Chapter 7

Series-Parallel Circuits

Objectives

Analyze series-parallel circuitsAnalyze loaded voltage dividersAnalyze ladder networks Analyze a Wheatstone bridge

Basic Idea

Given a circuit; steps to analyze a circuit:Find the total resistance

Determine all parallel resistors and series resistors

Simplify the given circuit Use KCL and Ohm’s law to find all currentsUse Ohm’s law to find all voltages

Find the total resistance

R1 + R2 || R3 + R4 || R5

Find the total resistance

R1 + R6 || (R5 + (R4 || (R2 + R3)))

R1 || (R2 + R3 || (R5 || R4))

Find RT, IT, I2, and I4; Vs=50V

Find RT, I(RL1), I3

Find RT, IT, I2

Find RT, IT and V(AB) VS=10V

Loaded Voltage Dividers

When a load resistor RL is connected from the output to ground, the output voltage is reduced by an amount that depends on the value of RL.

Loading Effect of a Voltmeter

Multimeter

L

LloadR

RRRR

2

2

What happens if RL >> R2?

So, what is the internal resistance of a DMM?

Analysis of a Ladder Network A resistive ladder network

is a special type of series-parallel circuit.

One form of ladder network is commonly used to scale down voltages to certain weighted values for digital-to-analog conversion Called R/2R Ladder

Network To find total resistance of a

ladder network, start at the point farthest from the source and reduce the resistance in steps.

The R/R2 Ladder Network

Only Input 4 is HIGH

Only Input 3 is HIGH

Used for Digital-to-analog converter!

Examining Digital-to-Analog Conversion

For Extra credit: Change the circuit to generate this output: