Title: Lecture Notes
1ECE 206L
1
2DC Current vs. AC Current
- Direct current (DC) flows in one direction the
circuit. - Alternating current (AC) flows first in one
direction then in the opposite direction. - The same definitions apply to alternating voltage
(AC voltage) - DC voltage has a fixed polarity.
- AC voltage switches polarity back and forth.
- There are numerous sources of DC and AC current
and voltage. However Sources of DC are commonly
shown as a cell or battery, and for the AC
current Generators
2
3The Sinusoidal AC Waveform
- The most common AC waveform is a sine (or
sinusoidal) waveform. - The vertical axis represents the amplitude of the
AC current or voltage, in amperes or volts. - The horizontal axis represents the angular
displacement of the waveform. The units can be
degrees or radians. - The sine waveform is accurately represented by
the sine function of plane trigonometry y
rsinq - where y the instantaneous amplitude
- r the maximum amplitude
- q the horizontal
displacement
3
4DefinitionPeak and Peak-to-Peak Voltage
-
- Peak and peak-to-peak values are most often used
when measuring the amplitude of ac waveforms
directly from an oscilloscope display. - Peak voltage is the voltage measured from the
baseline of an ac waveform to its maximum, or
peak, level. Unit Volts peak (Vp) Symbol Vp - For a typical sinusoidal waveform, the positive
peak voltage is equal to the negative peak
voltage. Peak voltages are expressed without a
or - sign. -
- Peak-to-peak voltage is the voltage measured from
the maximum positive level to the maximum
negative level. Unit Volts peak-to-peak
(Vp-p) Symbol Vp-p - For a typical sinusoidal waveform, the
peak-to-peak voltage is equal to 2 times the peak
voltage. Peak-to-peak voltages are expressed
without a or - sign .
4
5Conversion
- Convert Vp to Vp-p Vp-p 2 Vp
- Convert Vp-p to Vp Vp 0.5Vp-p
- What is the peak-to-peak value of a sinusoidal
waveform that has a peak value of 10 V? - What is the peak value of a sine wave that has a
peak-to-peak value of 240 V?
5
6Instantaneous Current and Voltage
- i Ipsin?
- Where
- i instantaneous current in amperes Ip
the maximum, or peak, current in amperes ?
the angular displacement in degrees or radians - v Vpsin?
- Where
- v instantaneous voltage in volts Vp
the maximum, or peak, voltage in volts ? the
angular displacement in degrees or radians
6
7Average Voltage
- Average voltage is the average value of all the
values for one half-cycle of the waveform. Unit
Volts average (Vave) Symbol Vave - The average voltage of a sinusoidal waveform is
equal to 0.637 times its peak value. - Vave 0.637Vp
- The average voltage is determined from just one
half-cycle of the waveform because the average
value of a full cycle is zero. Average voltages
are expressed without a or - sign
7
8Average Voltage
- Convert Vp to Vave Vave 0.637Vp
- Convert Vave to Vp Vp 1.57Vave
- Determine the average value of a waveform that
measured 16 Vp. Ans 10.2 Vave - What is the peak value of a waveform that has an
average value of 22.4 V? Ans 35.1 Vp
8
9Root-Mean-Square (RMS) Voltage
-
- AC levels are assumed to be expressed as RMS
values unless clearly specified otherwise. - RMS voltage is the amount of dc voltage that is
required for producing the same amount of power
as the ac waveform. Unit Volts (V) Symbol
Vrms - The RMS voltage of a sinusoidal waveform is equal
to 0.707 times its peak value. - Vrms 0.707Vp
- In a dc circuit, applying 2 V to a 1 W resistance
produces 4 W of power. In an ac circuit,
applying 2 Vrms to a 1 W resistance produces 4 W
of power. - RMS voltages are expressed without a or -
sign.
9
10ConversionRoot-Mean-Square (RMS) Voltage
- Convert Vp to Vrms Vrms 0.707Vp
- Convert Vrms to Vp Vp 1.414Vrms
- Determine the RMS value of a waveform that
measures 15 Vp. Ans 10.6 V - Determine the peak value of 120 V.
