RL-RC Circuits & Applications SVES Circuits Theory.

RL-RC Circuits

&

ApplicationsSVES Circuits Theory

Introduction

• In this chapter, phasor algebra will be used to develop a quick, direct method for solving both the series and the parallel ac circuits.

• Describe the relationship between current and voltage in an RC & RL circuits

• Determine impedance and phase angle in RC and RL circuits

Impedance and the Phasor Diagram

• Resistive Elements• Use R=0° in the following polar format to ensure the proper phase relationship between the voltage and the current resistance:

• The boldface Roman quantity ZR, having both magnitude and an associate angle, is referred to as the impedance of a resistive element.

• ZR is not a phasor since it does not vary with time.• Even though the format R0° is very similar to the phasor

notation for sinusoidal current and voltage, R and its associated angle of 0° are fixed, non-varying quantities.

Resistive ac circuit.

Resistive ac circuit Voltage is 100 volts Peak

Waveforms for Last Example Resistive

Phasor diagram of Example Resistive

10020.0

Analysis of Resistive Circuits

• The application of Ohm’s law to series circuits involves the use of the quantities Z, V, and I as:

V = IZI = V/ZZ = V/IR = Z


• Capacitive Reactance (XC)

• Use C = – 90° in the following polar format for capacitive reactance to ensure the proper phase relationship between the voltage and current of an capacitor:

• The boldface roman quantity Zc, having both magnitude and an associated angle, is referred to as the impedance of a capacitive element.


• ZC is measured in ohms and is a measure of how much the capacitive element will “control or impede” the level of current through the network.

• This format like the one for the resistive element, will prove to be a useful “tool” in the analysis of ac networks.

• Be aware that ZC is not a phasor quantity for the same reason indicated for a resistive element.

Analysis of Capacitive ac Circuit

• The current leads the voltage by 90 in a purely capacitive ac circuit

Capacitive ac circuit.

Capacitive ac circuit, Voltage is 15 volts peak

Waveforms for Examplecurrent leads the voltage by 90 degrees

Phasor diagrams for Example

15.00

7.50


• Inductive Reactance (XL)

• Use L = 90° in the following polar format for inductive reactance to ensure the proper phase relationship between the voltage and the current of an inductor:

• The boldface roman quantity ZL, having both magnitude and an associated angle, in referred to as the impedance of an inductive element.


• ZL is measured in ohms and is a measure of how much the inductive element will “control or impede” the level of current through the network.

• This format like the one for the resistive element, will prove to be a useful “tool” in the analysis of ac networks.

• Be aware that ZL is not a phasor quantity for the same reason indicated for a resistive element.

Inductive ac circuit.

Inductive ac circuit Voltage is 24 volts Peak

Inductor Waveforms for Examplevoltage leads the current by 90 degrees

Phasor diagrams for Example.

24.0 V

8.0

Three cases of impedanceR – C series circuit

Illustration of sinusoidal response with general phase relationships of VR, VC, and I relative to the source voltage. VR and I are in the phase; VR leads VS; VC lags VS; and VR and VC are 90º out of phase.

Impedance of a series RC circuit.

Development of the impedance triangle for a series RC circuit.

Impedance of a series RC circuit.

Phase relation of the voltages and current in a series RC circuit.

Voltage and current phasor diagram for the waveforms

Voltage diagram for the voltage in a R-C circuit

An illustration of how Z and XC change with frequency.

As the frequency increases, XC decreases, Z decreases, and decreases. Each value of frequency can be visualized as forming a different impedance triangle.

Illustration of sinusoidal response with general phase relationships of VR, VL, and I relative to the source voltage. VR and I are in phase; VR lags VS; and VL leads VS. VR and VL are 90º out of phase with each

other.

Impedance of a series RL circuit.

Development of the Impedance triangle for a series RL circuit.

Impedance of a series RL circuit.

Phase relation of current and voltages in a series RL circuit.

Voltage phasor diagram for the waveforms .

Voltage and current phasor diagram for the waveforms

Voltages of a series RL circuit.

61 V

Voltages of a series RL circuit.

Reviewing the frequency response of the basic elements.

Frequency Selectivity of RC Circuits

• Frequency-selective circuits permit signals of certain frequencies to pass from the input to the output, while blocking all others

• A low-pass circuit is realized by taking the output across the capacitor, just as in a lag network

• A high-pass circuit is implemented by taking the output across the resistor, as in a lead network

The RC lag network (Vout = VC)

FIGURE 10-17 An illustration of how Z and XC change with frequency.

Frequency Selectivity of RC Circuits

• The frequency at which the capacitive reactance equals the resistance in a low-pass or high-pass RC circuit is called the cutoff frequency:

fc = 1/(2RC)

Normalized general response curve of a low-pass RC circuit showing the cutoff frequency and the

bandwidth

- 3 dB point

Cutoff point

normalized

Example of low-pass filtering action. As frequency increases, Vout decreases

The RC lead network (Vout = VR)

Example of high-pass filtering action. As frequency increases, Vout increases

High-pass filter responses.

High-pass filter responses, filters in series

Each r-c combination- 20dB / decade

Observing changes in Z and XL with frequency by watching the meters and recalling Ohm’s law

RL Circuit as a Low-Pass Filter

• An inductor acts as a short to dc• As the frequency is increased, so does the

inductive reactance– As inductive reactance increases, the output

voltage across the resistor decreases– A series RL circuit, where output is taken

across the resistor, finds application as a low-pass filter

Example of low-pass filtering action. Winding resistance has been neglected. As the input frequency increases, the

output voltage decreases

RL Circuit as a High-Pass Filter

• For the case when output voltage is measured across the inductor– At dc, the inductor acts a short, so the output

voltage is zero– As frequency increases, so does inductive

reactance, resulting in more voltage being dropped across the inductor

– The result is a high-pass filter

FIGURE 12-39 Example of high-pass filtering action. Winding resistance has been neglected. As the input frequency increases, the output voltage increases.

RL-RC Circuits & Applications SVES Circuits Theory.

Documents

Transcript of RL-RC Circuits & Applications SVES Circuits Theory.