lecture 3: dc & ac circuit analysis - mechatronics engineering...
TRANSCRIPT
MEP 382: Design of Applied Measurement Systems
Lecture 3:
DC & AC Circuit Analysis
Faculty of EngineeringFaculty of EngineeringFaculty of EngineeringFaculty of Engineering
Outline
• Voltage and Current
• Ohm’s Law
• Kirchoff’s laws
• Resistors – Series and Parallel
• Voltage Dividers
• Capacitors, Inductors and R-C circuits
Basic Electrical Circuit
Voltage Source
Higher electrical Potential
Light
Heat
Lower Electrical Potential
•Voltage – difference in potential energy, Current flows from regions of higher electrical
potential to regions of lower electrical potential.
•Electrical Energy only flows in a closed path – closed system
•DC (Direct Current) are those circuits with static or slowly varying values.
•AC (Alternating Current) signals are those with rapid change or regular periodic change
•source of these terms is a historical artifact
•Wires are considered ideal – no resistance to flow of electrical energy
•The filament wire in the light bulb is a resistor that converts energy to light and heat
Simple Analogy• Voltage is a measure of electrical potential energy (units are volts)
– You can think of it as potential energy like water in a reservoir at the top of a hill
– The lowest energy state in the circuit is called Ground – standing water at the bottom of the hill
• Current is the flow of electrons from a high energy state to a lower energy state (units are amperes)
– You can think of it as water flowing through pipes from the top to the bottom of a hill
• Resistance is like narrow parts of the pipe (units are ohms)
– The more constrictions that are put in series, the slower the flow rate
– Total flow capacity is divided among parallel paths but the water has the same energy at the top and bottom of each parallel path
• Capacitance is like a little tank along the way (units are farads)
– Water (and potential energy in the form of a charge) can accumulate in the tank
• Just as the water’s potential energy is converted to kinetic energy (velocity) as it moves down the hill, so is electrical energy converted into other forms of energy along the way (heat, light, mechanical energy)
• If you take this analogy too far, it breaks down, but it is a good place to start
Water Analogy
Tank at the
top of the hill
Tank at the Bottom
of the Hill (Ground)
A voltage source
Is like a pump moving
water from low
potential energy (low
altitude) to higher
potential energy
(higher altitude)
Resistors are like pipes
Capacitors are like little
tanks along the way
Current Definitions
• Current is defined as flowing from higher potential energy to
lower potential energy
• This is often expressed as flow from + to –
• This convention existed before the discovery of the electron,
the basic atomic unit that carries electrical energy
• Electrons are negatively charged, so they actually flow from –
to +, the opposite of current
• In almost all applications, we use the concept of current as
our model/reference system
• Current is almost always represented by the variable I (i)
Voltage Sources – Series and Parallel
• In series, voltage sources add to increase voltage with no increase in current capacity
– Actual current may rise as voltage rises with a fixed resistive load
• In parallel, voltage sources do not increase voltage but they do increase the current capacity
– Exactly predicting the voltages requires a current loop analysis
1.5V
1.5V
1.5V1.5V
+
-
+
-3 volts
1.5 Volts
Kirchoff’s Laws
• Voltage– The sum of voltage drops and rises around
any path in a circuit in a closed path (start and end at the same point) must equal zero
– Since the voltage at any point in a circuit is an electrical energy potential, any path around the circuit must end up at the same energy potential or else the law of conservation of energy would be violated
• Current– The sum of all the current entering a node
of a circuit and leaving the node of a circuit must equal zero
• Since current is just the flow of electrons and electrons have an energy state and mass this is just a restatement of the laws of conservation of energy and conservation of mass
V
R
R
I
-.5V
-.5V
+V
i3 out = i1 + i2
i1 in
i2 in
Ohm’s Law• Voltage = Current x Resistance
• V = voltage, I = current, R = resistance
• V= IR, I = V/R, R = V/I – if you know 2 can calculate the third
• Almost every measuring circuit in this course will use this relationship
AA Battery
1.5 Volts1 KiloOhm resistor
Also called the Load
Current I = 1.5 Volts/1000 Ohms = .0015 amperes = 1.5 milliamps
Ω
+
-
Symbol for resistor
1.5 Volts
0 Volts
Short Circuits and Open Circuits
• A short circuit is when the + and – of a voltage source are directly connected with zero or essentially zero resistance
– A wire or a piece of metal can do this
– Due to Ohm’s law, when R is zero or near zero then current goes to infinity (V/R=I)
– This results in rapid heating and overloading the voltage supply
• An open circuit is when the + and – of a voltage source are not connected or connected by a very high resistance (> 100 Megaohms)
– In this case no current flows
Voltage Sources In Series and Parallel
Load
tot
Loadtot
R
VI
IRVVV
=
=+= 21
1.5V
1.5V
+
-
+
-
1.5V1.5V
R
Load
R
Load
I
Vtot
V1
V2
I1 I2
Itot
V1 V2Load
tot
Load
R
VIII
RIIVV
max21
2121 )(
=+=
+==Vmax
For parallel sources, Vmax is the highest of the two voltages. Exactly predicting the
voltages requires a current loop analysis
Property of material
Resistors – Series • Resistors in series add
• This type of circuit is a voltage divider – if resistors are equal the intermediate voltage will be half
V1
R1
R2 V3
Vtot
I
V2
)(
)(
)(
21
213
23
21
1
211
1
321
21
RR
RVV
IRV
RR
VI
RRIV
IRV
VVV
RRR
tot
tot
+=
=
+=
+=
=
+=
+=
Resistors - Parallel
• Resistors in parallel – add inverse
• This type of circuit is a current divider – if
resistances are equal, current down one leg is
half of the current of a single resistor
V R1 R2I1 I2
Itottot
tot
tot
R
V
R
V
R
VI
III
=+=
+=
21
21
V V
21
21
21
2
1...