. - (Assume 120 V is in RMS) Ans 170 Vp
10
11 Resistors in Series
11
12Resistors in Parallel
12
13Measuring Voltage
Total Voltage VR1VR2
13
14Voltage Dividers
The voltage is divided up in such that it is
proportional to the resistances of the resistors
in a series circuit.
14
15Statistical Evaluation of Measurement Data and
Errors
- Average or mean value of a set of measurement
- Deviation from the average value
- Average value of the deviation
- Standard deviation(from the concept of RMS)
- Probability of error size in one observation
16The Decibel (dB)
- The decibel, or dB, is a means of expressing
the gain of an active device (such as an
amplifier) or the loss in a passive device (such
as an attenuator or length of cable). It is
simply the ratio of output to input expressed in
logarithmic form. The decibel was developed by
the telephone company(Bel, to express the gain or
loss in telephone transmission systems.
17Calculating the Decibel (dB)
- Now, imagine for a moment what it would be like
to calculate the total gain of a string of
amplifiers. It would be a cumbersome task at
best, and especially so if there were portions of
the cascade which were lossy and reduced the
total gain, thereby requiring division as well as
multiplication. - log (A x B) log A log B
- log (A/B) log A - log B
- Using the Decibel
-
- G 10 log (Po/Pi) ,
- Where
- G Gain in dB
- Po Power output from the device
- Pi Power input to the device
- Ex. A length of coaxial transmission line is
being fed with 150 watts from a transmitter, but
the power measured at the output end of the line
is only 112 watts. What is the line loss in dB? - G 10 log (112/150)
- G 10 log 0.747
- G 10 (-0.127)
- G -1.27 dB
-
18Capacitors
- Capacitors consist of two plates with a
dielectric material in-between. When a potential
difference is placed across the plates, a charge
builds up until it is large enough to cause a
discharge across the plates through the material.
18
19Reading Capacitors
Larger capacitors have the number of microfarads
written on them directly. Smaller capacitors use
a code based on the number of picofarads. We
generally use microfarads, so XYZ
XY 10Z 10-6 mF
19
20Capacitors in Series
20
21Capacitors in Parallel
21
22Impedance vs. Resistance
- Resistance is a property of a material that
causes a reduction in the rate of flow of
electrons. - Impedance is the reduction in the rate of flow of
electrons caused by the material (resistance) AND
other the properties of the component involved
(reactance). - Resistors have no reactance. So the impedance of
a resistor is equal to its resistance only. - Reactance varies with the frequency of the input.
Resistance remains the same at all frequencies. - Both impedance and resistance are measured in
ohms.
23ImpedanceDefinition
- A general measure of how a component or group of
components pushes against the current flowing
through it. - Impedance resistance reactance
- Impedance is used to refer to the behavior of
circuits with resistors, capacitors and other
components. - When we consider components in a theoretical
circuit diagram, the impedance of inductors and
capacitors is their reactance only. Any
resistance is modeled separately as a resistor.
So theoretical capacitors and inductors have
impedance, but no resistance.
24Capacitor Impedance
Real capacitors have effectively no resistance,
so impedance is reactance for all capacitors.
24
25What is Reactance
- Reactance is the property of resisting or
impeding the flow of ac current or ac voltage in
inductors and capacitors. Note particularly we
speak of alternating current only ac, which
expression includes audio af and radio
frequencies rf. NOT direct current dc. - Inductive Reactance
- When ac current flows through an inductance a
back emf or voltage develops opposing any change
in the initial current. This opposition or
impedance to a change in current flow is measured
in terms of inductive reactance. 2 pi f L - where 2 pi 6.2832 f frequency in hertz
and L inductance in Henries - Capacitive Reactance
- When ac voltage flows through a capacitance an
opposing change in the initial voltage occurs,
this opposition or impedance to a change in
voltage is measured in terms of capacitive
reactance. 1 / (2 pi f C) - where 2 pi 6.2832 f frequency in hertz
and C capacitance in Farads
26Some examples of Reactance
- What reactance does a 6.8 uH inductor present at
7 Mhz? Using the formula above we get - 2 pi f L
- where 2 pi 6.2832 f 7 X 106 Hz and L
6.8 X -6 Henries - Answer 299 ohms
- What reactance does a 33 pF capacitor present at
7 Mhz? Using the formula above we get - 1 / (2 pi f C)
- where 2 pi 6.2832 f 7 X 106 Hz and C
33 X -12 Farads - Answer 689 ohms
27Inductors
An inductor is a coil of wire through which a
current is passed. The current can be either AC
or DC.
