In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that scaling techniques can later adjust these values to more practical levels.

Scaling a circuit can be done in two ways: magnitude (or impedance) scaling and frequency scaling. These methods adjust the circuit's components to work within practical ranges. Magnitude scaling changes the size of the components without affecting how the circuit responds to different frequencies. On the other hand, frequency scaling moves the circuit's response to higher or lower frequencies on the spectrum.

Magnitude Scaling:

Magnitude scaling involves adjusting the sizes of the circuit components (such as resistors, inductors, and capacitors) by a certain factor, but without changing the way the circuit responds to different frequencies. The impedances of the circuit are in terms of resistors (R), inductors (L), and capacitors (C) in a circuit. When magnitude scaling Km is applied, these components are transformed as follows:

Equation 1

Equation 2

Frequency Scaling:

Frequency scaling shifts the frequency response of a circuit along the frequency axis, either up or down, without altering the impedance levels. This is achieved by multiplying the frequency by a scaling factor, denoted by Kf. The new values of the inductance and capacitance are determined by:

Equation 3

Equation 4

If a circuit is scaled for both the parameters- magnitude and frequency at the same time, then:

Equation 5

Equation 6

If magnitude and frequency scaling factors are equal, neither magnitude nor frequency scaling occurs.

Tags
ScalingCircuit AnalysisResonant CircuitsStandard Element ValuesMagnitude ScalingFrequency ScalingImpedance ScalingCircuit ComponentsResistorsInductorsCapacitorsFrequency ResponseScaling Factors

Del capítulo 9:

article

Now Playing

9.14 : Scaling

Frequency Response

191 Vistas

article

9.1 : Network Function of a Circuit

Frequency Response

186 Vistas

article

9.2 : Frequency Response of a Circuit

Frequency Response

151 Vistas

article

9.3 : Gain

Frequency Response

137 Vistas

article

9.4 : Bode Plots

Frequency Response

189 Vistas

article

9.5 : Transfer function and Bode Plots-I

Frequency Response

193 Vistas

article

9.6 : Transfer function and Bode Plots-II

Frequency Response

171 Vistas

article

9.7 : Bode Plots Construction

Frequency Response

204 Vistas

article

9.8 : Series Resonance

Frequency Response

99 Vistas

article

9.9 : Characteristics of Series Resonant Circuit

Frequency Response

146 Vistas

article

9.10 : Parallel Resonance

Frequency Response

130 Vistas

article

9.11 : Frequency Response of Op Amp Circuits

Frequency Response

180 Vistas

article

9.12 : Passive Filters

Frequency Response

184 Vistas

article

9.13 : Active Filters

Frequency Response

200 Vistas

article

9.15 : Design Example

Frequency Response

106 Vistas

JoVE Logo

Privacidad

Condiciones de uso

Políticas

Investigación

Educación

ACERCA DE JoVE

Copyright © 2025 MyJoVE Corporation. Todos los derechos reservados