LABORATORY 1
IDENTIFICATION OF CIRCUIT IN A BLACK-BOX
OBJECTIVES
1. To identify the configuration of an electrical circuit enclosed in a two-terminal
black box.
2. To determine the values of each component in the black box circuit.
INFORMATION
In this experiment the components of a simple circuit (inside a black box) will be identified
based on their response to dc voltages and ac voltages of different frequencies.
Five simple circuits will be investigated:
1. Resistance in series with diode – Figure 1.1.
2. Resistance in series with Zener diode – Figure 1.2.
3. Resistance in parallel with a capacitor – Figure 1.3.
4. Inductor in parallel with a capacitor – Figure 1.4.
5. Resistance in series with a parallel combination of inductor and capacitor- Figure 1.5.
Note : The value of the resistance R is at least 100Ω
1
R
D
R
1
2
Figure 1.1
1
R
Dz
2
Figure 1.2
C
1
2
C
L
Figure 1.3
Figure 1.4
1
C
2
R
L
Figure 1.5
1-1
2
The following properties of different circuit components are exploited in determining the
circuit configuration:
• A resistance is a bilateral devise and conducts in a similar manner in either
direction.
• A diode conducts only if forward biased beyond a certain specific voltage (0.7V for
silicon diode).
• A zener diode behaves like a normal diode when forward biased. When reverse
biased it conducts beyond a specific voltage, known as zener voltage.
• In steady state an inductor acts like a short circuit for dc voltages and ac voltages of
very low frequencies. With ac voltages of very high frequencies it acts like an open
circuit. Further, an inductor is a bilateral device.
• In steady state a capacitor acts like an open circuit for dc voltages and ac voltages
of very low frequencies. With ac voltages of very high frequencies it acts like a
short circuit. A capacitor is also a bilateral device.
EQUIPMENT
1.
2.
3.
4.
5.
6.
7.
8.
Digital multimeter (Fluke 8010A, BK PRECISION 2831B)
Digital oscilloscope Tektronix TDS 210
Function Generator Wavetek FG3B.
Phase meter.
DC voltage supply
PROTO-BOARD PB-503 (breadboard)
Black box.
Resistor 1 kΩ, 10 kΩ
PRE-LABORATORY PREPARATION
There is no specific pre-laboratory preparation for this lab exercise.
Familiarize yourself with the laboratory procedure before attending the lab session.
The circuits in black boxes will be identified by examining their performance during the
following tests.
1. Impedance Test
The impedance of the circuit is measured both in forward and reverse direction using a
digital multimeter.
2. DC Test
A known dc voltage Vdc is applied across the circuit and the current is measured. The
polarity of the voltage is reversed and the current is measured again. A current limiting
resistor Re = 1 kΩ is always inserted in series with the circuit to restrict current to safe
levels, as it is shown in Figure 1.6.
1-2
BLACK BOX
I
Vdc
Re
Vo
.
Figure 1.6. Circuit for DC Test
3. AC Test
An ac voltage of fixed magnitude Vin is applied across the circuit as shown in Figure 1.7.
A current limiting resistor Re is inserted in series with the circuit to constrain the current
within safe values. The source frequency is varied from a very low (20Hz) to a very high
(1 MHz) frequency. For different frequencies the output voltage Vo and the phase
difference Θ between input and output voltages are recorded.
BLACK BOX
.
I
Vo∠Θ
Vin
Re
.
Figure 1.7. Circuit for AC Test
4. BEHAVIOUR OF DIFFERENT CIRCUITS
Circuit 1. Resistance R in series with diode D – Figure 1.1.
•
•
Impedance test
Finite resistance only in forward direction
Open circuit in reverse direction
•
DC Test
Conducts when diode is forward biased
I=
Vo Vdc − 0.7V
=
Re
R + Re
1-3
Equation (1.1)
where R = unknown resistor
Re= current limiting resistor of 1 kΩ
•
Does not conduct for large negative polarity voltages (i.e. less than –10V).
•
AC Test
Conducts only in positive half cycle.
Circuit 2. Resistance R in series with zener diode Dz – Figure 1.2.
•
•
•
•
Impedance test
Finite resistance only in forward direction.
Open circuit in reverse direction.
DC Test
Conducts when diode is forward biased
For large negative polarity voltages (i.e. more than –6V) current I flows and is
given by Equation (1.2)
I=
Vo Vdc − V z
=
Re
R + Re
Equation (1.2)
where Vz = zener voltage.
•
•
AC Test
Conducts in positive half cycle voltage.
Conducts in negative half cycle voltage only when voltage magnitude is higher
than zener voltage.
Circuit 3. Resistance R in parallel with a capacitor C – Figure 1.3.
•
•
•
•
•
Impedance test
Finite resistance will be measured, which is same in both directions.
DC Test
Circuit conducts for both polarities of dc voltage.
V
Vdc
I= o =
Re R + R e
Equation (1.3)
AC Test
Very low frequencies: Vo and Vin have same phase but different magnitudes.
Very large frequencies: Vo and Vin have same phase and magnitudes.
At any intermediate frequency ω=2πf
1-4
I=
V in
 1 