27
28Inductors
This generates a magnetic field, which induces a
voltage proportional to the rate of change of the
current.
28
29Combining Inductors
- Inductances add like resistances
- Series
- Parallel
29
30Inductor Impedance
Real inductors always have a small resistance
(that is not shown in these circuits). The
impedance of the theoretical inductor shown is
only its reactance.
30
31Comparison of Components
32ImpedanceDefinition
- A general measure of how a component or group of
components pushes against the current flowing
through it. - Impedance resistance reactance
- Impedance is used to refer to the behavior of
circuits with resistors, capacitors and other
components. - When we consider components in a theoretical
circuit diagram, the impedance of inductors and
capacitors is their reactance only. Any
resistance is modeled separately as a resistor.
So theoretical capacitors and inductors have
impedance, but no resistance.
33Equipment Impedances
- Each measuring device changes the circuit when
you use it. - The impedance of the device helps you understand
how much. - Device Impedances
- Function Generator 50 ohms
- Scope 1Meg ohms
- DMM (DC voltage) 10Meg ohms
- DMM (AC voltage) 1Meg ohms
- DMM (DC current) 5 ohms (negligible)
33
34Effect of Impedance on Circuit
Function generator thinks it is putting out the
same thing.
Output is clearly different.
34
35Effect of Impedance on Circuit
The function generator has an output impedance of
much less than 50O, so we can ignore it.
35
36Kirchoffs Laws
sum of currents entering a junction is the same
as the sum of the currents leaving a junction
sum of voltages in any loop is zero
37Circuit Analysis (Combination Method)
38 SI Suffixes
pico p 10-12
nano n 10-9
micro ? (u) 10-6
milli m 10-3
Kilo k 103
Mega M (Meg) 106
Giga G 109
Tera T 1012
39Oscilloscope Tutorial
- The oscilloscope is basically a graph-displaying
device - It draws a graph of an electrical signal.
- In most applications the graph shows how signals
change over time - the vertical (Y) axis represents voltage
- the horizontal (X) axis represents time.
40Oscilloscopes
Horizontal sweeps at a constant rate. Vertical
plates are attached to an external voltage, the
signal you attach to the scope.
41Cathode Ray Tubes
Variation in potential difference (voltage)
placed on plates causes electron beam to bend
different amounts. Sweep refers to refreshing
repeatedly at a fixed rate.
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43Scope (Cont)
- This simple graph can tell you many things about
a signal - You can determine the time and voltage values of
a signal. - You can calculate the frequency of an oscillating
signal. - You can see the "moving parts" of a circuit
represented by the signal. - You can tell if a malfunctioning component is
distorting the signal. - You can find out how much of a signal is direct
current (DC) or alternating current (AC). - You can tell how much of the signal is noise and
whether the noise is changing with time.
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45How does an Analog Scope work?
46How does a Digital Scope work?
47Triggering Stabilizes a Repeating Waveform
48Waveform shapes tell you a great deal about a
signal
49If a signal repeats, it has a frequency. The
frequency is measured in Hertz (Hz) and equals
the number of times the signal repeats itself in
one second
50Voltage, Current, Phase
51Performance Terms
- Bandwidth
- The bandwidth specification tells you the
frequency range the oscilloscope accurately
measures. - Rise Time
- Rise time may be a more appropriate performance
consideration when you expect to measure pulses
and steps. An oscilloscope cannot accurately
display pulses with rise times faster than the
specified rise time of the oscilloscope. - Vertical Sensitivity
- The vertical sensitivity indicates how much the
vertical amplifier can amplify a weak signal.
