Time Response of RC and RL Circuits
and
The Operational Amplifier
1.
Time Response of RC and RL Circuits
Response means the current in every branch and the voltage at every node of the circuit as a result
of the input supply signal or switching action.
This part of the laboratory study deals with the response of RC and RL circuits to a current or
voltage waveform.
When a sketch of an exponential waveform is required, remember that after 3- the response has
reached 95% of the steady state value.
If the input waveform repeats every 0.1-, the output will look a lot different than if the input
waveform repeats in 10-.
In fact, when the ratio of the input squarewave period to - is less than 0.1, the resulting output
waveform will look more like a triangular waveform.
When the input squarewave period is many times larger than -, the resulting waveform retains the
appearance of a squarewave.
Assume that a resistor behaves like a pure resistance.
A practical (manufactured) capacitor may be modelled as an ideal capacitance with a very high
value of resistance in parallel.
An inductor may be modelled as an inductance with a small series resistance and with a very
small capacitance in parallel with the series inductance and resistance.
Oscilloscope Circuit Model:
One should review the IL-2 w.r.t. DC and AC coupling. Note the frequency response
associated with the series and the parallel capacitors.
By selecting “DC” coupling one will have a parallel RC circuit response for the oscilloscope input
circuit.
Remember that the oscilloscope input circuit model is a parallel RC circuit with Rin = 1 M6 and
Cin = 20pF + Clead capacitance
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Figure 1. DC Coupling
By selecting “AC” coupling , one will have a series RinC circuit response with a time constant of
about 20 ms. There is a series capacitor, C, added to the input circuit of the oscilloscope. The
Cin and Clead are part of the low pass response where the frequency is in MHZ. The series
capacitor will cause attenuation of the frequencies below 100 Hz.
Figure 2. AC Coupling
“AC” coupling will cause distortion of any waveform that has a frequency less than 50 Hz.
This high pass response can be checked using a 10 Hz to 50 Hz squarewave supply.
2.
Measuring the Time Constant (-) of a Circuit
As was discussed in Il-2, risetime is usually measured from 10% to 90% of the voltage difference.
As shown below, the risetime equals 2.2-.
If
vout(t)
Vpeak(1e t/-),
then
t(vout)
- loge(1 vout(t)
Vpeak
)
One can subtract two particular measurements of the voltage vout to get
2.2-
t90%t10% t(vout
0.9Vpeak) t(v out
0.1Vpeak)
where - = RC, the circuit time constant.
In this case, t10% to t90% is the time it takes for the voltage to rise from 10% to 90 % of Vpeak .
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3.
The Operational Amplifier (OP AMP)
The operational amplifier is a high gain amplifier with differential (positive and negative) inputs1.
The amplifier has high input resistance and low output resistance. The operational amplifier is a
highly versatile circuit building block.
Operational Amplifier Symbols
Some confusion often exists over just what is represented by the standard triangular op amp
symbol. In this lab study the symbols shown in figure 3 are considered to be equivalent.
Figure 3. The Operational Amplifier
The “Simple Symbol” of the Op Amp at left in figure 3 is a functional schematic.
The wiring schematic on the right is implied by the use of the functional schematic (ie. the power
supply connections are assumed to be made).
The pin-out diagram for an IC shows the TOP view, and the location of pin #1 is identified by an
indent in the top of the IC case as shown in figure 4.
MC1741 Pin-Out from a top view.
V+ is the connection for the +15 volt dc bias.
V- is the connection for the -15 volt dc bias.
Offset Null will not be used in this lab
NC means “not connected”.
Information courtesy of Motorola Semiconductor.
Figure 4. MC1741
1
It amplifies the difference of the input signals.
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4.
Bread Boarding Integrated Circuits
The integrated circuit (IC) should be inserted in a position to straddle the
centre channel so that each lead is electrically isolated.
Great care must be taken when inserting or removing ICs with the breadboard
because the pins are easily bent or broken.
Always make sure that all pins are straight before attempting to insert the IC
and ensure that all pins are entering the correct slots before pressing the IC
into place.
Figure 5. Superstrip
On removal, be sure to lift the IC straight out rather than prying up on one
end.
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