Materials Needed Resistors: 1k Potentiometer: 1k, 5k, or 10k Capacitor: 0.22μf Inductor: 3.3mH TL082CN op amp IC Background Frequency Response of Circuits A circuit is a system with input x(t) and output y(t). Usually, the input is a voltage source x(t) =vs(t), but a current source may also be used, x(t) = is(t). The output is identified as a voltage or current in the circuit. Phasor representation is used in AC circuit analysis to understand the steady-state response of sinusoidal inputs signals. A voltage signal V = Acos(@₁t+0) is represented in phasor form as AZO in polar coordinates or Acos(0) + jAsin(0) in rectangular coordinates. Frequency response of a circuit is the behavior of the system as it processes sinusoids of different frequencies. The frequency response (or transfer function), H(@), is found mathematically using the impedance method or through experimental measurements by comparing the amplitude and phases of the input and output waveforms. Experimental Determination of Frequency Response Examine Figure 1, which shows the input-output behavior of a circuit with frequency response function H(@) and sinusoidal input with amplitude A, and frequency 01 rad/sec. The steady-state Aicos (wit) A。cos(@it+6) H() Figure 1: Input Output behavior of a linear circuit in steady state. The output amplitude, A., and the output phase, o, depend on H() as follows: A₁ = A¡ |H[1]] and $=ZH(1) To determine H(@) from experimental measurements of a circuit, find the steady-state sinusoidal response to a wide range of input frequencies. From each sinusoidal response, measure A. and . Fill in a table such as the one below for each input frequency. @₁ | 0=H(@1)||H(@1)|=A。/A₁| 20log | H(1)| Consider, for example, the response, y(t), of a system with input x(t)=sin(3лt) shown below. For this input, ₁=3л, and A₁ = 1. For the signal in steady-state, measure A. and AT, the time lag. The phase lag in degrees is calculated from == 360° AT T if the output is shifted to the right and $ = 360° where T is the period of the signal. AT T if the output is shifted to the left
Materials Needed Resistors: 1k Potentiometer: 1k, 5k, or 10k Capacitor: 0.22μf Inductor: 3.3mH TL082CN op amp IC Background Frequency Response of Circuits A circuit is a system with input x(t) and output y(t). Usually, the input is a voltage source x(t) =vs(t), but a current source may also be used, x(t) = is(t). The output is identified as a voltage or current in the circuit. Phasor representation is used in AC circuit analysis to understand the steady-state response of sinusoidal inputs signals. A voltage signal V = Acos(@₁t+0) is represented in phasor form as AZO in polar coordinates or Acos(0) + jAsin(0) in rectangular coordinates. Frequency response of a circuit is the behavior of the system as it processes sinusoids of different frequencies. The frequency response (or transfer function), H(@), is found mathematically using the impedance method or through experimental measurements by comparing the amplitude and phases of the input and output waveforms. Experimental Determination of Frequency Response Examine Figure 1, which shows the input-output behavior of a circuit with frequency response function H(@) and sinusoidal input with amplitude A, and frequency 01 rad/sec. The steady-state Aicos (wit) A。cos(@it+6) H() Figure 1: Input Output behavior of a linear circuit in steady state. The output amplitude, A., and the output phase, o, depend on H() as follows: A₁ = A¡ |H[1]] and $=ZH(1) To determine H(@) from experimental measurements of a circuit, find the steady-state sinusoidal response to a wide range of input frequencies. From each sinusoidal response, measure A. and . Fill in a table such as the one below for each input frequency. @₁ | 0=H(@1)||H(@1)|=A。/A₁| 20log | H(1)| Consider, for example, the response, y(t), of a system with input x(t)=sin(3лt) shown below. For this input, ₁=3л, and A₁ = 1. For the signal in steady-state, measure A. and AT, the time lag. The phase lag in degrees is calculated from == 360° AT T if the output is shifted to the right and $ = 360° where T is the period of the signal. AT T if the output is shifted to the left
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Transcribed Image Text:Materials Needed
Resistors: 1k
Potentiometer: 1k, 5k, or 10k
Capacitor: 0.22μf
Inductor: 3.3mH
TL082CN op amp IC
Background
Frequency Response of Circuits
A circuit is a system with input x(t) and output y(t). Usually, the input is a voltage source x(t) =vs(t),
but a current source may also be used, x(t) = is(t). The output is identified as a voltage or current in
the circuit.
Phasor representation is used in AC circuit analysis to understand the steady-state response of
sinusoidal inputs signals. A voltage signal V = Acos(@₁t+0) is represented in phasor form as AZO in
polar coordinates or Acos(0) + jAsin(0) in rectangular coordinates.
Frequency response of a circuit is the behavior of the system as it processes sinusoids of different
frequencies. The frequency response (or transfer function), H(@), is found mathematically using the
impedance method or through experimental measurements by comparing the amplitude and phases
of the input and output waveforms.
Experimental Determination of Frequency Response
Examine Figure 1, which shows the input-output behavior of a circuit with frequency response
function H(@) and sinusoidal input with amplitude A, and frequency 01 rad/sec. The steady-state
![Aicos (wit)
A。cos(@it+6)
H()
Figure 1: Input Output behavior of a linear circuit in steady state.
The output amplitude, A., and the output phase, o, depend on H() as follows:
A₁ = A¡ |H[1]] and $=ZH(1)
To determine H(@) from experimental measurements of a circuit, find the steady-state sinusoidal
response to a wide range of input frequencies. From each sinusoidal response, measure A. and . Fill
in a table such as the one below for each input frequency.
@₁ | 0=H(@1)||H(@1)|=A。/A₁| 20log | H(1)|
Consider, for example, the response, y(t), of a system with input x(t)=sin(3лt) shown below. For this
input, ₁=3л, and A₁ = 1. For the signal in steady-state, measure A. and AT, the time lag. The phase
lag in degrees is calculated from
==
360°
AT
T
if the output is shifted to the right and
$
=
360°
where T is the period of the signal.
AT
T
if the output is shifted to the left](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffd600fe-b230-44f0-9c9c-45818dd23665%2F30703424-0e25-42b7-8a07-c2498bc77dd2%2F3mby18m_processed.png&w=3840&q=75)
Transcribed Image Text:Aicos (wit)
A。cos(@it+6)
H()
Figure 1: Input Output behavior of a linear circuit in steady state.
The output amplitude, A., and the output phase, o, depend on H() as follows:
A₁ = A¡ |H[1]] and $=ZH(1)
To determine H(@) from experimental measurements of a circuit, find the steady-state sinusoidal
response to a wide range of input frequencies. From each sinusoidal response, measure A. and . Fill
in a table such as the one below for each input frequency.
@₁ | 0=H(@1)||H(@1)|=A。/A₁| 20log | H(1)|
Consider, for example, the response, y(t), of a system with input x(t)=sin(3лt) shown below. For this
input, ₁=3л, and A₁ = 1. For the signal in steady-state, measure A. and AT, the time lag. The phase
lag in degrees is calculated from
==
360°
AT
T
if the output is shifted to the right and
$
=
360°
where T is the period of the signal.
AT
T
if the output is shifted to the left
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