Vertical sensitivity is usually given in
millivolts (mV) per division. - Sweep Speed
- For analog oscilloscopes, this specification
indicates how fast the trace can sweep across the
screen, allowing you to see fine details. The
fastest sweep speed of an oscilloscope is usually
given in nanoseconds/div. - Gain Accuracy
- The gain accuracy indicates how accurately the
vertical system attenuates or amplifies a signal.
- Time Base or Horizontal Accuracy
- The time base or horizontal accuracy indicates
how accurately the horizontal system displays the
timing of a signal. - Sample Rate
- On digital oscilloscopes, the sampling rate
indicates how many samples per second the ADC can
acquire. Maximum sample rates are usually given
in megasamples per second (MS/s). The faster the
oscilloscope can sample, the more accurately it
can represent fine details in a fast signal.. - ADC Resolution (Or Vertical Resolution)
- The resolution, in bits, of the ADC indicates how
precisely it can turn input voltages into digital
values. - Record Length
- The record length of a digital oscilloscope
indicates how many waveform points the
oscilloscope is able to acquire for one waveform
record.
52Grounding
- Proper grounding is an important step when
setting up to take measurements. - Properly grounding the oscilloscope protects you
from a hazardous shock and protects your circuits
from damage. - Grounding the oscilloscope is necessary for
safety. If a high voltage contacts the case of an
ungrounded oscilloscope, any part of the case,
including knobs that appear insulated, it can
give you a shock. However, with a properly
grounded oscilloscope, the current travels
through the grounding path to earth ground rather
than through you to earth ground. - To ground the oscilloscope means to connect it to
an electrically neutral reference point (such as
earth ground). Ground your oscilloscope by
plugging its three-pronged power cord into an
outlet grounded to earth ground. - Grounding is also necessary for taking accurate
measurements with your oscilloscope. The
oscilloscope needs to share the same ground as
any circuits you are testing. - Some oscilloscopes do not require the separate
connection to earth ground. These oscilloscopes
have insulated cases and controls, which keeps
any possible shock hazard away from the user.
53Scope Probes Most passive probes have some
degree of attenuation factor, such as 10X, 100X,
and so on. By convention, attenuation factors,
such as for the 10X attenuator probe, have the X
after the factor. In contrast, magnification
factors like X10 have the X first
54Vertical Controls
- Position and Volts per Division
- The vertical position control lets you move the
waveform up or down to exactly where you want it
on the screen. - The volts per division (usually written
volts/div) setting varies the size of the
waveform on the screen. A good general purpose
oscilloscope can accurately display signal levels
from about 4 millivolts to 40 volts. - Often the volts/div scale has either a variable
gain or a fine gain control for scaling a
displayed signal to a certain number of
divisions.
55Input Coupling
- Coupling means the method used to connect an
electrical signal from one circuit to another.
56Horizontal Controls
- Position and Seconds per Division
- The horizontal position control moves the
waveform from left and right to exactly where you
want it on the screen. - The seconds per division (usually written as
sec/div) setting lets you select the rate at
which the waveform is drawn across the screen
(also known as the time base setting or sweep
speed). This setting is a scale factor. For
example, if the setting is 1 ms, each horizontal
division represents 1 ms and the total screen
width represents 10 ms (ten divisions). Changing
the sec/div setting lets you look at longer or
shorter time intervals of the input signal.
57Trigger Position
- The trigger position control may be located in
the horizontal control section of your
oscilloscope. It actually represents "the
horizontal position of the trigger in the
waveform record." Horizontal trigger position
control is only available on digital
oscilloscopes. - Varying the horizontal trigger position allows
you to capture what a signal did before a trigger
event (called pretrigger viewing). - Digital oscilloscopes can provide pretrigger
viewing because they constantly process the input
signal whether a trigger has been received or
not. A steady stream of data flows through the
oscilloscope the trigger merely tells the
oscilloscope to save the present data in memory.
I - n contrast, analog oscilloscopes only display the
signal after receiving the trigger.
