1. AC Circuit Analysis

2. Exponential Function Properties of exponential function:
Essentially all waveforms encountered in practice
can be expressed as a sum of exponential functions
(2) The response of a “Linear Time-Invariant” (LTI)
system to an exponential function e st is also an
exponential function, H(s)e st
So we only need to know H(s) – the transfer function.

3. The Complex Plane  j RHP LHP - What about negative frequencies? -j
exponentially
decreasing
signals
increasing -
What about negative frequencies?
-j

4. Imaginary axis projection with phase t
unit circle
A phasor can represent either voltage or current.

5. Rotating Phasor at radian frequency 
Im axis
Re axis
Projection onto
real axis
imaginary axis
Cosine Function
Sine Function
Phasor

6. ? Voltage and current are in phase (0 ) Current leads voltage
by 90 (= /2)
Voltage leads current
by 90 ?
Resistor
Capacitor
Inductor
Voltage in blue
Current in red
Phasors shown projected onto real axis.

8. A phasor is a complex number whose magnitude is the magnitude of a corresponding sinusoid, and whose phase is the phase of that corresponding sinusoid.
A phasor is complex, and does not exist. Voltages and currents are real, and do exist.
A voltage is not equal to its phasor. A current is not equal to its phasor.
A phasor is a function of frequency, w. A sinusoidal voltage or current is a function of time, t. The variable t does not appear in the phasor domain. The square root of –1, or j, does not appear in the time domain.
Phasor variables are often given as upper-case boldface variables, with lowercase subscripts. For hand-drawn letters, a bar are typically placed over the variable to indicate that it is a phasor.

9. Example: R-L Circuit
i(t)
v(t) R L

10. General Form of H(s)

11. A representative pole-zero diagram

12. Plot of H(s) 3 poles 2 zeros jw 