Circuit Analysis For Dummies
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Although circuit analysis is typically used to analyze what a circuit is doing, you can also use circuit analysis to design a circuit to perform a particular function. Knowing how to analyze circuits allows you to add the appropriate elements to a circuit during the design phase so that the circuit performs the way you want it to. Here are ten of practical applications for circuits.


Dimmer switches are actually adjustable voltage dividers referred to as potentiometers in the electrical engineering world. From a circuit analysis perspective, you can model a potentiometer as two resistors connected in series. The connection or junction point between the two resistors is where the wiper arm is located to vary the resistance.

By varying the amount of resistance, you vary the amount of voltage. In the case of dimmer switches, this variance allows you to adjust the lighting in a room.

Homemade capacitors: Leyden jars

The Leyden jar, a simple capacitor, consists of one piece of metal foil coating the inside of a glass jar and another piece of metal foil coating the outside. The jar serves as the dielectric insulator between the two conducting foils. The Leyden jar holds electricity where energy is stored within the glass.

Digital-to-analog conversion using op amps

To talk to the real world, a computer needs digital-to-analog converters. You can use an operational amplifier (op amp) with multiple inputs to feed an inverting summer using an op amp. To reduce the number of resistors using an inverting summer, you use an R-2R network.

Only two resistor values are needed in an R-2R network for any number of digital inputs. When analyzing this circuit, you use superposition and the Thévenin equivalent.

Two-speaker systems

A two-speaker system has one speaker called a tweeter that handles high-frequency music and another speaker called the woofer that handles the low frequencies. The input audio signal feeds across the series connection of a capacitor and resistor. The resistor terminals feed the input of the tweeter, and the capacitor terminals feed the woofer.

To analyze a two-speaker system from a frequency perspective, you need to know about high-pass and low-pass filters.

Interface techniques using resistors

You can connect resistors to a device load in order to avoid exceeding the device’s power ratings. For example, you can connect a resistor in series or in parallel to a device wherever you want to limit the voltage across and/or the current through the device.

Say you want to show that a light emitting diode (LED) is turned on. You need to limit the current going through the LED; otherwise, you may destroy it with too much current. To limit the current, you connect resistors to limit the current or voltage of the diode. Circuit analysis helps you determine how much resistance you need to protect the diode.

Interface techniques using op amps

You can take a physical variable such as temperature range and convert it to a voltage range. For example, suppose you need an amplifier to pump up a weak signal from a temperature transducer. (A transducer converts a physical variable to an electrical variable.)

The amplifier’s output is fed to a two-input summer with gain. The other input is a constant voltage source that moves the signal up and down the desired voltage range via a potentiometer (variable resistor).

The Wheatstone Bridge

The Wheatstone Bridge is a circuit used to measure unknown resistances. Mechanical and civil engineers measure resistances of strain gauges to find the stress and strain in machines and buildings.

The bridge network has three precision resistors and one unknown resistor. Two of the known resistors are potentiometers, which are adjusted to balance the bridge network and thus determine the unknown resistor. The accelerometer uses a Wheatstone Bridge arrangement of strain gauges.


You can use an array of strain gauges to develop accelerometers. A common strain gauge consists of a flexible backing that supports a metallic foil pattern. The strain gauge leverages the changes of its physical dimensions when mechanical force acts on the strain gauge.

Suppose that inside a rocket, you have a miniaturized cantilever beam with a mass hanging at one end. You’ve placed a pair of strain gauges at the top and another pair at the bottom of the cantilever beam. When there’s an upward accelerated force, the cantilever beam bends downward.

The strain gauges on top stretch from the upward acceleration, resulting in an increase in resistance; meanwhile, the strain gauges at the bottom get compressed, decreasing the resistance of the strain gage. Because of the difference of resistances in the strain gauges, you can use voltage divider arrangements and a bridge network (called a Wheatstone Bridge) to determine the amount of acceleration.

Electronic studfinders

You can modify the Wheatstone Bridge by replacing two of the four resistors with two capacitors and setting the other known resistors equal. You have two resistor-capacitor (RC) series branches connected in parallel fed by an AC source. You take each point between the RC series combination and feed it to an audio differential amplifier connected to a beeper.

The capacitances between the metal plates vary as the plates pass over the stud. The capacitors are equal when the stud finder is centered on the stud, and the Wheatstone Bridge is said to be balanced. When the stud is off-center, the capacitors are unequal and a sound is emitted.

555 timer circuits

The 555 timer chip is an integrated circuit. You can use an external resistor and capacitor network to change the timing interval by the careful choice of resistors and capacitors.

You can configure the 555 chip to work like a cooking timer (a one shot). After you set the timer and a certain amount of time elapses, the timer goes off. Or you can configure the 555 chip as a two-state clock (astable), triggering a series of pulses at regular intervals.

Other applications of a 555-timer include a Morse code call-sign generator, a metronome circuit, and an alarm circuit when your vehicle’s windshield wiper fluid runs low.

About This Article

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About the book author:

John M. Santiago Jr., PhD, served in the United States Air Force (USAF) for 26 years. During that time, he held a variety of leadership positions in technical program management, acquisition development, and operation research support. While assigned in Europe, he spearheaded more than 40 international scientific and engineering conferences/workshops.

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