Name: circuit gain and phase shift
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 15 s
Channel: JoVE

In communication systems, gain quantifies the extent of signal amplification or attenuation.
Power gain denotes the common logarithm of the ratio of output power to input power and is expressed in bels.
For practical measurements, a decibel is commonly used. It is a subunit equivalent to one-tenth of a bel.
Consider a network with input and output voltages and resistances. If the output power equals the input power in this network, the gain is zero decibels.
When the output power becomes twice the input power, the gain is of three decibels. Conversely, if the output power falls to half the input power, the gain is of minus three decibels.
Alternatively, power can be represented using voltage and resistance.
The rules of logarithms are applied to obtain an expression for power gain in terms of the voltage and resistance ratios.
When the input resistance equals the load resistance, the gain becomes proportional to the output and input voltage ratio.
Similarly, the gain can be represented in terms of the current and resistance ratios.

gain

Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.
<img alt="V(t)=Acos(&#969;t) formula; amplitude modulation; signal analysis concept." src="/files/ftp_upload/15139/15139_Equation_1.svg" style="text-align: center; height: 20px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
<img alt="AC waveform equation: V_out(t) = B cos(&#969;t + &#952;), sinusoidal signal analysis, formula." src="/files/ftp_upload/15139/15139_Equation_2.svg" style="text-align: center; height: 16px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
The input and output signals have the amplitude A and B and a phase angle of 0&#176; and &#952;&#176;, respectively.
The gain of the circuit gives the relationship between the sizes of the input and output sinusoids. In particular, the gain (K) is the ratio of the output sinusoid's amplitude to the input sinusoid's amplitude.

<img alt="K=Gain=B/A, formula for calculating system gain, educational use, equations in control theory." src="/files/ftp_upload/15139/15139_Equation_3.svg" style="text-align: center; height: 28px;" data-altupdatedat="1762173717000" data-alt="Equation 3" />
When the gain K is greater than unity, it implies amplification, whereas a gain less than one indicates attenuation. The gain is described using a logarithmic scale. When expressed in decibels (dB), gain provides a convenient way to represent very large and very small numbers on the same scale. The gain in decibels is calculated using the formula:
<img alt="Decibel calculation formula, dB = 20log(K), related to sound intensity measurement." src="/files/ftp_upload/15139/15139_Equation_4.svg" style="text-align: center; height: 15px;" data-altupdatedat="1762173717000" data-alt="Equation 4" />
Where:
dB is the gain in decibels,
K is the gain,
log is the logarithm base 10.
 Phase Shift:
Phase shift refers to the amount by which the phase of the output signal is delayed or advanced compared to the phase of the input signal. It is the angular difference between the output and input sinusoids. The input and output signal has a phase angle of 0&#176; and &#952;&#176; respectively, then the phase shift (&#952;shift) is given by:
<img alt="Angle shift equation, &#952;&#176; shift = &#952;&#176; - 0&#176;, mathematical formula, static equilibrium analysis." src="/files/ftp_upload/15139/15139_Equation_5.svg" style="text-align: center; height: 18px;" data-altupdatedat="1762173717000" data-alt="Equation 5" />
A positive &#952;shift indicates that the output signal lags the input signal, while a negative means that the output signal leads the input signal.

Gain

In communication systems, gain quantifies the extent of signal amplification or attenuation.
Power gain denotes the common logarithm of the ratio of ...

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JoVE Core

Electrical Engineering

Unit 1

Frequency Response

KEY TERMS AND CONCEPTS

circuit gain and phase shift

Circuit gain and phase shift describe how a linear circuit changes a sinusoidal input voltage or current. These properties matter in circuits with reactive elements, because the response depends on the input frequency. As the frequency changes, the gain and phase shift also change.

Gain compares the size of the output sinusoid to the size of the input sinusoid. If Vin is the input and Vout is the output, the gain K is the ratio of the output amplitude to the input amplitude. A gain greater than one means the circuit amplifies the signal, while a gain less than one means the circuit attenuates it.

Gain is often written on a logarithmic scale. When gain is expressed in decibels, or dB, it gives a practical way to show very large and very small values on the same scale. The dB value is found from the gain K using a base-10 logarithm.

Phase shift describes how much the output waveform is delayed or advanced compared with the input waveform. It is the angular difference between the input and output sinusoids. If the input has a phase angle of 0° and the output has a phase angle of θ°, then the phase shift is θ shift.

A positive phase shift means the output lags behind the input. A negative phase shift means the output leads the input. Together, gain and phase shift show both the size change and the timing change caused by a linear circuit.

Circuit Gain and Phase Shift

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key terms and concepts

Learn how linear circuits change sinusoidal signals through gain and phase shift, including amplitude ratio, decibels, and lag or lead.

Circuit Gain and Phase Shift | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Circuit Gain and Phase Shift

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