for the given circuit calculate the input impedance, output impedance and voltage gain?

To calculate the input impedance, output impedance, and voltage gain of a given circuit, we first need to understand the components involved and their configuration. Let's break down the process step by step, assuming we are dealing with a common amplifier circuit, such as a transistor amplifier or an operational amplifier configuration.

Input Impedance Calculation

The input impedance (Zin) is the impedance seen by the source connected to the input of the circuit. For a simple transistor amplifier, the input impedance can be calculated using the formula:

• If using a BJT (Bipolar Junction Transistor), Zin can be approximated as:
• Zin = β * (re + R_E)

Here, β is the current gain of the transistor, re is the small-signal emitter resistance, and R_E is the external emitter resistor. For an operational amplifier, the input impedance is typically very high, often in the megaohm range, making it suitable for high-impedance sources.

Output Impedance Calculation

The output impedance (Zout) is the impedance seen from the output terminals of the circuit. For a transistor amplifier, the output impedance can be calculated as:

• Zout = R_C || r_o

In this equation, R_C is the collector resistor, and r_o is the output resistance of the transistor. For operational amplifiers, the output impedance is generally low, often in the range of tens of ohms, which helps in driving loads effectively.

Voltage Gain Determination

The voltage gain (Av) of the circuit is defined as the ratio of the output voltage (Vout) to the input voltage (Vin). For a common-emitter BJT amplifier, the voltage gain can be approximated as:

• Av = - (R_C / re)

The negative sign indicates a phase inversion between the input and output signals. For operational amplifiers configured in a non-inverting mode, the voltage gain can be calculated using:

• Av = 1 + (R_f / R_in)

Here, R_f is the feedback resistor, and R_in is the resistor connected to the input. This configuration allows for precise control over the gain.

Example Calculation

Let’s say we have a BJT amplifier with the following parameters:

• β = 100
• re = 26 mΩ (at room temperature)
• R_E = 1 kΩ
• R_C = 4.7 kΩ
• r_o = 50 kΩ

Calculating the input impedance:

• Zin = 100 * (26 mΩ + 1 kΩ) = 100 * 1.026 kΩ = 102.6 kΩ

Calculating the output impedance:

• Zout = 4.7 kΩ || 50 kΩ ≈ 4.6 kΩ

Calculating the voltage gain:

• Av = - (4.7 kΩ / 26 mΩ) ≈ -180.77

This means the amplifier has a high input impedance, a relatively low output impedance, and a significant voltage gain, which is typical for a common-emitter amplifier configuration.

Understanding these calculations helps in designing and analyzing circuits effectively, ensuring that they meet the desired specifications for various applications.