111
RR
RRRtot
n
RRRR ntot
+=
=
++=
Voltage divider as the basis for instrumentation
Circuits• For all resistive sensors, the voltage divider is the primary circuit used in
instrumentation– Resistive sensors are those whose resistance value changes with
change in the measured quantity – e.g. Resistance Temperature Detector (RTD) resistance changes with
temperature, Strain Gage resistance changes with strain)
Known Resistor
(Rknown)
Resistive Sensor
(Rsensor)
Known
Voltage
(V1)
Voltage
Measurement
Proportional To
Sensor Value (V2)
)( 21
2
12
VV
RVeTemperaturR
RR
RVV
knownsensor
sensorknown
sensor
−=∝
+=
Sensors for Current• Two types of sensors are used for current- Ammeters
– A shunt – which is a precision very low resistance resistor over which a
voltage drop is observed
• Typically large blocks of metal to dissipate heat
• Must cause minimum additional voltage drop – typically 50-100
millivolts
– A clamp
• An inductive sensor which surrounds a wire converting the
electromagnetic field into a small AC current that can be read by a
smaller meter with a shunt
• Current through only one conductor is measured
– If put both in the meter, they cancel out
Use of Digital Multi Meter (DMM)
• To measure voltage (voltmeter function), measure ACROSS the load
– In parallel with the load
• To measure current (ammeter function), you have to measure through the load
– In series with the load
• To measure resistance (ohmmeter function), the circuit must be unpowered and then measure across the load
– You may have to remove the component to get an accurate reading as there may be other paths through the circuit that the ohmmeter function will measure
Load DMM
+
-
Using DMM as
voltmeter or
ohmmeter
DMM
+
-
Using DMM as ammeter
Resistor Color Code
Color 1st and 2nd Band 3rd Band
Black 0 x 1
Brown 1 x10
Red 2 x100
Orange 3 x1000
Yellow 4 x10,000
Green 5 x100,000
Blue 6 x1,000,000
Violet 7 x10,000,000
Gray 8 x100,000,000
White 9 x1,000,000,000
DC Power
• Power = Voltage x Current = VI• Since V=IR (Ohms Law), Power also = I^2R for purely
resistive direct current circuits– Direct current (DC) – where there is no periodic
change in voltage or current– Alternating current (AC) – where there is periodic
change in frequency and current• Power is in watts• A 9V battery with a 1000 ohm resistor (1 kilo-ohm)
across the terminals will have .009 amps running through it which will generate .081 watts
• A 9V battery with a 10 ohm resistor across it will have .9 amps which will generate 8.1 watts
Capacitors and Inductors• Capacitors store electrical energy in static charge
– Current is a function of the change in voltage with respect
to time
– Often made by a dielectric between two parallel plates
• Inductors store electrical energy in an electromagnetic field
– Voltage is a function of the change in current
– Often implemented by a coil of wire
Symbol for inductorSymbol for capacitor
Introduction To Capacitors• Capacitance of a device made from
two parallel plates separated by a dielectric is
– The dielectric constant times the area of the plate divided by the distance between the plates
– Capacitance is larger as the area of the plates increases and is smaller as the distance between the plates increases
– Capacitance measured in FARADS which are very large units of measure.
– Most electronic circuits uses capacitances in the micro-farad to picofarad range
– Most batteries are just special capacitors Energy stored in a capacitor
• One half of the capacitance times the voltage squared 2
2CV
E =
D
AC
ε=
Symbol for capacitor
Capacitors
• Can act as integrators and ac
filters
• Can act as differentiators and
DC blocks
R
C
C
R
Alternate
Symbol
for
capacitor
RC Circuit
• Is like filling a closed tank, current keeps flowing until the tank is full, and then it stops flowing
• Labview VI simulates and predicts this
AA Battery
1.5 Volts 1 KiloOhm
resistorΩ
1 microfarad
capacitor
Charge-Discharge of a 1 microfarad capacitor with a 1 MegaOhm resistor
Discharge initiated at t=2000 msec