Exp.4
Transient analysis of the first order
dynamic circuits
1. Experiment objectives:
:
 Experimental verification of students knowledge about transient
responses of the linear RL and RC systems
 Comparison of some transient responses parameters obtained
from analytical formulas with the measurements and computer
simulations
2. Measurements and calculations
2.1. First order RC circuit. Time constant measurement using pulse
generator and oscilloscope.
.
vs
R
generator
RW
R=1kΩ
C=0.1μF
C
‘0’ of the
generator
‘0’ of the
oscilloscope
‘hot wire’ of the
oscilloscope
Fig.1. Linear RC circuit
The main aim of the experiment is to measure time constant of the
transient voltage response of the capacitor and steady state voltage
1
measured across capacitor. To preserve proper measurements set
frequency of the pulse generator to 300-600Hz. Adjust time and
voltage scales ensuring maximal accuracy – one single dynamic state
per screen.
(300 do 600Hz).
Remark: Internal generator resistance should be calculated from the
formula (1) where R=1kΩ, Vs. is the measured generator voltage,
Vload is the voltage measured across output terminals loaded by the
resistor R.
V  Vload R
RG  s
(1)
Vload
TABLE 1
R
C
Vs
Vload
RG
Req
τm
τc
τs
kΩ
μF
V
V
kΩ
kΩ
ms
ms
ms
1.0
0.1
τm – time constant’ obtained from experiment measurements
τc –‘time constant’ calculated from analytical formula
τs – time constant’ obtained from computer simulations
2.2. First order RL circuit. Time constant measurement using
pulse generator and oscilloscope.
vs(t)
L
inductor
generator
RL
RG
R
„0” of the
generator
„0” of the
oscilloscope
R=1kΩ
„hot wire” of the
oscilloscope
2
Fig.2. Linear RL circuit under test
TABLE 2
R
L
Vs
RL
RG
Req
τm
τc
τs
kΩ
mH
V
kΩ
kΩ
kΩ
ms
ms
ms
1.0
Observe current flow of the inductor. Calculation of the time constant
are similar to that performed for RC circuit.
Internal resistance of the inductor should be measured by ohmmeter.
Report should contain :
1. Analytical solution of the single dynamic state of the RC
(capacitor voltage) and RL (inductor current) circuits (response
of the single pulse increasing slope).
2. Definition and graphical interpretation of the time constant.
3. Short description of the method of time constant calculations
using circuits from Fig.1 and 2
4. SPICE simulation results (plots and circuits models)
a. RC circuit simulation with DC generator
b. RC circuit simulation with pulse generator modeling the
generator using during the laboratory experiment
Requirements for STUDENTS:
Students should be able to:
a) define dynamic and steady state of the system
b) formulate differential equations of the first order circuits
c) find solution of the first order systems
d) define and calculate time constant of RL and RC circuits
e) know how to find time constant analyzing the transient response curve!!!!!!!!
3