DC Analysis
Engr. Fahmi Samsuri, FKEE, UMP
4/8/2015
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DC Circuit Analysis
• Capacitors and Inductors in DC Circuits
have a transient (temporary) response.
During the transient period, capacitors build
up charge and stop the flow of current
(acting like infinite resistors.)
• Inductors build up energy in the form of
magnetic fields, and become more
conductive. In steady-state (long term
behavior), capacitors become open circuits
and inductors become short circuits.
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• For DC analysis, you can replace a
capacitor with an empty space and an
inductor with a wire. The only circuit
components that remain are voltage
sources, current sources, and resistors.
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Capacitors and Inductors at DC
• DC steady-state (the circuit has been in the same
state for a long time), capacitors act like open
circuits and inductors act like shorts. The below
figures show the process of replacing these circuit
devices with their DC equivalents. In this case, all
that remains is a voltage source and a lone resistor.
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Resistors
• If a circuits contains only resistors either in combination of
parallel or series connections then an equivalent resistance is
determined. Ohm's Law is used to determine the current
flowing in the main circuit. A combination of voltage and
current divider rules are then used to solve for other required
currents and voltages.
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Combined parallel and series
circuits
R1
R2
R4
R3
To calculate V4||V23
To calculate i of R2 & R3
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Transient Analysis
• A circuit can be analyzed at different points in time.
• Whenever a switch is closed in a circuit, the
voltages and currents in the circuit take some time
to settle down to their final values; the components
of voltages and currents that die down are called
as transients.
• Transient analysis of a circuit is done at the time of
switching to study the effects of the transients as
well as to determine the time taken by the system
to settle down.
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• The behavior of the circuit as a function of time is
studied under transient analysis.
• The inductors in the circuit are replaced by their
equivalent current sources and resistances, and the
capacitors in the circuit are replaced by their
equivalent voltages sources and resistances.
• The circuit voltages and currents are calculated at
the time of switching (usually at t = 0); this is the
initial condition solution.
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• The voltages across the capacitors and the currents
across the Inductors are used to calculate the
circuit voltages and currents at each time step; this
is done repeatedly for a designated amount of time
and the results are then plotted.
• Constraints provide an elegant means of stating
relationship among objects that should be
maintained by the underlying system.
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AC Analysis
• The AC analysis is a small signal analysis in the
frequency domain. Basically this type of simulation
uses the same algorithms as the DC analysis.
• The AC analysis is a linear modified nodal analysis.
Thus no iterative process is necessary. With the Ymatrix of the components, i.e. now a complex
matrix, and the appropriate extensions it is
necessary to solve the equation system similar to
the (linear) DC analysis.
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• Non-linear components have to be linearized at the
DC bias point. That is, before an AC simulation with
non-linear components can be performed, a DC
simulation must be completed successfully.
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Comparison of Analyses
• In dc analysis a voltage or a current or a global
parameter (resistor, temperature) is swept - and
the resulting voltage resp. current distribution in
the network is computed. Important: During this
analysis all ac relevant parts (capacitor,
inductor) are set to ZERO. This analysis is
important for producing characteristic transfer
curves like Ic=f(Vbe).
DC Analysis
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• During TRANSIENT analysis first an initial
operating point is calculated (based on dc
values) and after that all momentary
voltages and currents are computed as the
result of a time dependent voltage or
current source - including, of course, the
influence of capacitors and inductors as
well as all non-linearities (clipping effects
due to voltage limits etc.)
Transient Analysis
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• AC-analysis does NOT take into
consideration any non-linearities. Based on
the actual bias point the small signal
behaviour is analyzed (using the slope of
characteristic functions). Therefore, the input
signal may be as large as you want (best
choice: 1 volt or 1 amp).
AC Analysis
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Additional Notes
• Transient Analysis – SPICE
- Lecture notes
• AC Analysis - PSPICE
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