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university:courses:alm1k:circuits1:alm-cir-5 [27 Feb 2018 17:04] – add breadboard figure Doug Merceruniversity:courses:alm1k:circuits1:alm-cir-5 [03 Nov 2021 20:14] (current) – [Activity: Transient Response of RC Circuit] Doug Mercer
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-======Activity 5: Transient Response of RC Circuit======+======Activity: Transient Response of RC Circuit, For ADALM1000======
  
 =====Objective:===== =====Objective:=====
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 In this lab activity you will apply a pulse waveform to the RC circuit to analyses the transient response of the circuit. The pulse-width relative to a circuit's time constant determines how it is affected by an RC circuit.  In this lab activity you will apply a pulse waveform to the RC circuit to analyses the transient response of the circuit. The pulse-width relative to a circuit's time constant determines how it is affected by an RC circuit. 
  
-Time Constant (t): A measure of time required for certain changes in voltages and currents in RC and RL circuits. Generally, when the elapsed time exceeds five time constants (5t) after switching has occurred, the currents and voltages have reached their final value, which is also called steady-state response. +Time Constant (τ): Denoted by the Greek letter tau, τ, it represents a measure of time required for certain changes in voltages and currents in RC and RL circuits. Generally, when the elapsed time exceeds five time constants (5τ) after switching has occurred, the currents and voltages have reached their final value, which is also called steady-state response. 
  
 The time constant of an RC circuit is the product of equivalent capacitance and the Thévenin resistance as viewed from the terminals of the equivalent capacitor.  The time constant of an RC circuit is the product of equivalent capacitance and the Thévenin resistance as viewed from the terminals of the equivalent capacitor. 
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 From Kirchhoff's laws, it can be shown that the charging voltage V<sub>C</sub> (t) across the capacitor is given by:  From Kirchhoff's laws, it can be shown that the charging voltage V<sub>C</sub> (t) across the capacitor is given by: 
  
-<m>V_C(t) =V( 1- e^(-t/RC ))  t >= 0</m>(3) +<m>V_C(t) =V( 1- e^( -t/RC ))  for t >= 0</m> (3) 
  
-where, V is the applied source voltage to the circuit for t = 0. RC = t is the time constant. The response curve is increasing and is shown in figure 2. +where, V is the applied source voltage to the circuit at time t = 0. The product RC is the time constant. The response curve is increasing and is shown in figure 2. 
  
 {{ :university:courses:alm1k:circuits1:alm-cir-lab5-fig2.png?500 |}} {{ :university:courses:alm1k:circuits1:alm-cir-lab5-fig2.png?500 |}}
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 The discharge voltage for the capacitor is given by:  The discharge voltage for the capacitor is given by: 
  
-<m>V_C (t) = V_o e^(-t/RC)  t >= 0</m> (4) +<m>V_C (t) = V_o e^( -t/RC )     for  t >= 0</m> (4) 
  
-Where Vo is the initial voltage stored in capacitor at t = 0, and RC = t is time constant. The response curve is a decaying exponential as shown in figure 3. +Where Vo is the initial voltage stored in capacitor at t = 0.  
 +The product RC is often referred to the so called time constant, τ. 
 +The response curve is a decaying exponential as shown in figure 3. 
  
 {{ :university:courses:alm1k:circuits1:alm-cir-lab5-fig3.png?500 |}} {{ :university:courses:alm1k:circuits1:alm-cir-lab5-fig3.png?500 |}}
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 {{ :university:courses:alm1k:circuits1:breadboard_rc.png?400 |}} {{ :university:courses:alm1k:circuits1:breadboard_rc.png?400 |}}
 +<WRAP centeralign>Figure 5. Breadboard diagram of RC circuit R<sub>1</sub> = 2.2 KΩ and C<sub>1</sub> = 1 µF.</WRAP>
  
 2. Set the channel A AWG Min value to 0.5 and Max value to 4.5V to apply a 4Vp-p square wave centered on 2.5 V as the input voltage to the circuit. From the AWG A Mode drop down menu select the SVMI mode. From the AWG A Shape drop down menus select Square. From the AWG B Mode drop down menu select the Hi-Z mode. 2. Set the channel A AWG Min value to 0.5 and Max value to 4.5V to apply a 4Vp-p square wave centered on 2.5 V as the input voltage to the circuit. From the AWG A Mode drop down menu select the SVMI mode. From the AWG A Shape drop down menus select Square. From the AWG B Mode drop down menu select the Hi-Z mode.
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 {{ :university:courses:alm1k:circuits1:alm-cir-lab5-screen1.png?650 |}} {{ :university:courses:alm1k:circuits1:alm-cir-lab5-screen1.png?650 |}}
  
