MIDTERM EXAM 1 Not graded on curve – students are not in competition Graded based on what I feel is average (B-, 71.5%) and minimally acceptable (C-, 55%) Mean: 79 Median: 77 Low: 38 High: 100 (6 students) A’s8738% of class B’s7935% of class C’s5122% of class F’s9 4% of class

Dependent Voltage 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 V 1 and manually adjust a voltage source V s to be 2 times this value. This constitutes a voltage-dependent voltage source. V1V1 + - Circuit A V s =2V Circuit B This is just a (silly) manual example, but we can create such dependent sources electronically. We will create a new symbol for dependent sources.

Dependent Voltage 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. A diamond-shaped 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. + - c d V cd + - V = A v x V cd Here the voltage V is proportional to the voltage across the element c-d.

EXAMPLE OF THE USE OF DEPENDENT SOURCE IN THE MODEL FOR AN AMPLIFIER V 0 depends only on input (V +  V - ) +  A V+V+ VV V0V0 Differential Amplifier AMPLIFIER SYMBOL +  +  V0V0 AV 1 +  V1V1 RiRi Circuit Model in linear region AMPLIFIER MODEL 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.

G m V cd Voltage-controlled current source … I = G m V cd A i I c Current-controlled current source … I = A i I c +-+- R m I c Current-controlled voltage source … V = R m I c The 4 Basic Linear Dependent Sources Voltage-controlled voltage source … V = A v V cd A v V cd +-+- Parameter being sensedConstant of proportionality Output

NODAL ANALYSIS WITH DEPENDENT SOURCES Example circuit: Voltage controlled voltage source in a branch Write down node equations for nodes a, b, and c. (Note that the voltage at the bottom of R 2 is “known” so current flowing down from node a is (V a  A v V c )/R 2.) CONCLUSION: Standard nodal analysis works

ANOTHER EXAMPLE OF NODAL ANALYSIS WITH DEPENDENT SOURCES Standard technique, except an additional equation is needed if the dependent variable is an unknown current as here. I2I2 I = V a / R 2 + (V a - R m I 2 )/ R 3 and I 2 = V a / R 2 Solving: I = V a (1/ R 2 + 1/ R 3 - R m / R 2 R 3 ) So V a = I R 2 R 3 /(R 2 + R 3 - R m ) R 4 I 2 R 2 I R 3 R 1 V a + - R m I 2 Dependent voltage sources also have unknown current—so no KCL at attached nodes. Supernode around floating dependent voltage sources!

Thevenin Equivalent Revisited 1 Calculate V OC. V T = V OC 2a) If have only resistors and independent voltage/current sources, turn off independent voltage/current sources and simplify remaining resistors 2b) If only dependent sources and resistors present, you will need to apply test voltage, calculate i and use i v R TEST T  2c) If both independent and dependent sources (with resistors) present, you may find I SC and let R T =V OC /I SC, or turn off independent sources and use i v R TEST T 

THEVENIN EQUIVALENT: DEPENDENT SOURCES Apply V TEST, measure unassociated current I RT = V TEST / I = 20  Rework using “trick”: Assign a value to any one voltage or current—why not Ix?

MORE THEVENIN TRICKS: SOURCE TRANSFORMATIONS R I = V/R B A R V B A +_+_ =

EXAMPLE: SOURCE TRANFORMATIONS Use source transformation when only independent sources and resistors present Find V T = 69 V, R T = 7.3 