Download Amateur Extra Licensing Class

Amateur Extra Licensing Class
Circuits & Resonance
for All!
Lake Area Radio Klub
Spring 2012
Amateur Radio Extra Class
Element 4 Course Presentation
 ELEMENT 4 Groupings
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•
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Rules & Regs
Skywaves & Contesting
Outer Space Comms
Visuals & Video Modes
Digital Excitement with Computers & Radios
Modulate Your Transmitters
Amps & Power Supplies
Receivers with Great Filters
Amateur Radio Extra Class
Element 4 Course Presentation
 ELEMENT 4 Groupings
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•
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Oscillate & Synthesize This!
Circuits & Resonance for All!
Components in Your New Rig
Logically Speaking of Counters
Optos & OpAmps Plus Solar
Test Gear, Testing, Testing 1,2,3
Antennas
Feedlines & Safety
Amateur Radio Extra Class
Circuits & Resonance for All!
•
Resonance can cause the voltage across reactances in series to
be larger than the voltage applied to them.
E5A01…
Let’s go through the math step by step………
Amateur Radio Extra Class
Circuits & Resonance for All!
1
XC 
xL  2FL
2FC
Resonance occurs in a circuit
1 when XL is equal to XC.
2FL 
2 πFC
Therefore…..
What we do to the left
side of the equation, we must
1 we do to the numerator
2 and what
do to the right side,
f 
we must do to the denominator,
2L2to
C maintain equality
f 
2
1
 2 
2
LC
Amateur Radio Extra Class
Circuits & Resonance for All!
f 
2
1
 2 
2
LC
1
o 
2π LC
f
This is the resonant frequency formula.
Amateur Radio Extra Class
Circuits & Resonance for All!
Resonance in an electrical circuit is the frequency at which the
capacitive reactance equals the inductive reactance.
•
E5A02…
•
E5A03…
The magnitude of the impedance of a series R-L-C circuit at
resonance is approximately equal to circuit resistance.
At resonance, a series resonant circuit L
and C present a low impedance so the
circuit resistance is set by the resistor.
•
The magnitude of the impedance of a circuit with a resistor, an
inductor and a capacitor all in parallel, at resonance is approximately
equal to circuit resistance.
E5A04…
At resonance, a parallel resonant
circuit presents a very high
impedance across the resistor.
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The magnitude of the current at the input of a series R-L-C circuit as
the frequency goes through resonance is Maximum.
E5A05…
At resonance a series circuit presents a low impedance and current would
be limited by the resistor Tuning to either side of resonance would cause
additional reactive resistance and therefore lower current flow in the circuit.
Series and Parallel Resonant Circuits.
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The magnitude of the circulating current within the components
of a parallel L-C circuit at resonance is at a maximum.
E5A06…
Variation of Inductive and capacitive reactance with frequency
(graph not to exact log-log scale)
Amateur Radio Extra Class
Circuits & Resonance for All!
The magnitude of the current at the input of a parallel R-L-C
circuit at resonance is at a Minimum.
•
E5A07…
•
E5A08…
•
E5A09…
The voltage and the current through and the voltage across a
series resonant circuit are in phase.
The current through and the voltage across a parallel resonant
circuit are in phase. (also true for a series circuit at resonance)
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The phase angle between the voltage across and the current
through a series R-L-C circuit if XC is 500 ohms, R is 1 kilohm, and XL is
250 ohms is 14.0 degrees with the voltage lagging the current.
E5B07…
Tangent of θ = Y / X
Tangent of θ = 250/1000
Tangent of θ = .25
θ = 14.04°
Series RLC Circuits for Phase angle Calculations
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The phase angle between the voltage across and the current
through a series R-L-C circuit if XC is 100 ohms, R is 100 ohms, and XL
is 75 ohms is 14 degrees with the voltage lagging the current.
E5B08…
Tangent of θ = Y / X
Tangent of θ = (75-100)/100
Tangent of θ = -.25
θ = -14.04°
Rules for calculating impedances and phase angles
1) Impedances in series add together
2) Admittance is the reciprocal of impedance
3) Admittances in parallel add together
4) Inductive and capacitive reactance in series cancel
5) 1/j=-j
Complex number
axis diagram.
