The Transient Analysis allows you to
analyze the voltage or current versus time behavior of the circuit.
It starts out with the Transient Analysis Limits window.
The time range defaults to 1u for
one micro second. You must change it to a period appropriate to the
signal period you will be using. For example the 1m for one millisecond shown above will allow two full periods of a 2 kHz signal to be
analyzed and displayed or one cycle of a 1kHz signal. The display
above also shows two waveforms to be displayed on a single graph with time
as the x-axis variable. The two y-axis variables are the node voltage
at the plus terminal of the voltage source named V1 and the emitter voltage
of transistor Q1 the node numbers could also be used, but this illustrates
an alternate method of specifying the desired node voltage. Note
that both x and y scales have been set to linear. The fifth button
in front of each expression allows the specified waveform to be saved to
a waveform file to be used later as a user defined waveform source for
another circuit. The picture below shows the circuit to be analyzed
including the dc voltages found during an ac analysis of the circuit.
Since the Operating Point box has
been checked the transient analysis will start with the voltages shown
above. That is C1 will be charged to 11.085 volts positive on the
base side and C2 will be charged with 10.324 volts plus to minus from emitter
to load resistor. as the analysis runs these voltages will be changed
as the differential equations describing the complete circuit are solved
numerically. The solver will adjust the time step size to try and
get a smooth curve while not calculating too many intermediate points.
The first run of the simulation is shown below with the amplitude of the
sine source set to A=6 giving an input voltage signal of 6sin(2 pi 1000
t) volts. As can be seen this in enough to cause the amplifier to
saturate on the first cycle for a short time. It is also enough to
cause it to cutoff at the lower portion of the waveform.
See the top waveform distorting
and clipping as starting form 10.324 volts the emitter voltage can not
go up the full 6 volts of the signal waveform before saturating, since
the battery voltage is only 15 volts. Then at the bottom of the wave
form it is clipped due to cutoff of the transistor. As the input
voltage drops the collector current drops toward zero and the base-emitter
junction actually becomes reverse biased as the charge on C2 maintains
the emitter slightly above 5 volts. The time constant of the C2-(Re
+ RL) circuit is 200 ms which allows little change in the voltage during
the time of about .136 ms that the transistor is cutoff. The waveform
in the first half cycle as it approaches the peak is not smooth and as
shown in the next picture is actually off by a very noticeable amount due
to the large step size chosen by the program.
The maximum step size can be
specified in the analysis limits window. Shown below is the value
0.01 ms used o get the plot above. This limits the program to increasing
the time step to no more than 0.01 ms during the calculations. Note
the shape of the waveform can also be seen on the output voltage, v(2),
shown on this graph. The saturation does not occur on the second
cycle because the capacitors have been charged to new voltages by the non
symmetrical waveform.
These new voltages are shown below.
Note that now there is almost a full
6 volts between the emitter DC voltage and the collector voltage.
There will actually be a short time when the transistor is saturated at
the very top of the waveform