Analysis of Resistive circuits and Revision Week of 1st September 2008

Questions from last week

Operational Amplifier – Inverting and Non-Inverting inputs Input V1 is called the non-inverting input because Vout is in phase with V1. V2 is called the inverting input because Vout is 180° out of phase with V2. In some applications, only the noninverting input is used and the inverting input is grounded. In other applications, only the inverting input is active and the non-inverting input is grounded ( LABS 4 and 5 )

Lissajous figures

Waveforms from lab – 4 ( VI Characteristics for Resistor, LDR, Thermistor)

Current Controlled Current Source

Current controlled Voltage Source

Version of Multisim

Page 77

Voltage and Current Sources

Node Voltage analysis of circuits with Current Sources - 103

The ideal model can be called the first approximation. Ideal voltage source Maintains a constant output voltage, regardless of the value of RL. RL VRL= 10 Volts 10 V The ideal model can be called the first approximation.

Approximations Widely used in industry Useful for troubleshooting Useful for circuit calculations

Voltage Sources An ideal source has no internal resistance The second approximation of a voltage source has internal resistance A stiff voltage source has an internal resistance that is 1/100 of load resistance

Real Voltage Source This model is called the the second approximation. Has an internal resistance in series with the source RS RL VRL< 10 Volts 10 V This model is called the the second approximation. When RL is equal to or greater than 100 times RS, a real voltage source is stiff and the first approximation can be used.

Ideal current source Maintains a constant output current, regardless of the value of RL. RL 1 A IRL= 1 Ampere The ideal model can be called the first approximation.

Real current source This model is called the the second approximation. Has a large internal resistance in parallel with the source RL 1 A RS IRL< 1 Ampere This model is called the the second approximation. When RS is equal to or greater than 100 times RL, a real current source is stiff and the first approximation can be used.

Thevenin’s Theorem Used to replace any linear circuit with an equivalent voltage source called VTH and an equivalent resistance called RTH

Thevenin Example Original Circuit

Thevenin’s theorem can be used to replace any linear circuit with an equivalent voltage source called VTH and an equivalent resistance called RTH. 6 kW 4 kW VTH 72 V RL 3 kW RTH Calculate or measure Thevenin’s resistance (RTH) Remove the source. Remove the load. Calculate or measure VTH across the open terminals.

Thevenin’s Voltage

Voltmeter Tip The input impedance of a voltmeter should be at least 100 times greater than the Thevenin resistance to avoid meter loading. Meter loading errors cause inaccurate measurements. DMMs are usually not a problem since they typically have an input impedance of 10 MW.

Original circuit Thevenin equivalent circuit 6 kW 4 kW Original circuit 72 V RL 3 kW 6 kW (RTH) Thevenin equivalent circuit RL 24 V (VTH)

Norton’s Theorem Used to replace any linear circuit with an equivalent current source called IN and an equivalent resistance called RN

Norton’s Current IN = 4 mA RN = 6 KW

A Thevenin equivalent circuit The Norton dual 6 kW (RTH) A Thevenin equivalent circuit RL 24 V (VTH) VTH Circuit Conversion RN = RTH IN = RTH 6 kW (RN) RL 4 mA (IN) The Norton dual

Superposition Theorem

1st in-semester exam Two hours – Monday (8th ) 9 am to 11 am. All that covered in class and lab Focus on the problems from Dorf. Verification and Design problems are optional.

Two-loop problem – Superposition theorem – Current through R2

Circuit Theorems Refer Chapter 5 from book of Dorf and/or Chapter 1 of Malvino. Chapter 5 of Dorf is much more comprehensive.

Thevenin’s circuit application to two loop problem – Calculate current through R2

Norton’s theorem – Current through R2