Amateur Radio Extra Class
Circuits & Resonance for All!
•
Here is more detail. In an ac circuit, when calculating
the impedance of the circuit, the reactance and resistance
must be added vectorially rather than algebraically. This
vector addition can be understood best by looking at the
following diagram:
Vector Addition
Amateur Radio Extra Class
Circuits & Resonance for All!
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The relationship between the current through and the voltage
across a capacitor is that the current leads the voltage by 90 degrees.
E5B10… The relationship between the current through an inductor and
the voltage across an inductor is that the voltage leads current by 90
Remember: ELI the ICE man….
degrees.
E5B11… The phase angle between the voltage across and the current
through a series RLC circuit if XC is 25 ohms, R is 100 ohms, and XL is
50 ohms is 14 degrees with the voltage leading the current.
E5B09…
Tangent of θ = Y / X
Tangent of θ = (50-25)/100
Tangent of θ = .25
j 50
- j 25
100 Ω
θ = 14.04°
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The phase angle between the voltage across and the current
through a series RLC circuit if XC is 75 ohms, R is 100 ohms, and XL is
50 ohms is 14 degrees with the voltage lagging the current.
E5B12…
Tangent of θ = Y / X
j50
- j 75
Tangent of θ = (50-75)/100
Tangent of θ = -.25
100 Ω
θ = -14.04°
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The phase angle between the voltage across and the current
through a series RLC circuit if XC is 250 ohms, R is 1 kilohm, and XL is
500 ohms is 14.04 degrees with the voltage leading the current.
E5B13…
Tangent of θ = Y / X
Tangent of θ = (500-250)/1000
Tangent of θ = 0.25
j 500
- j 250
1000 Ω
θ = 14.04°
Amateur Radio Extra Class
Circuits & Resonance for All!
The Rectangular coordinate system is often used to display the
resistive, inductive, and/or capacitive reactance components of
impedance.
•
E5C13…
•
E5C09…
When using rectangular coordinates to graph the impedance of
a circuit, the horizontal axis represents the voltage or current
associated with the resistive component.
Amateur Radio Extra Class
Circuits & Resonance for All!
Rectangular Coordinates
Amateur Radio Extra Class
Circuits & Resonance for All!
Polar Coordinates
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In rectangular coordinates, what is the impedance of a network
comprised of a 10-microhenry inductor in series with a 40-ohm
resistor at 500 MHz?
E5C22…
R = 40Ω
XL= (2 π FL)
XL = (6.28 x 500 x 10+6 x 10 x 10-6)
XL = 31,416 Ω
Remember Inductive Reactance is positive so the answer is:
40 + j 31,400
•
In rectangular coordinates, the impedance of a circuit that has an
admittance of 5 millisiemens at -30 degrees is 173 + j100 ohms.
E5C17…
Polar Impedance (Z) =1/admittance
Z= 1/.005
Z= 200Ω
Polar angle = 1/admittance angle
= 1/- 30°
= +30°
Cos θ= resistance (R) / Impedance (Z) R = 200Ω x Cosine 30° R = 200Ω x .866 173.2 Ω
Sin θ= reactance (j) / Impedance (Z) j = 200 x Sine 30° j = 200Ω x .50
j100Ω
Don’t be tempted to use a “-j” in front of the reactance
with the admittance given initially with -30o angle.
Amateur Radio Extra Class
Circuits & Resonance for All!
When using rectangular coordinates to graph the impedance of
a circuit, the vertical axis represents the voltage or current associated
with the reactive component.
•
E5C10…
•
E5C11…
•
E5C12…
The two numbers used to define
a point on a graph using rectangular
coordinates represent the coordinate
values along the horizontal and
vertical axes.
If you plot the impedance of a circuit using the rectangular
coordinate system and find the impedance point falls on the right side
of the graph on the horizontal line, you know the circuit is equivalent
to a pure resistance.
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In Figure E5-2, point 4
best represents that impedance
of a series circuit consisting of a
400 ohm resistor and a 38
picofarad capacitor at 14 MHz.
E5C19…
R = 400 Ω
XC = 1/ (2 π FC)
XC= 1/(6.28 x 14 x .000038)
XC = -300 Ω
Remember:
Capacitive reactance is negative.
