ELEC 225
Circuit Theory I
Fall 2007
Review Topics for Exam #2
The following is a list of topics that could appear in one form or another on the exam. Not all of
these topics will be covered, and it is possible that an exam problem could cover a detail not
specifically listed here. However, this list has been made as comprehensive as possible. You
should be familiar with the topics on the previous review sheet in addition to those listed below.
Remember to include units in answers, especially with sinusoidal quantities!
Thévenin and Norton equivalent circuits
- TEC and/or NEC is associated with a specific set of terminals; a different set of
terminals in the same circuit has a different TEC/NEC
- open-circuit voltage (voc) appears at terminals with external circuit removed
- short-circuit current (isc) flows through short between terminals with external circuit
removed
- polarity of voc vs. direction of isc
- Thévenin voltage (vth) = voc
- Norton current (iN) = isc
- Thévenin and Norton equivalent resistance, Rth = RN = voc / isc = vth / iN
- Thévenin (Norton) resistance can be found via three possible methods:
o Find voc and isc and then evaluate the ratio Rth = RN = voc / isc
o If no dependent sources are present, deactivate all independent sources
(replace voltage sources with shorts and current sources with opens), and find
Req of the circuit using series/parallel combination formulas
o If dependent sources are present, deactivate all independent sources, apply a
test source (vt or it), and evaluate the ratio Rth = RN = vt / it
Source transformations
- any voltage source in series with a resistor is equivalent to a current source in parallel
with a resistor (transform TEC to NEC)
- any current source in parallel with a resistor is equivalent to a voltage source in series
with a resistor (transform NEC to TEC)
Superposition and linearity
- principle of superposition: Any voltage or current in a circuit is a weighted sum of
the contributions from the individual independent sources driving the circuit. Stated
another way, any voltage or current in circuit can be expressed as a linear
combination of independent voltage and current sources.
- only applies if all components have linear voltage-to-current relationships. These
kinds of components include:
o all independent sources (voltage or current)
o resistors
o dependent sources (voltage or current) with constant coefficient (gain)
o capacitors and inductors (differential relationships are linear)
o linearity: If a source is scaled by a certain factor, then the portions of the
circuit’s voltages and currents due to that source are scaled by the same factor.
1
-
procedure to apply superposition:
o activate one independent source at a time; deactivate all others (i.e., replace
indep. voltage sources with shorts and indep. current sources with opens)
o leave dependent source alone
o find desired voltage(s) and/or current(s) due to the active source
o repeat the above 3 steps for each individual independent source in the circuit
o add together the components of the desired voltage(s) and/or current(s) due to
the individual sources to find the actual (total) voltage(s) and/or currents(s)
Operational amplifiers
- ideal op-amp characteristics
o infinite open-loop gain A
o infinite input resistance Ri between input terminals
o zero output resistance Ro
o zero current flow into the inverting and noninverting inputs
- op-amp equivalent circuit model (for ideal case)
o open circuit between input terminals, with voltage v between terminals
o voltage-controlled voltage source determines output voltage (vo = Av)
o only applies when op-amp operates linearly (i.e., output voltage not being
restricted by power supply voltages)
- closed-loop voltage gain vs. open-loop voltage gain
- virtual short if neg. feedback is present and op-amp output is not clipped
- ideal op-amp: v = 0; non-ideal op-amp: v typically in the range of V
- actual output voltage limited by power supply voltages (clipping)
- voltage bus notation (esp. useful for power supply voltages VPOS and VNEG in PSpice
modeling)
- analysis of ideal op-amp circuits
o nodal analysis is your friend
o most important goal (usually): closed-loop gain = vo/vin
o assumption of ideal behavior is often sufficient for good accuracy
o no effect of RL (load resistance) on gain
- inverting amplifier circuit
- noninverting amplifier circuit
Sinusoidal voltages and currents (sometimes called AC)
- standard EE representation: v(t) = A cos (t + )
- A = amplitude (in units of Vpk, if voltage)
- relationship of Vpk (peak) to Vpp (peak-to-peak) units
-  = radian frequency, in rad/s
- f = linear or cyclic frequency, in Hz (cycles/s)
- T = period, in s
-  = 2f, T = 1/f
-  = phase (can be expressed in degrees; but must be in radians if adding to t)
- transient (short-term) vs. steady-state (long-term) response of circuit to applied
voltage or current; sinusoidal steady-state analysis applies to the latter
- in the steady state, a sinusoidal source causes all other voltages and currents in a
circuit (the response) to be sinusoidal at the same frequency as source but generally
not at the same magnitude and phase
Inductors
- time-varying magnetic field causes voltage to appear across terminals (this voltage is
sometimes called the “back emf,” where emf stands for “electromotive force”)
- unit is the Henry (H)
2
-
-
circuit symbol
current-voltage relationships
o passive sign convention – use pos. form if i flows into pos. side of v
di t 
o vt    L
dt
1 t
o i t     v( )d  i t o 
L t0
voltage leads current by 90° (ELI in “ELI the ICE man”); the voltage peaks occur 90°
before the current peaks in a plot of voltage and current vs. time
equivalent inductance formulas
o series: Leq  L1  L2    L N
o parallel: Leq 
-
-
1
1
1
1


L1 L2
LN
energy storage in magnetic field
1
o W t   Li 2 t  ; energy storage is always positive
2
o energy increasing → inductor absorbs power (pos. power)
o energy decreasing → inductor supplies power to rest of circuit (neg. power)
current through L must be continuous over time, but not voltage across L; i.e., voltage
across L can change instantaneously, but not current through L
Capacitors
- unit is the Farad (F)
-
-
-
-
circuit symbol
current-voltage relationships
o passive sign convention – use pos. form if i flows into pos. side of v
dvt 
o i t   C
dt
1 t
o vt     i ( )d  vt o 
C to
voltage lags current by 90° (ICE in “ELI the ICE man”); the voltage peaks occur 90°
after the current peaks in a plot of voltage and current vs. time
equivalent capacitance formulas
1
o series: Ceq 
1
1
1


C1 C 2
CN
o parallel: C eq  C1  C 2    C N
energy storage in electric field
1
o W t   Cv 2 t  ; energy storage is always positive
2
o energy increasing → capacitor absorbs power (pos. power)
o energy decreasing → capacitor supplies power to rest of circuit (neg. power)
voltage across C must be continuous over time, but not current through C; i.e., current
through C can change instantaneously, but not voltage across C
3
Relevant course material:
HW:
Labs:
Textbook:
#4-#6
#2-#3
Secs. 4.9-4.13, 5.1-5.5 and 5.7; 6.1-6.3; 9.1- 9.2
4