Circuits with Dependent Sources

1
Circuits with Dependent Sources

• Strategy
• Apply KVL and KCL, treating dependent source(s)
  as independent sources.
• Determine the relationship between dependent
  source values and controlling parameters.
• Solve equations for unknowns.

2
Example Inverting Amplifier

• The following circuit is a (simplified) model for
  an inverting amplifier created from an
  operational amplifier (op-amp).
• It is an example of negative feedback.

3
Inverting Amplifier
4
Inverting Amplifier

• Apply KVL around loop
• -10V 1kW I 4kW I 10KW I 100 Vf 0
• Get Vf in terms of I
• Vf 4kW I 100Vf 0
• Vf 4kW/101 I

5
Inverting Amplifier

• Solve for I
• I 1.961mA
• Solve for Vf
• Vf -0.194V
• Solve for source voltage
• Vs -19.4V

6
Amplifier Gain

• Repeat the previous example for a gain of 1000

7
Answer

• Vs -19.94V

8
Another Amplifier

• Find the output voltage Vs for this circuit,
  assuming a frequency of w5000

9
Find Impedances
10
Another Amplifier

• Apply KVL around loop
• -10V?0? 1kW I 4kW I - j2kW I
• 100 Vf 0
• Get Vf in terms of I
• Vf - j2kW I 100 Vf 0
• Vf j2kW/101 I

11
Another Amplifier

• Solve for I
• I 2mA?-0.2?
• Solve for Vf
• Vf 39.6mV?89.8?
• Solve for source voltage
• Vs 3.96V?89.8?

12
Transistor Amplifier

• A small-signal linear equivalent circuit for a
  transistor amplifier is the following
• Find V

13
Apply KCL at the Top Node

• 5mA V/6kW 5?10-4V V/3kW
• 5mA 1.67?10-4V 5?10-4V 3.33?10-4V
• V5mA(1.67?10-4 5?10-4 3.33?10-4)
• V5V