Inductance, capacitance and
resistance
• As previously discussed inductors and
capacitors create loads on a circuit.
• This is called reactance.
• It varies depending on current and frequency.
• At no frequency, or DC there is no reactance.
• At low frequency capacitors create the most
reactance
• At high frequency inductors create the most
reactance
Inductance, capacitance and
resistance
• Since inductive reactance varies with
frequency and inductance the formula for this
is Xl=2πfL where f is frequency and L is
Henrys and Xl is in Ohms.
• Ohms law for inductance is the same as that
used to combine resistances in series and
parallel circuits.
• An inductor will cause current to lag behind
voltage because induced voltage resists
current changes.
Inductance, capacitance and
resistance
• Since capacitive reactance varies with
frequency and capacitance the formula for
this is Xc=1/(2πfC) where f is frequency and C
is Farads and Xc is in Ohms.
• Ohms law for capacitance is inverted from
that used to combine resistances in series
and parallel circuits.
• A capacitor will cause voltage to lag behind
current because at 0 volts charge the circuit
will be at maximum current.
Inductance, capacitance and
resistance
• Therefore capacitive and inductive reactance
counter, or cancel each other.
• Their effect on phase counters the other’s
phase effect.
• ELI the ICEman
• E leads I with an L (inductor)
• I leads E with a C (capacitor)
Inductance, capacitance and
resistance
• Since resistance doesn’t effect phase the net
of the two reactances, with the lessor
subtracted from the greater, will act upon total
impedance at 90° to resistance.
• But since reactance is already expressed in
the form of Ohms in a purely reactive circuit
Ohms laws applies normally for a purely
inductive or capacitive circuit.
Inductance, capacitance and
resistance
• Since both reactance’s cause current to lead
or lag by 90° they must be added to
resistances using the Pythagorean theorem.
• C2 = A 2 + B 2
• Zt2 = R2 + X(c-l or l-c)2
• Zt = the circuits total opposition to current
flow.
• If the circuit has no AC, or inductors and
capacitors then Zt = Rt
Inductance, capacitance and
resistance
• Ohms law works for AC circuits with
inductors, capacitors and resistances.
• Series circuits solve for impedance first, in
parallel solve for currents since the V-drop is
the same across each leg.
Inductance, capacitance and
resistance
• Resonance is when the frequency is
such that a capacitor in series with an
inductor cancel each other’s reactance.
• Similar resonance in a parallel circuit
with an inductor and capacitor will have
infinite resistance at a resonant
frequency.
Inductance, capacitance and
resistance
• Power factor is 100% in DC circuits.
• It is the ratio of apparent power to true
power.
Inductance, capacitance and
resistance
• Apparent Power is that derived from
measuring voltage and current in an AC
circuit and multiplying them.
• True power is the power actually used by the
resistive load and does not contain the power
lost to reactance.
• Power factor = 100 X True Power / Apparent
Power
Inductance, capacitance and
resistance
270 Ω
110V 400hz
Xl= 2πfL
Xc= 1/(2πfC)
Rt= R
Z2= Rt2 + (Xc-Xl)2
It = E/Z
300µf
31mH
Inductance, capacitance and
X = 2πfL
resistance
l
Xc= 1/(2πfC)
Rt= R
It = E/Z
270 Ω
300µf
110V 400htz
31mH
Z = R·Xl·Xc/v(Xl2·Xc2+(R·Xl-R·Xc)2)
Transformers
• A transformer is a set of two or more inductors in
close proximity whose purpose is to exchange
voltage for current in an AC circuit.
• If the voltage or current is incorrect for a given
application it can be transformed up or down.
• The catch is if one goes up, the other must go down.
• The other catch is this will lose some power within
the circuit.
Transformers
Transformers
• Essentially one inductive coil will have thicker
wire with fewer loops or turns than the other.
• They can be high current or high voltage coils
depending on what they need for output.
Transformers
Transformers
Transformers
• Generally a “step up” or “step down”
transformer refers to the voltage being
“stepped”.
• The unit can include a rectifier to convert the
output to DC.
• It can have multiple coils tapped into at
various points internally for a series of
different outputs from one unit.
Transformers
Transformers
• They can be cooled, often in an oil bath.