58Trigger Controls (cont)
59Pulse and Rise Time Measurements
60Multimeter tutorial
- A meter is a measuring instrument. An ammeter
measures current, a voltmeter measures the
potential difference (voltage) between two
points, and an ohmmeter measures resistance. - A multimeter combines these functions, and
possibly some additional ones as well, into a
single instrument.
61To measure current, the circuit must be broken to
allow theammeter to be connected in
series Ammeters must have a LOW resistance
62To measure potential difference (voltage), the
circuit is not changed the voltmeter is
connected in parallelVoltmeters must have a
HIGH resistance
63To measure resistance, the component must be
removed from the circuit altogether Ohmmeters
work by passing a current through the component
being tested
64Digital MultimetersDigital meters give an
output in numbers, usually on a liquid crystal
display.Most modern multimeters are digital and
traditional analogue types are destined to become
obsolete.Digital multimeters come in a wide
range of sizes and capability. Everything from
simple 3 ½ digit auto ranging pocket meters to
larger 8 ½ digit bench model with operator or
computer (IEEE488 compatible) settable range
selection
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66Function Generator
- An electronic instrument that generates various
waveforms such as - Sine wave
- Square wave
- Pulse trains
- Sawtooth
- The amplitude, DC offset, frequency are
adjustable.
67Function Generators (cont)
- Like multimeters there is a wide variety of
device offering various - Amplitude characteristics
- Bandwidth
- Adjustments of rise and fall times
- Modulation capability (AM, FM, Pulse, etc.)
68Power Supply
- This is the device that transfers electric power
from a source to a load using electronic
circuits. - Typical application of power supplies is to
convert utility's AC input power to a regulated
voltage(s) required for electronic equipment. - Depending on the mode of operation of power
semiconductors PS can be linear or switching. - In a switched-mode power supply, or SMPS power
handling electronic components are continuously
switching on and off with high frequency in order
to provide the transfer of electric energy. By
varying duty cycle, frequency or a phase of these
transitions an output parameter (such as output
voltage) is controlled. Typical frequency range
of SMPS is from 20 kHz to several MHz.
69Power Supply (cont)
- Power supplies like many of the other electronic
instruments, come in many varieties with a wide
range of capabilities - Parameters that are Power Supply specific
include - Voltage levels
- Current
- Regulation
- Protection
- Output impedance
- Noise (ripple)
- Its the designer (or researcher) responsibility
to identify the characteristics required.
70Oscilloscope
71Oscilloscope(continue)
72Capacitance (continue from before)
- A capacitor simply consists of two conductors
which are electrically isolated from one
another. This means that no current can readily
flow from one conductor to the other. - the units of the capacitance must equal one
coulomb per volt, which is defined to be one
farad, F - One Farad one(coulomb/volts)
- 1F1C/V
73RC Circuitsqualitative description
assume the switch is thrown to position B at the
time t 0. When the switch is at the position
B the circuit consists of the single loop which
contains, starting at point B and moving around
the circuit clockwise, the resistor R, the
capacitor C, and finally the voltage source
DVs. In this configuration the voltage source
attempts to push charge around the circuit in a
clockwise direction (remember that the power
source tries to push current out of its positive
terminal).
74RC Circuitsqualitative description(continue)
After some time at position B, we will throw the
switch to position A. (The time since the switch
was thrown to position A is called a new time t
. The prime on a symbol is used to denote
the fact that this is the value of the quantity
under consideration since the switch was thrown
to position A. It therefore follows that the
switch is thrown to the position A at the time t
0.) After the switch has been thrown to
position A the circuit consists solely of the
resistor and the capacitor, with no voltage
source. In this case there is no external energy
being used to move charges around the circuit
loop.
75RC Circuitsqualitative description(continue)
The behavior of the voltage across the capacitor
as a function of time and the current around the
circuit (and in particular, through the resistor)
as a function of time for the case in which the
switch has been thrown to position B. (This is
the case of the charging capacitor.) Then after
that is the case in which the switch has been
thrown to position A (the case of the discharging
capacitor).