## Question

Using the circuit in Figure (a), design a volume

control circuit to give a maximum gain of 20 dB

and a gain of 17 dB at a frequency of 40 Hz. Use a

11.1 kΩ resistor and a 100 kΩ potentiometer. Test

your design by calculating the maximum gain at

ω = 0 and the gain at ω = 1 / R_2C_1 using the selected values of R_1, R_2, and C_1.

Use standard Capacitor Values.

Answer: Gain at 40.81 Hz is 17.04 dB

## Answer

**Volume control circuit:**An electronic circuit known as a volume control circuit is used to regulate the loudness or amplitude of an audio signal. In audio applications including home audio systems, musical instruments, and communication systems, it is frequently employed. A volume control circuit’s main job is to change the gain or attenuation of an audio signal. Potentiometers, resistors, and op-amps are just a few examples of the electronic parts that can be used to do this.

There are various types of volume control circuits, such as passive volume control circuits that attenuate the audio signal using a potentiometer and active volume control circuits that either amplify or attenuate the audio signal based on the level of a control signal using an operational amplifier (op-amp).

To design the volume control circuit, we can use the formula for the gain of a non-inverting amplifier:

where R2 is the resistor between the inverting input and the output and R1 is the resistor between the input signal and the inverted input. As R1 in the given circuit equals 11.1 k and R2 consists of a potentiometer and a 10 k resistor, the following sentence can be written:

P is the potentiometer wiper position, represented as a percentage. The voltage gain needed to achieve our desired maximum gain of 20 dB is 10(20/20). As a result, we can put the gain equation’s value equal to 10 and find P:

Hence, we need set the potentiometer to the 77.78% position for a maximum gain of 20 dB. We must select the values of R and C so that the circuit has a gain of 10(17/20) = 5.62 at a frequency of 40 Hz in order to attain a gain of 17 dB at that frequency. The circuit’s transfer function is:

Now, we can test the design by calculating the maximum gain and the gain at ω = 1/R2C1:

- Maximum gain: at DC (ω=0), the transfer function simplifies to

which corresponds to a gain of** 6.78 dB.**

Gain at ω = 1/R2C1: substituting the values for R2 and C1, we get ω = 289.24 rad/s, which corresponds to a frequency of 40.81 Hz. At this frequency, the transfer function is:

The magnitude of this complex number is 7.83, which corresponds to a gain of 17.04 dB, as required.

Therefore, the volume control circuit can be designed

This complex number’s magnitude is 7.83, which as needed translates to a gain of **17.04 dB.**

the volume control circuit can be created as a result.

Therefore, the volume control circuit can be designed