• They are limited by the apparent power being
driven through them.
• Excessive power input or output can overheat
them.
• They can have different cores from iron to air.
Transformers
Transformers
• They can fully isolate one part of a circuit
from another such that electrons do not
actually travel through the transformer.
• or they can be wired such that the circuit is
not isolated.
• They are very efficient, loosing a little power
to heat and hysterisis.
• But they are inductors so will effect the
impedance of the AC circuit.
Transformers
Transformers
Transformers
Transformers
Transformers
Transformers
Transformers
Transformers
Transformers
• Transformers will cause the voltage of an AC
circuit to be 180° out of phase between the
primary and secondary windings.
• This is because the current is 90° out of
phase with the primary voltage and the
secondary voltage is 90° out of phase with
that current.
• Consequently a circuit with multiple
transformers must be designed to
accommodate phase effect.
Transformers
Transformers
• Another neat feature of transformers is that
they use almost no power when “idling” in an
AC circuit.
• In other words when there is no load on the
secondary circuit the counter EMF in the
primary cancels out almost all current flow in
that winding.
Transformers
• They can be single dual or three phase.
• Each winding will need a reciprocal winding.
Transformers
Transformers
Transformers
• Their cores will be laminated to reduce eddy
current effects.
• And they can have a core that moves into and
out of the coil.
• This makes it an adjustable transformer
which can be used to tune a circuit.
• Capacitors can also be made variable for the
same reason.
Transformers
Motors
• Motors are electronic devices. If it operates
by internal combustion it is properly called an
engine.
• Like a generator, the relationship of motion,
current flow and direction of the magnetic
lines of flux will determine what an electric
motor will do.
Motors
Motors
• Since the left hand rule for generators defines
current flow based upon motion direction a
reverse rule, the right hand rule for motors
defines the motion direction based upon
current flow.
• Each respective finger remains the same
with the index finger defining the lines of flux
from north to south, the thumb defines the
motion force, and the middle finger points to
the direction of current flow.
Motors
• This is because of the original left hand rule
which describes the behavior of flux around a
current carrying conductor.
• In this case the lines of force below the
conductor are in the same direction and
repel, while the lines above are opposite and
attract.
Motors
• Since this force applied will vary depending
on the direction the conductor travels, and
since the direction varies since the conductor
is on a rotating “armature” it would eventually
hit neutral force and then begin to reverse
force.
• So, more than one conductor is used, there is
a switching commutator, and the armature
has a lot of mass to ensure momentum.
Motors
Motors
• In some strategies they have more than one
brush assembly riding on the commutator.
• This allows more than one set of conductors
to apply torque at the same time, but it will
also require a second set of field poles.
Motors
• Motors, like anything, have different phases
of operation, and different operating needs to
meet each specific application.
• All will need special attention to start
spinning, some make their power through
high RPM and low torque, other have a
reverse need.
• Some are also combined with a generator
function.
Motors
• Like generators there are permanent magnet
and electro magnet motors.
• Typically permanent mag motors are only
used in small unit application.
• Whereas high load/torque units usually utilize
electro magnetic fields.
• These can also be wired in series or parallel
with the armature, or both with a split field.
Motors
• Like generators, motors a have problems
with armature reaction.
• They also generate counter EMF as a result
of their motion.
• This is in fact what limits their maximum
speed.
• As a motor approaches this maximum no
load speed it’s current flow will reduce to very
little.
Motors
• If load is applied, RPM will reduce, current
flow will increase attempting to reestablish
EMF and counter EMF balance.
• As load is increased, RPM is decreased, and
current is increased.
Motors
• In a series wound motor all the current
travels through both the field and armature.
• This allows for a very high torque at low
speeds.
• This is a good design for high load low speed
such as a starter motor.
• But these don’t limit well and will go to very
high speed if not loaded.
• Field windings are heavy with fewer turns.
Motors
Motors
Motors
Motors
• In a parallel, or shunt would motor the field is
wound with finer wire since there is no
armature in line to provide resistance.
• Consequently these motors don’t start well,
but are fairly stable in “cruise” RPM.
• These units are often known as constant
speed motors, although they do vary RPM
slightly due to changes in load.
Motors
Motors
• But, they will need some strategy to get
started.
