SMV ELECTRIC TUTORIALS
Aditya Kuroodi
2016
ALTERNATING CURRENT:
AN INTRODUCTION
Direct Current (DC)

DC is unidirectional current and
constant amplitude (e.g. a battery)

From Ohm’s Law, DC implies a single
polarity (+/-) and constant voltage

Water analogy: the tank will constantly
push water in one direction until it is
empty
Alternating Current (AC): What is it?

AC is current that
switches direction
(voltage with
alternating polarity)

One of the most
common AC waveforms
is a sine wave
Common AC Waveform Terminolgy

Root Mean Squared:
The practical
average
describes no-load
scenario. Doing
work with load 
power
Power is
proportional to
square of voltage
or current, hence
the use of RMS
RMS value is the
DC value that
when connected
to load would
deliver same
power as the AC
wave.
Common AC Waveforms
Alternating Current: How Do We Make It?

A common way to get AC is from a generator  gives sinusoidal AC

Faraday’s Law: Any change in magnetic environment of a coil of wire
will induce a voltage in the wire

Use water, wind, etc. to rotate a coil in a magnetic field and generate
a sinusoidal voltage waveform
Alternating Current: Why Do We Need It?

AC has 3 main uses: Power distribution, motors, signal transmission

Power from a generator is sent to households in AC to minimize losses

The use of transformers with AC allows for higher voltage (lower current)
transmission  hence less IR loss on transmission line

The sinusoidal nature of AC makes it easy to work with rotary mechanics

Communication signals (radio, satellite, phone, etc.) are always AC

Note: a pulsed DC wave is rather similar to AC, making AC even more
widepsread
Capacitors and Inductors
Capacitors
Inductors

Two conductors sandwiched around
an insulator

A coil of wire, often wrapped
around a magnetic core

Stores charge in electric field when
voltage applied across the plates


Dependent on (opposes) changes in
voltage
Stores kinetic energy in magnetic
field when current flows through
coil

Dependent on (opposes) changes in
current

Applications: Filters, radio
receivers, DC-DC converters [DC]

Applications: Power supply [DC],
reducing noise ( decoupling +
bypassing), filters
Phase and AC

AC flowing through
L,C components will
experience phase
shifts

AC through Inductor
causes: Voltage
across it to LEAD
current through it by
90

AC through Capacitor
causes: Current
through it to LEAD
voltage across it by
90

No phase shift for
resistors
Complex Numbers

We use complex numbers to describe voltages/currents in AC circuits

Complex numbers have both magnitude and phase just like AC waveforms

As AC travels through circuit, its waveform changes in magnitude and phase

Voltage drops occur (magnitude change) and L/C components induce phase shifts

Reference is always the AC power supply
AC Reactance

Reactance (X) is to inductors/capacitors like resistance is to resistors, used in
AC and thus depends on frequency

Reactance + Resistance jointly called Impedance (Z)

Using phases and impedance allows us to use Ohm’s Law in AC circuits
“Ohm’s Law” for Inductor (above) and
Capacitor (below). On the right are their
reactances.
AC Circuit Example: Series RLC
Note: Often times a “j” is
used in reactance equations
to denote phase shifts of 90
Once we write each
component in impedances,
we can use Ohm’s Law to
analyze the circuit as usual
(V = IZ).
Low Pass Filter

Remember potential divider equation?

Voltage across R2 is given by:


𝑅2
1 +𝑅2
𝑉𝑜𝑢𝑡 = 𝑉𝑏𝑎𝑡𝑡𝑒𝑟𝑦 𝑅
1
Now substitute R2 with reactance 𝑋𝑐 = 2𝜋𝑓𝐶

Can you do it?

1
𝑉𝑜𝑢𝑡 = 𝑉𝑏𝑎𝑡𝑡𝑒𝑟𝑦 2𝜋𝑓𝐶𝑅+1

Increase resistance = lower 𝑉𝑜𝑢𝑡

Increase capacitance = lower 𝑉𝑜𝑢𝑡

Increase frequency = lower 𝑽𝒐𝒖𝒕

This is a LOW PASS FILTER.

Can tune 𝑅 and 𝐶 to cancel out the right requencies.
𝑉𝑜𝑢𝑡
𝑉
High Pass Filter

What if we turn around the circuit, so that capacitor is on the top?
𝐶
𝑅
𝑉


𝑉𝑜𝑢𝑡 = 𝑉
𝑅2
𝑅1 +𝑅2
substitute 𝑋𝑐 =
1
2𝜋𝑓𝐶

Can you simplify it?

This time low frequencies are
attenuated

This is a high pass filter.
𝑉𝑜𝑢𝑡
for 𝑅1 .
Note: if signal has f = 0, it is
completely eliminated

DC is blocked. Only signals that
change in time make it through
15
R = 1 kOhm
C = 0.22 microF
Resonant Filtering: Band Pass

You can tune your L and C values (and placement) in a circuit to pick out a
resonant frequency (or usually, a range of frequencies)


Have to set reactances equal to each other
At resonant frequency, depending on the arrangement of components, the
impedance can either approach infinity (open circuit) or zero (short circuit)
The LC parallel “tank circuit” will present
HIGH impedance only at frequencies in
resonant range. Otherwise it’ll short out the
load, effectively blocking out low and high
frequencies.
The series RLC has 0 impedance at
resonant frequency (passes those
signals to load) and blocks other
frequencies.