EECS 42 Spring 2001 Lecture 14. W. G. Oldham MORE NODAL ANALYSIS. Today: Dependent Sources Examples

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1 MOE NODAL ANALYSIS Today: Dependent Sources Examples 1

2 Dependent oltage and Current Sources A linear dependent source is a voltage or current source that depends linearly on some other circuit current or voltage. Example: you watch a certain voltmeter 1 and manually adjust a voltage source s to be 2.5 times this value. Digital oltmeter Circuit A 1 You set s s =2.5 1 Circuit B 2

3 Dependent oltage Source Example The voltage s source depends linearly on 1 (because you set it to 2.5 times 1, no matter what 1 is. If you and the voltmeter are placed inside a box, the box functions as a voltagedependent voltage source. Digital oltmeter Circuit A 1 You set s s =2.5 1 Circuit B voltagedependent voltage source Note that the red box has two wires in (to read the input voltage) and two wires out (to deliver the output voltage). 3

4 Dependent oltage and Current Sources A linear dependent source is a voltage or current source that depends linearly on some other circuit current or voltage. We can have voltage or current sources depending on voltages or currents elsewhere in the circuit. Here the voltage is proportional to the voltage across the element cd. c d cd = A v x cd A diamondshaped symbol is used for dependent sources, just as a reminder that it s a dependent source. Circuit analysis is performed just as with independent sources. 4

5 WHY DEPENDENT SOUCES? EXAMPLE: MODEL FO AN AMPLIFIE AMPLIFIE SYMBOL input output Differential Amplifier A 0 0 = A( ) 0 depends only on input ( ) EXAMPLE: A =20 Then if input ( ) = 10m; o = 200m. An actual amplifier has dozens (to hundreds) of devices (transistors) in it. But the dependent source allows us to model it with a very simple element. 5

6 EXAMPLE OF THE USE OF DEPENDENT SOUCE IN THE MODEL FO AN AMPLIFIE AMPLIFIE SYMBOL Differential Amplifier A 0 0 = A( ) AMPLIFIE MODEL Circuit Model in linear region i 1 A depends only on input ( ) See the utility of this: this Model when used correctly mimics the behavior of an amplifier but omits the complication of the many many transistors and other components. 6

7 The 4 Basic Linear Dependent Sources Constant of proportionality Parameter being sensed Output oltagecontrolled voltage source = A v cd Currentcontrolled voltage source = m I c Currentcontrolled current source I = A i I c oltagecontrolled current source I = G m cd A v cd m I c A i I c G m cd 7

8 NODAL ANALYSIS WITH DEPENDENT SOUCES Example circuit: oltage controlled voltage source in a branch 1 a 3 b 5 c AA 2 Avc 4 6 I SS Write down node equations for nodes a, b, and c. (Note that the voltage at the bottom of 2 is known so current flowing down from node a is ( a A v c )/ 2.) A a AA a v c b = b b a b c = a 0 c 0 5 b c 6 = I SS CONCLUSION: Standard nodal analysis works 8

9 ANOTHE EXAMPLE OF NODAL ANALYSIS WITH DEPENDENT SOUCES 1 a 3 b I I m I 2 I Standard technique, except an additional equation is needed if the dependent variable is an unknown current as here. Note b is redundant. I = a / 2 ( a m I 2 )/ 3 and I 2 = a / 2 Solving: I = a (1/ 2 1/ 3 m / 2 3 ) So a = I 2 3 /( 2 3 m ) 9

10 NODAL ANALYSIS WITH DEPENDENT SOUCES Finding Thévenin Equivalent Circuits with Dependent Sources Present Method 1: Use oc and I sc as usual to find T and T (and I N as well) Method 2: To find T by the ohmmeter method turn off only the independent sources; let the dependent sources just do their thing. See examples in text (such as Example 4.3) and on blackboard 10

11 NODAL ANALYSIS WITH DEPENDENT SOUCES Example : Find Thévenin equivalent of stuff in red box. a 3 c 2 A vcs 6 I SS S With method 2 we first find open circuit voltage ( T ) and then we measure input resistance with source I SS turned off. See blackboard for solution. 11