Re + R 
 jωC 
=
Vo
Re
Equation (1.4)
Vin ∠0
V ∠Θ
= o
R
Re
Re +
1 + jωRC
or
Equation (1.5)
where, Vo = output voltage rms
Vin = intput voltage rms
R = unknown resistance
C = unknown capacitance
Re = current limiting resistor
Θ = phase difference between input and output terminals, as measured by phase
meter.
Circuit 4. Inductor L in parallel with a capacitor C – Figure 1.4.
•
•
•
•
•
Impedance test
Finite resistance will be measured, which is same in both directions.
DC Test
Circuit conducts for both polarities of dc voltage. The conducted current is
described by the Equation (1.3).
AC Test
Very low frequencies: Vo and Vin have same phase and magnitudes.
Very large frequencies: Vo and Vin have same phase and magnitudes.
At any intermediate frequency ω=2πf
I=
or
also
V in
 1 

Re + ( jωL ) 
 jω C 
=
Vo
Re
Equation (1.6)
Vin ∠0
V ∠Θ
= o
jω L
Re
Re +
2
1 − ω LC
Equation (1.7)


ωL
Θ = − tan −1 

2
 Re 1 − ω LC 
(
1-5
)
Equation (1.8)
where, L = unknown inductor
C = unknown capacitance
Θ = phase difference between input and output terminals, as measured by phase
meter.
•
At resonant frequency ωο =2πfo impedance of black box circuit becomes infinite
and current goes to zero. Also the phase of output voltage changes it’s sign.
1 − ω 02 LC = 0
ω 0 = 2πf 0 =
Equation (1.9)
1
Equation (1.10)
LC
Circuit 5. Resistor R in series with a parallel combination of Inductor L
and capacitor C – Figure 1.5.
•
•
•
•
•
Impedance test
Finite resistance will be measured, which is same in both directions.
DC Test
Circuit conducts for both polarities of dc voltage.
described by the Equation (1.3).
AC Test
Very low frequencies: Vo and Vin have same phase but different magnitudes.
Very large frequencies: Vo and Vin have same phase but different magnitudes.
At any intermediate frequency ω=2πf
I=
or
The conducted current is
V in
(R + Re ) + ( jωL )  1 
 jω C 
Vin ∠0
=
(R + Re ) + jω2L
1 − ω LC
=
Vo
Re
Vo ∠Θ
Re
Equation (1.11)
Equation (1.12)


ωL
Equation (1.13)
Θ = − tan −1 

2
(
)
R
R
1
ω
LC
+
−
e


where, L = unknown inductor
C = unknown capacitance
R = unknown resistance
Θ = phase difference between input and output terminals, as measured by phase
meter.
also
(
1-6
)
1. At resonant frequency ωο =2πfo impedance of black box circuit becomes infinite
and current goes to zero. Also the phase of output voltage changes its sign.
1 − ω 02 LC = 0
ω 0 = 2πf 0 =
Equation (1.14)
1
Equation (1.15)
LC
PROCEDURE
*) Note down the number of the black box circuit that you are provided for evaluation
and make sure to record it in your report
1. Use the multimeter to perform an impedance test of the black box circuit, to
identify if there is a diode or zener present.
2. To perform a dc test on the given black box, connect the dc power supply and the
external resistor Re=1kΩ, as shown in Figure 1.6. Set the Vdc = 10V and measure
the output voltage Vo. If your black box circuit contains diode or zener diode, use
Equations (1.1) and (1.2) to determine the values of R and Vz. If no diode or zener
diode presents, obtain the value of circuit resistance as evident from circuit
behaviour.
3. Perform the ac test as shown in Figure 1.8 and plot the frequency response for a
widely varying range of frequencies. Set function generator FG to provide Vin=1V
and observe both input and output signals using the oscilloscope.
CH1
CH2
PHASE METER
CH2
BLACK
CH1
BOX
FG Vin
GND
CH2
R
CH1
1k
Vo
GND
OSCILLOSCOPE
CH1
CH2
GND
Figure 1.8. AC test measurements
4. For each of the selected frequencies read the RMS voltage of the Vin ( CH1) and
Vout (CH2) from the oscilloscope display and record the data in Table 1.1. For the
same frequencies record the Phase Meter readings (display will show the phase
angle between these two signals in [deg]).
For each of the measurements calculate the voltage gain in Av
1-7
AV =
f [Hz]
50
75
100
200
500
1k
2k
5k
10k
20k
50k
100k
200k
500k
1M
Vin [V]
Vout
Vin
Vout [V]
Equation (1.16).
Θ[deg]
Av
Table 1.1. Black box frequency response
5. Observe if any resonance occurs in the circuit. This is evidenced by a output
current and Vo decreasing to a very low level and the output signal phase changing
its sign.
6. Use the relevant formulas for different circuits to compute the circuit parameters.
Do your calculations for three different frequencies and obtain average consistent
result.
REPORT
Write a systematic report of how you identified the circuit configuration values.
Make sure to include the black box # in your report
Note: You must copy/print the Signature and Marking Sheet from your manual
before coming to the lab session.
1-8
SIGNATURE AND MARKING SHEET – LAB 1
To be completed by TA during your lab session
Student Name:______________________
TA Name:___________________
Student # : _________________________
Check
boxes
Task
Max.
Marks
Pre-lab completed
0
Impedance Test completed
5
DC test completed
5
AC Test completed
5
Component values calculations
5
Overall Report Preparation
80
TOTAL MARKS
100
1-9
Granted
TA
Marks Signature