Figure E5-2
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In Figure E5-2, Point 3 best
represents the impedance of a
series circuit consisting of a 300
ohm resistor and an 18 microhenry
inductor at 3.505 MHz.
E5C20…
R =300 Ω
XL = (2 π FL)
XL = (6.28 x 3.505 x 18)
XL = 396.4 Ω
Remember:
Inductive reactance is positive
Answer is 300 Ω + j 395 Ω
Figure E5-2
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In Figure E5-2, Point 1 best
represents the impedance of a
series circuit consisting of a 300
ohm resistor and a 19 picofarad
capacitor at 21.200 MHz.
E5C21…
R = 300 Ω
XC = 1/ (2 π FC)
XC = 1/(6.28 x 21.2 x .000019)
XC = -395.1 Ω
Remember:
Capacitive reactance is negative
Answer is 300 Ω –j 395
Figure E5-2
Amateur Radio Extra Class
Circuits & Resonance for All!
•
On Figure E5-2, Point 8 best
represents the impedance of a
series circuit consisting of a 300ohm resistor, a 0.64-microhenry
inductor and an 85-picofarad
capacitor at 24.900 MHz.
E5C23…
R = 300 Ω
XC = 1/ (2 π FC)
XC = 1/(6.28 x 24.9 x .000085)
XC = -75.19 Ω (XC is negative)
XL = (2 π FL)
XL = (6.28 x 24.9 x .64)
XL = 100.12 Ω (XL is positive)
Net reactance is the sum of XC and XL
-75.19 + 100.12 = +24.9
Answer is 300 Ω + j 24.9
Figure E5-2
Amateur Radio Extra Class
Circuits & Resonance for All!
•
•
The Polar coordinate system is often used to display the phase
angle of a circuit containing resistance, inductive and/or capacitive
reactance.
E5C04… In polar coordinates, the impedance of a network consisting of a
400-ohm-reactance capacitor in series with a 300-ohm resistor is 500
ohms at an angle of -53.1 degrees.
E5C14…
Z= √(X² + (XL –XC)²)
Z= √( 300² + (0-400)²)
Z= √(250,000)
Z= 500 Ω
θ = arc tan (reactance/resistance)
arc tan (-400/300)
arc tan (- 1.33)
-53.13°
300Ω
-j400
Amateur Radio Extra Class
Circuits & Resonance for All!
Complex Numbers (Real and Imaginary and Operator j
Amateur Radio Extra Class
Circuits & Resonance for All!
j Operator as Vector Rotator
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In polar coordinates, the impedance of a network consisting of a
100-ohm-reactance inductor in series with a 100-ohm resistor is 141 ohms
at an angle of 45°.
E5C01…
Z= √(X² + Y²)
Z= √(100² + 100²)
j 100
Z= √( 20,000)
Z= 141.42 Ω
θ = arc tan (reactance/resistance)
arc tan 100/100
arc tan 1 or 45°
100 Ω
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In polar coordinates, the impedance of a network consisting of a
400-ohm-reactance inductor in parallel with a 300-ohm resistor is 240
ohms at an angle of 36.9 degrees.
E5C05…
Impedance =
=
θ = arctan 1/ (Reactance/Resistance)
θ= arctan 1/ (400 / 300)
θ= arctan 1/ 1.333
arctan =.750
θ =36.87°
= 120,000 / 500 = 240 Ω
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In polar coordinates, the impedance of a network consisting of a
100-ohm-reactance inductor, a 100-ohm-reactance capacitor, and a 100ohm resistor, all connected in series is 100 ohms at an angle of 0 degrees.
E5C02…
Z= √( R² + (XL –XC)²)
Z= √( 100² + (100-100)²)
Z= √( 10,000)
j 100
100 Ω
Z= 100 Ω
θ = arc tan (reactance/resistance)
arc tan 0/100
arc tan 0
- j 100
0°
Note- the Y side is the vector sum of the
inductive reactance and capacitive
reactance or (XL –Xc) j 100-j 100100 Ω
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In polar coordinates, the impedance of a network consisting of a
300-ohm-reactance capacitor, a 600-ohm-reactance inductor, and a 400ohm resistor, all connected in series is 500 ohms at an angle of 37
degrees.
