplifier can be adjusted by varying the gain of the exponential amplifier (U2). This can be done by changing the value of the feedback resistor R2.
8. Practical Considerations:
In practical implementations, factors like temperature stability, noise, and bandwidth limitations need to be taken into account. Additional circuitry may be required to address these concerns.
By following this approach, you can design a square root amplifier using op-amps to achieve a nonlinear relationship between the input and output signals.