Snapshot of the front panel of the simulator:
Description of the simulated system
In this simulator an RC-circuit is simulated. It consists of a resistor R [Ohm]
and a capacitor C [Farad] connected in a circuit, see the front panel of the simulator.
In the tasks below the dynamic properties of the RC-circuit will be observed
through simulations. In the simulator the input signal is a sum of two
independent sinusoids and a bias (a constant).
The aim of this simulator is to increase the understanding of the RC-circuit
as a dynamic system.
In applikations where a simple analog lowpass filter is needed, the
RC-circuit is commonly used, as in I/O equipment (input/output) for attenuation
of measurement noise.
It can be shown that the relation between the input voltage v1
and the output voltage v2 is given by the following
(1) RC*dv2/dt = v1
By taking the Laplace transform of this differencial equation we find
the following transfer function, H(s), from v1 to v2:
(2) H(s) = 1/(Ts+1)
(3) T = RC [s]
is the filter time constant.
frequency response theory, it can be found that the bandwidth of the
(4) fb = (1/T)/(2p) [Hz]
Unless otherwise stated you should use default values of the various
parameters (you get the the default value via right-click on the front panel element).
- The step resonse of the filter:
In this subtask, you should suppress the sinusoids (by setting the
amplitudes to zero).
- Calculate (by hand) the time constant T according to Eq. (3)
above. Is the result the same as can be seen on the front panel of
the simulator when the simulator runs? Then run a simulation where
you adjust the signal component B as a step, and read off the time
constant from the response. Is the observed time constant the same
as the calculated time constant?
- Run a simulation with some constant input signal, say V1.
What is the corresponding steady-state value, v2s, of the
output voltage response? From these results, what is the relation
between V1 and v2s? Can you calculate this
relation directly from the model (1)?
- Frequency response of the filter:
Set the signal component B to zero. Use default values of R and C.
- Let the sinusoid v1a have amplitude 0.5 and frequency 0.05Hz,
and let sinusoid v1b have amplitude 0.5
and frequency 1Hz. Thus, signal component v1a has a
smaller frequency than the bandwidth, which is 0.16Hz, while the
component v1b has larger frequency than the
bandwidth. In other words, v1a are in the passband
of the filter, while v1b is in the
stoppband of the filter. Run the simulator! Can you observe
from the simulation that signal component that component 1 is
in the passband, while v1b is in the stoppband?
- The bandwidth is defined as the frequency where the amplitude
gain of the filter is 1/sqrt(2) = 0.71 = -3dB. In other words,
if the sinusoidal input signal has frequency equal to the bandwidth,
the amplitude of the output signal is 71% of the amplitude of the
input signal. Verify this by running a simulation.
Updated 30. May 2008.