E5C03…
Z= √(R² + (XL –Xc)²)
Z= √( 400² + (600-300)²)
Z= √( 250,000)
j 600
Z= 500 Ω
θ = arc tan (reactance/resistance)
300/400
arc tan .75
36.9°
- j300
400Ω
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In polar coordinates, the impedance of a network consisting of a
100-ohm-reactance capacitor in series with a 100-ohm resistor is 141
ohms at an angle of -45 degrees.
E5C06…
Z= √(X² + (XL –Xc)²)
Z= √( 100² + (-100)²)
Z= √(20,000)
•
Angle is arctan 1/ (reactance/resistance)
arctan 1/ (100/100)
arc tan (- 1)
-45°
Z= 141.4 Ω
E5C07… In polar coordinates, the impedance of a network comprised of
a 100-ohm-reactance capacitor in parallel with a 100-ohm resistor is
71 ohms at an angle of -45 degrees.
Admittance = 1/100 +( -j/100)
0.01 + j 0.01
Angle = arc tan .01/.01
45°
(-45° in polar coordinates)
Impedance = 1/ (√ ( (.01)² x (.01)² ))
1/(.0141)
70.71 Ώ
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In polar coordinates, the impedance of a network comprised of a
100-ohm-reactance capacitor in parallel with a 100-ohm resistor is 71
ohms at an angle of -45 degrees.
E5C07…
Admittance = 1/100 +(-j/100)
0.01 +j 0.01
Angle =arc tan .01/.01
45°
•
(-45° in polar coordinates)
Impedance = 1/ (√ ( (.01)² x (.01)² ))
1/(.0141)
70.71 Ώ
In polar coordinates, the impedance of a network comprised of a
300-ohm-reactance inductor in series with a 400-ohm resistor is 500 ohms
at an angle of 37 degrees.
E5C08…
Z= √(X² + (XL –XC)²)
Z= √( 400² + (0-300)²)
Z= √(250,000)
Z= 500 Ω
Angle is arc tan (X/R)
arc tan (300/400)
arc tan (.75)
j300
36.86°
400Ω
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In polar coordinates, the impedance of a circuit of 100 -j100 ohms
impedance is 141 ohms at an angle of -45 degrees.
E5C15…
Z= √(X² + (XL –XC)²)
Z= √( 100² + ( -100)²)
Z= √(20,000)
Z= 141.42 Ω
•
Angle is arc tan (X/R)
arc tan (-100/100)
arc tan (-1)
-45°
In polar coordinates, the impedance of a circuit that has an
admittance of 7.09 milli-siemens at 45 degrees is 141 ohms at an angle of
-45 degrees.
E5C16…
Polar Impedance (Z) =1/admittance
Polar angle = 1 / j (admittance angle)
Z= 1/.00709
1/j(45°)
Z= 141.04Ω
-j45°
Amateur Radio Extra Class
Circuits & Resonance for All!
•
In polar coordinates, the impedance of a series circuit
consisting of a resistance of 4 ohms, an inductive reactance of 4 ohms,
and a capacitive reactance of 1 ohm is 5 ohms at an angle of 37
degrees.
E5C18…
Z= √(X² + (XL –Xc)²)
-j1
Z= √( 4² + (4-1)²)
Z= √(25) or Z= 5 Ω
+j4
Angle is arc tan (X/R)
arc tan (3/4)
arc tan (.75)
36.86°
4Ω
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The bandwidth of the
circuit's frequency response
can be used as a relative
measurement of the Q for a
series-tuned circuit.
E4B17…
The Narrower the bandwidth the
higher the Q of the circuit.
A large loading coil on a
mobile whip helps antennas
achieve high Q resonance.
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The half-power bandwidth of a parallel resonant circuit that has
a resonant frequency of 1.8 MHz and a Q of 95 is 18.9 kHz.
E5A10…
B/W = Frequency/Q
1,800 KHz/95
18.94 KHz
For tuned circuits
the quality factor,
Q, is:
For tuned
circuits with Q
greater than 10:
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The half-power bandwidth of a parallel resonant circuit that has a
resonant frequency of 7.1 MHz and a Q of 150 is 47.3 kHz.
