Driving Point Impedance and Transfer Function

Introduction

• Overview of driving point impedance and transfer function in electrical networks.
• Aim: Understand how to find these parameters in given networks.

Driving Point

• Definition: Terminals of a circuit where an energy source is connected (voltage/current source).
• One-Port Network: The single port acts as the driving point.
• Multi-Port Network: The port where the power supply is connected acts as the driving point.

Driving Point Impedance

• Definition: Impedance seen through the driving point when a voltage source is connected.
• For a one-port network:
  • Driving Point Impedance, Z(s) = V(s) / I(s)
  • Both V(s) and I(s) are in the S-domain.
• Two-Port Network:
  • For Port 1: Z11 = V1(s) / I1(s)
  • For Port 2: Z22 = V2(s) / I2(s)
• Driving Point Admittance:
  • Y11 = I1(s) / V1(s) (inverse of impedance at Port 1)
  • Y22 = I2(s) / V2(s) (inverse of impedance at Port 2)

Finding Driving Point Impedance

1. Identify the equivalent S-domain representation for the circuit components (Resistor, Capacitor, Inductor).
2. Combine components in series and parallel to find the overall impedance.
3. Example provided in the lecture for clarity:
   • Given a circuit, find the equivalent impedance across terminals.
   • Use Thevenin’s equivalent impedance to simplify calculations.

Transfer Function

• Definition: Relates voltage/current of one port to voltage/current of another port. Requires at least two ports.
• Types of Transfer Functions:
  1. Voltage Transfer Function (VTF):
     • VTF = V2(s) / V1(s) (output to input voltage ratio)
  2. Current Transfer Function (CTF):
     • CTF = I2 / I1 (output to input current ratio)
  3. Transfer Impedance:
     • Z12 = V2 / I1 (output voltage to input current ratio)
  4. Transfer Admittance:
     • Y12 = I2 / V1 (output current to input voltage ratio)

Finding Transfer Function

1. Analyze the circuit to find the S-domain representation.
2. Apply Kirchhoff's Current Law (KCL) to nodes to derive relationships between voltages and currents.
3. Example provided to calculate transfer function (Vout/Vi).

Conclusion

• Summarized steps to determine driving point impedance and transfer functions for electrical networks.
• Encouraged students to ask questions for further clarification.