-<WRAP centeralign>Figure 5: Oscilloscope Configuration.</WRAP>+<WRAP centeralign>Figure 6: Oscilloscope Configuration.</WRAP>
  
 This configuration uses the oscilloscope to look at the input of the circuit on channel A and the output of the circuit on channel B. Make sure you have checked the Sync AWG selector.  This configuration uses the oscilloscope to look at the input of the circuit on channel A and the output of the circuit on channel B. Make sure you have checked the Sync AWG selector. 
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 a. Pulse width >> 5t : Set the frequency of AWG A output such that the capacitor has enough time to fully charge and discharge during each cycle of the square wave. So let the pulse width be 15t and set the frequency according to equation (2). The value you have found should be approximately 15 Hz. Determine the time constant from the waveforms obtained on the screen if you can. If you cannot obtain the time constant easily, explain possible reasons.  a. Pulse width >> 5t : Set the frequency of AWG A output such that the capacitor has enough time to fully charge and discharge during each cycle of the square wave. So let the pulse width be 15t and set the frequency according to equation (2). The value you have found should be approximately 15 Hz. Determine the time constant from the waveforms obtained on the screen if you can. If you cannot obtain the time constant easily, explain possible reasons. 
  
-b. Pulse width = 5t : Set the frequency such that the pulse width = 5t (this should be approximately 45 Hz). Since the pulse width is 5t, the capacitor should just be able to fully charge and discharge during each pulse cycle. From the figure determine t (see figure 2 and figure 6 below.)+b. Pulse width = 5t : Set the frequency such that the pulse width = 5t (this should be approximately 45 Hz). Since the pulse width is 5t, the capacitor should just be able to fully charge and discharge during each pulse cycle. From the figure determine t (see figure 2 and figure 7 below.)
  
 {{ :university:courses:alm1k:circuits1:alm-cir-lab5-fig6.png?600 |}} {{ :university:courses:alm1k:circuits1:alm-cir-lab5-fig6.png?600 |}}
  
-<WRAP centeralign>Figure 6: Measuring the time constant t approximately by counting the number of squares.</WRAP>+<WRAP centeralign>Figure 7: Measuring the time constant t approximately by counting the number of squares.</WRAP>
  
 c. Pulse width << 5t : In this case the capacitor does not have time to charge significantly before it is switched to discharge, and vice versa. Let the pulse width be only 1.0t in this case and set the frequency accordingly.  c. Pulse width << 5t : In this case the capacitor does not have time to charge significantly before it is switched to discharge, and vice versa. Let the pulse width be only 1.0t in this case and set the frequency accordingly. 
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 2. Discuss the effects of changing component values.  2. Discuss the effects of changing component values. 
  
-**For Further Reading:**+**Resources:**
  
-[[university:tools:m1k:alice:desk-top-users-guide|ALICE Oscilloscope User's Guide]]+  * Fritzing files: [[downgit>education_tools/tree/master/m1k/fritzing/rc_filt_bb |rc_filt_bb]] 
 +  * LTSpice files: [[downgit>education_tools/tree/master/m1k/ltspice/rc_filt_ltspice | rc_filt_ltspice]] 
 + 
 +**For Further Reading:**
  
-**Return to Lab Activity [[university:courses:alm1k:alm_circuits_lab_outline|Table of Contents]]**+[[university:tools:m1k:alice:desk-top-users-guide|ALICE Oscilloscope User's Guide]]\\ 
 +[[university:courses:alm1k:intro:oscilloscope-terminology|Oscilloscope Terminology]]
  
 +**Return to [[university:labs:intro_ee|Introduction to Electrical Engineering]] Lab Activity Table of Contents**\\
 +**Return to [[university:courses:alm1k:alm_circuits_lab_outline|Circuits]] Lab Activity Table of Contents**
university/courses/alm1k/circuits1/alm-cir-5.1519747471.txt.gz · Last modified: 27 Feb 2018 17:04 by Doug Mercer

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