ABE425 Engineering Measurement Systems Circuit Analysis Dr. Tony E. Grift Dept. of Agricultural & Biological Engineering University of Illinois

Agenda Fundamental laws of electricity in circuits Kirchoff’s Current Law (KCL) Kirchoff’s Voltage Law (KVL) Basic circuits Series resistance Parallel resistance Voltage divider Current divider Circuit simplification Thevenin equivalent Norton equivalent

Fundamental laws of electricity in circuits Kirchoff’s Current Law In a node the algebraic sum of currents equals zero Kirchoff’s Voltage Law In a loop the algebraic sum of voltages equals zero

The equivalent resistance of two resistances in series is the sum of the resistances.

The equivalent resistance of two resistances in parallel is the product divided by the sum of the resistances.

If you have a voltage divider and you want to know the voltage drop across one resistor, you take that resistor itself, you divide by the sum of both resistors and you multiply by the voltage drop across both of them.

Let’s see how a voltage divider works. Let’s calculate the current i to get all voltages.

Now we can use Ohm’s Law to calculate voltage DROPS.

Now we can calculate all the voltages.

Let’s verify the voltage DROPS using the Voltage Divider rule.

If you have a current divider and you want to know the current through one resistor, you take the opposite resistor, you divide by the sum of both resistors and you multiply by the current into both of them.

Thevenin equivalent circuit Thevenin: replace a complicated circuit with a simple voltage source with a series resistance Thevenin Equivalent

Thevenin equivalent circuit procedure Step 1: Identify the circuit of which the Thevenin equivalent is to be determined Step 2: Determine the Open Voltage across the terminals of interest Step 3: Turn OFF voltage sources, (short voltage sources, open-circuit all current sources and determine the equivalent series resistance that a voltage source at the load location would see Step 4: Replace the circuit with its equivalent Voltage source and the equivalent series resistance computed in steps 2 and 3

Step 1: Identify the circuit of which the Thevenin equivalent is to be determined Thevenin equivalent circuit procedure

Step 2: Determine the Open Voltage across the terminals of interest Thevenin equivalent circuit procedure

Step 3: Turn OFF voltage sources, (short voltage sources, open-circuit all current sources) and determine the equivalent series resistance that a voltage source at the load location would see Thevenin equivalent circuit procedure

Step 4: Replace the circuit with its equivalent Voltage source and the equivalent series resistance computed in steps 2 and 3 Thevenin equivalent circuit procedure

1) Compute the Open Voltage Thevenin equivalent circuit procedure

1A) Contribution of Voltage source Remember that the internal resistance of the current source is infinite! Thevenin equivalent circuit procedure

1B) Contribution of Current source Remember that the internal resistance of the Voltage source is 0! Thevenin equivalent circuit procedure

1B) Contribution of Current source Remember that the internal resistance of the Voltage source is 0! Thevenin equivalent circuit procedure

1C) Add contributions of both sources In linear circuits this is allowed and called superposition Thevenin equivalent circuit procedure

1C) Add contributions of both sources In linear circuits this is allowed and called superposition Thevenin equivalent circuit procedure

2A) Compute the equivalent series resistance that a voltage source at the load location a,b would see Thevenin equivalent circuit procedure

2A) Compute the equivalent series resistance that a voltage source at the load location a,b would see Thevenin equivalent circuit procedure

Step 4: Replace the circuit with its equivalent Voltage source and the equivalent series resistance computed in steps 2 and 3 Thevenin equivalent circuit procedure

Norton: replace a complicated circuit with a simple current source with a parallel resistance Norton Equivalent Norton equivalent circuit

Step 1: Identify the circuit of which the Norton equivalent is to be determined Step 2: Determine the short current across the terminals of interest Step 3: Turn OFF voltage sources, (short voltage sources, open-circuit all current sources and determine the equivalent parallel resistance that a voltage source at the load location would see Step 4: Replace the circuit with its equivalent Current source and the equivalent parallel resistance computed in steps 2 and 3 Norton equivalent circuit procedure

1) Compute the Short Current through load Norton equivalent circuit procedure

1A) Contribution of Voltage source Remember that the internal resistance of the current source is infinite! Norton equivalent circuit procedure

1B) Contribution of Current source Current will take the path of least resistance! Norton equivalent circuit procedure

1C) Contribution of Current source Current will take the path of least resistance! Norton equivalent circuit procedure

1D) Add contributions of both sources In linear circuits this is allowed and called superposition Norton equivalent circuit procedure

1D) Add contributions of both sources In linear circuits this is allowed and called superposition Norton equivalent circuit procedure

2) Compute the equivalent parallel resistance that a current source at the load location would see Norton equivalent circuit procedure

2) Compute the equivalent parallel resistance that a current source at the load location would see Norton equivalent circuit procedure

2) Compute the equivalent parallel resistance that a current source at the load location would see Norton equivalent circuit procedure

Compare Thevenin and Norton procedures

ABE425 Engineering Measurement Systems Circuit Analysis The End Dept. of Agricultural & Biological Engineering University of Illinois