E5A11…
B/W = Frequency/Q
7,100 KHz/150
47.3 KHz
An amplifier’s voltage gain will
vary with frequency. At the cutoff
frequencies, the voltage gain drops
to 0.070 of what is in the mid-band.
These frequencies f1 and f2 are
called the half-power frequencies.
If the output voltage is 10 volts
across a 100-ohm load when the
gain is A at the mid-band, then
the power output, PO at mid-band
is:
Amateur Radio Extra Class
Circuits & Resonance for All!
•
At the cutoff frequency, the output voltage will be
0.707 of what is at the mid-band; therefore, 7.07 volts.
The power output is:
Power Ratio in dB
The power output at the cutoff frequency points is
one-half the mid-band power. The half-power
bandwidth is between the frequencies f1 and f2.
The power output at
the 0.707 frequencies
is 3 dB down from the
mid-band power.
The half-power bandwidth of a parallel resonant circuit that has a
resonant frequency of 3.7 MHz and a Q of 118 is 31.4 kHz.
E5A12…
B/W = Frequency/Q
3,700 KHz/118
31.36 KHz
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The half-power bandwidth of a parallel resonant circuit that has
a resonant frequency of 14.25 MHz and a Q of 187 is 76.2 kHz.
E5A13…
B/W = Frequency/Q
•
14,250 KHz/187
76.20 KHz
The resonant frequency of a series RLC circuit with R of 22 ohms,
L of 50 microhenrys and C of 40 picofarads is 3.56 MHz.
E5A14…
50 mh
The equation can be solved with:
L in Henries or Micro Henries and
C in Farads or Micro Farads
22 ohms
40 pf
1
1
FR =
2π
=
LxC
6.28 x
50x10^-6 x 40 x10^-12
= 3.56 MHz
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The resonant frequency of a series RLC circuit with R of 56
ohms, L of 40 microhenrys and C of 200 picofarads is 1.78 MHz.
E5A15…
1
1
FR =
2π
•
=
LxC
6.28 x
= 1.78 MHz
The resonant frequency of a parallel RLC circuit with R of 33
ohms, L of 50 microhenrys and C of 10 picofarads is 7.12 MHz.
E5A16…
1
1
FR =
2π
•
40x10^-6 x 200x10^-12
=
LxC
= 7.121 MHz
6.28 x
50x10^-6 x 10x10^-12
The resonant frequency of a parallel RLC circuit with R of 47
ohms, L of 25 microhenrys and C of 10 picofarads is 10.1 MHz.
E5A17…
1
1
FR =
2π
=
LxC
= 10.1 MHz
6.28 x
25x10^-6 x 10x10^-12
Amateur Radio Extra Class
Circuits & Resonance for All!
•
One time constant is the term for the time required for the
capacitor in an RC circuit to be charged to 63.2% of the supply voltage.
E5B01…
Schematics
Curves
Amateur Radio Extra Class
Circuits & Resonance for All!
•
One time constant is the time it takes for a charged capacitor in an
RC circuit to discharge to 36.8% of its initial value of stored charge.
E5B02…
Conversely a time constant is the time it takes a discharged
capacitor to reach 63.2% of the applied voltage.
Time Constants
Charge % of applied voltage
Discharge % of starting voltage
1
63.20%
36.80%
2
86.50%
13.50%
3
95.00%
5.00%
4
98.20%
1.80%
5
99.30%
0.70%
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The capacitor in an RC circuit is discharged to 13.5% percentage of
the starting voltage after two time constants.
E5B03…
%= (100-((100 x .632)) – (100 – (100 x.632) x .632))
100+(- 63.2 – 23.25)
13.54%
•
The time constant of a circuit having two 220-microfarad capacitors
and two 1-megohm resistors all in parallel is 220 seconds.
E5B04…
TC (seconds) = R (megohms) x C (microfarads)
TC =(1/2) x (220 x 2)
0.5 x 440
220 seconds
Remember that capacitors in parallel add and resistors of equal value in
parallel are equal to one resistor divided by the number of resistors.
Amateur Radio Extra Class
Circuits & Resonance for All!
•
It will take .020 seconds (or 20 milliseconds) for an initial
charge of 20 V DC to decrease to 7.36 V DC in a 0.01-microfarad
capacitor when a 2-megohm resistor is connected across it.