• One is to unload them during start, another is
to include a small series field to assist
starting, or they may have alternative starting
strategies if they are an AC motor.
Motors
Motors
• DC motors are easily reversible.
• Just switch the lead polarity of either the field
or the armature.
• Switching the polarity of both will net the
same direction of rotation due to the right
hand rule.
Motors
Motors
• This is very easy in a permanent magnet
motor.
• One way would be to have two opposite
would fields in the motor, picking one for each
direction.
• This is common for things like landing gear or
flap motors.
Motors
Motors
• Brush, commutator and bearing maintenance
is the same as that of a generator.
• Brush arcing may be more of a problem in
motors with a high variability of load.
• Brush phase is critical to RPM and load due
to armature reaction.
Motors
•
Some units incorporate the use of magnetic brakes
and clutches.
• This allows for a greater control during either starting
or stopping the unit.
• Can be used to prevent undue binding on the
mechanical linkage connected to the motor or may
disengage the motor when not needed as in the case
of the bendix drive used in starter motors.
• They may also incorporate speed or thermal limiting
devices.
Motors
Motors
Motors
• Many motors are duty limited.
• They can produce more heat then they can
reject during a given period of operation.
• Starter motors, and landing gear motors my
be an example of this.
Motors
• Not all motors are designed to output rotating
motion.
• Some put out linear motion.
• The simplest of these is the solenoid which is
a coil around a movable core.
• A spring moves the core one way, and the
energized field moves it the other way.
Motors
• Another type does spin, but this spinning
drives an internal worm gear which then gives
high torque linear motion.
• This is also a torque increasing gear
reduction system which is often used in both
linear and rotary motors.
Motors
• Although the previous discussion pertains to
both DC and AC motors, the two are very
different.
• The AC motor comes in tow main categories:
the induction motor, and the synchronous
motor.
• These can be single, two, or three phase
motors. (one could go with more phases but the added
complexity would not derive much benefit)
Motors
Motors
• In general the advantage of AC is that one
can get more power for less weight.
• The down side is batteries don’t do AC
without help.
• They also don’t self start as well as DC units
with equal torque load.
• A third type, the universal motor, works on
both AC and DC, but these are not efficient,
particularly at 400hz
Motors
• In essence the induction motor self induces
current in the armature, there are no brushes.
• This is done by winding the fields with each
phase of the AC generator in a staggered
manner much like the generator is wound.
• This causes each respective field generated
by the phase current to increase and
decrease in a manner that emulates a flow
around the field perimeter.
Motors
Motors
• This is similar to a row of lights with each bulb
sequentially turned on so that it looks like the
‘light’ moves along the path of bulbs.
• In truth, there is no flow, each bulb simply
turns on and off in phase.
Motors
Motors
• The rotor in this motor is a can shape with
copper bars running the length connected
together at the ends via a ring.
• As the current changes in the surrounding
field it induces current in these copper bars.
• The resultant flux will cause the bars to try to
follow the field until it reaches neutral.
• As such, higher “slip” causes more torque.
Motors
Motors
• So, as the load is increased, RPM is
decreased causing more slip, causing more
rotor current, causing more force to catch up
with the field.
Motors
• Self starting for AC motors is a challenge,
particularly single phase units.
• They are often coupled with a tickler winding
that is wired in series with a large electrolytic
capacitor.
• The capacitor splits the current phase from
the normal one causing those windings to pull
more at zero to low RPM.
• A centrifugal switch cuts out this winding.
Motors
Motors
• Another strategy is to split the field poles
slightly with a magnetically shaded side.
• This in effect curves the magnetic lines
causing them to pull at an angle slightly off
from the center of rotation.
• These units are very low torque starting and
have been replaced by the Cap start units.
Motors
• A synchronous motor is one where the AC
field is the same as the induction unit, but the
armature doesn’t self induce.
• It has DC applied to the rotor so it will stay
right in phase with the induction windings
since it needs no slip to induce rotor current.
• Typically uses 3 phase current, with a rectifier
to produce the rotor DC.
Motors
• Rotor speed in an AC motor is a function of
the AC hz, as well as the current being
applied and the load being driven.
• Like their DC counterparts as the load
increases current increases, heat generation
increases and melt down will eventually
happen.
Motors
•