Lecture 13 Dependent Sources ECE 205 Prof Ali

Lecture 13 Dependent Sources ECE 205 Prof. Ali Keyhani

Active Devices • Active Device: Device that are dependent on an external power supply to operate • Active Circuit: Circuits that contain one or more active devices • Linearly active devices: input-output relationship of the active devices is governed by the equation: y=Kx • K is called the proportionality factor

Dependent Sources • Linear active devices are usually modeled using resistors and dependent sources • Dependent sources: a voltage or current source whose output is controlled by a voltage or current in another part of the circuit • Depending on the type of the source and the control there are four types of dependent sources

Dependent Sources • Current Controlled Voltage Source (CCVS) • Voltage Controlled Voltage Source (VCVS) • Current Controlled Current Source (CCCS) • Voltage Controlled Current Source (VCCS)

Dependent Sources • All the linearly dependent sources have an output proportional to the input current or voltage as y=Kx • The proportionality factor is called gain in the dependent sources • Voltage gain: μ (dimensionless) • Current gain: β (dimensionless) • Transresistance (transfer resistance) : r (ohm) • Transconductance (transfer conductance): g(siemens)

Circuit Analysis with Dependent Sources • Turning on and off the dependent voltages sources requires turning on and off their independent sources • Superposition, source transformation and circuit reduction also apply to active circuits

Example 1 • What is the output voltage, current and power?

Current division to find ix: Dependent voltage source: Current division:

Input-output relationship of the circuit: Signal inversion: K=-6000 which means input and output have opposite signs Output power: Input power:

• Power gain of the system is greater than one:

Example 2 Find the output voltage vo in terms of input voltage vs.

Example 2 Solution:

Node Voltage Analysis with Dependent Sources • To write the node voltage equations first the dependent sources are treated as independent sources • After writing the symmetrical equations the dependent sources are expressed in terms of the node voltages • The new sets of non-symmetrical equations are solved to find the unknown node voltage equations

Example 3 a) Formulate node-voltage equations b) Find vo and io in terms of is.

• Solution: a) Symmetrical node-voltage equations: Since vx=v. A the equations can be simplified:

b) vo=v. B therefore by solving the equations the v. B is found:

Mesh Current Analysis with Dependent Sources • The same pattern as the node-voltage analysis is followed – The mesh current equations are written as if the sources are all independent – The dependent sources are then replaced by their equivalent expression in terms of unknown mesh currents

Example 4 Find current io with mesh analysis.