GAIN and IMPEDANCE of a complex Circuit

In summary, The conversation is about calculating the gain of a circuit and understanding the notation used. The attachment in a word file shows the circuit and Z is the generic term for effective resistance. The formula for Z is given as [jwL +(R/jwC)]/(R+1/jwC), and the user is asking for confirmation if this is correct. The gain is supposed to output Voltage/input voltage, and the user is confused if Z is the output voltage and jwL + Z is the input voltage. Another user, ehild, clarifies that Z is impedance and not voltage, and the gain is the magnitude of Zab/Z.
  • #1
JamesJames
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0
I am supposed to calculate the gain of the circuit given in the attachment. I have attached it in a word file.

Z is the generic term for the effective resistance. I get that Z is

Z = [jwL +(R/jwC)]/(R+1/jwC)

Can someone tell me if this is correct?

Also, now for the gain, it is supposed to output Voltage/input voltage. For this example, is Z the output voltage and jwL + Z the input voltage ?

James
 

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  • #2
To view the attachment, just click on it and say open.

Any help would be really useful.

Thanks, James
 
  • #3
Zab=(R/jwC)/(R+1/jwC),

Z = [jwL +(R/jwC)/(R+1/jwC)]



Also, now for the gain, it is supposed to output Voltage/input voltage. For this example, is Z the output voltage and jwL + Z the input voltage ?

GRRRRRR. Z is impedance, not voltage. The output voltage is Vo * Zab/Z. So the gain is the magnitude of Zab/Z.

ehild
 

1. What is gain in a complex circuit?

Gain in a complex circuit refers to the ratio of the output signal amplitude to the input signal amplitude. It is a measure of the amplification or attenuation of a signal as it passes through the circuit. Gain is typically expressed in decibels (dB) and can be positive (amplification) or negative (attenuation).

2. How is gain calculated in a complex circuit?

Gain can be calculated by dividing the output voltage by the input voltage, or by using the formula gain = 20log(Vout/Vin), where Vout is the output voltage and Vin is the input voltage. This formula is used for both voltage gain and current gain calculations.

3. What is impedance in a complex circuit?

Impedance in a complex circuit refers to the effective resistance to the flow of an alternating current (AC). It takes into account both the resistance and reactance (inductance or capacitance) in the circuit and is measured in ohms. Impedance affects the behavior of the circuit and can be used to calculate the voltage and current in the circuit.

4. How is impedance calculated in a complex circuit?

Impedance is calculated using the formula Z = √(R2 + X2), where Z is impedance, R is resistance, and X is reactance. If the circuit only contains resistive elements, the impedance will be equal to the resistance. However, if there are inductive or capacitive elements, the impedance will be a combination of both resistance and reactance.

5. How are gain and impedance related in a complex circuit?

Gain and impedance are inversely related in a complex circuit. This means that as gain increases, impedance decreases, and vice versa. This relationship is due to the fact that an increase in amplification (gain) requires a decrease in resistance to maintain the same output voltage. Similarly, an increase in impedance will result in a decrease in gain.

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