E5B05…
To discharge to 7.36 VDC would take one time constant
20V – (.632 x 20V)
7.36 Volts
TC = 2 x .01
0.02 seconds
20 milliseconds
•
It takes 450 seconds for an initial charge of 800 V DC to
decrease to 294 V DC in a 450-microfarad capacitor when a 1megohm resistor is connected across it.
E5B06…
To discharge to 294 VDC would take one time constant
800V – (.632 x 800V) = 294.4V
TC = 1 x 450
450 seconds
Amateur Radio Extra Class
Circuits & Resonance for All!
•
As frequency increases, RF current flows in a thinner layer of the
conductor, closer to the surface this is called skin effect.
E5D01…
RF
UHF
Current flow in cross section of a conductor
The resistance of a conductor is different for RF currents than for
direct currents because of skin effect.
•
E5D02…
•
E5D03…
•
A capacitor is a device that is used to store electrical energy in an
electrostatic field.
E5D04… The Joule is the unit of electrical energy stored in an electrostatic
field.
A Joule is defined as a quantity of energy equal to one Newton of force acting over 1 meter
Amateur Radio Extra Class
Circuits & Resonance for All!
•
•
The region surrounding a magnet through which a magnetic force
acts is a magnetic field.
E5D06… The direction of the magnetic field oriented about a conductor in
relation to the direction of electron flow is in a direction determined by
the left-hand rule.
E5D05…
Direction of
Magnetic
Field
Left-Hand Rule
Magnetic Field
surrounding
wire
Wire or Conductor
with current
through it
Amateur Radio Extra Class
Circuits & Resonance for All!
•
•
•
•
•
The amount of current determines the strength of a magnetic field
around a conductor.
E5D08… Potential energy is the term for energy that is stored in an
electromagnetic or electrostatic field.
E5D09… Reactive power is the term for an out-of-phase, nonproductive
power associated with inductors and capacitors.
E5D10… In a circuit that has both inductors and capacitors the reactive
power is repeatedly exchanged between the associated magnetic and
electric fields, but is not dissipated. (assuming perfect lossless components)
E5D11… The true power can be determined in an AC circuit where the
voltage and current are out of phase by multiplying the apparent power
times the power factor.
E5D07…
Apparent power is the voltage times the current into the circuit
True Power is the apparent power times the power factor
The only time true power and apparent power are the same is if the power factor
is 1.00 … (the phase angle is zero)
Amateur Radio Extra Class
Circuits & Resonance for All!
Apparent and True Power
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The power factor (PF) of an R-L circuit having a 60 degree phase
angle between the voltage and the current is 0.5.
E5D12…
PF is the cosine function of the voltage to current angle
►PF =cosine of 60°
PF= 0.5
•
80 watts are consumed in a circuit having a power factor of 0.2 if the
input is 100-V AC at 4 amperes.
E5D13…
Power Consumed = V x I x PF
100 x 4 x .2
80 watts
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The power is consumed in a circuit consisting of a 100 ohm
resistor in series with a 100 ohm inductive reactance drawing 1
ampere is 100 Watts.
E5D14…
Power (real) = I² x R
Power (real) = (1)² x 100
100 watts. (Only the circuit resistance consumes power)
•
E5D15…
•
E5D16…
Wattless, nonproductive power is reactive power.
The power factor of an RL circuit having a 45 degree phase
angle between the voltage and the current is 0.707.
PF = Cosine of 45°
PF = 0.707
Amateur Radio Extra Class
Circuits & Resonance for All!
•
The power factor of an RL circuit having a 30 degree phase
angle between the voltage and the current is 0.866.
E5D17…
PF Cosine of 30°
PF = 0.866
•
600 watts are consumed in a circuit having a power factor of 0.6
if the input is 200V AC at 5 amperes.
E5D18…
Power Consumed = V x I x PF
200 x 5 x .6
600 watts
•
The power consumed in a circuit having a power factor of 0.71 if
the apparent power is 500 watts is 355 W.
E5D19…
Power Consumed = Apparent power x PF
500 x .71
355 watts
Amateur Radio Extra Class
Circuits & Resonance for All!
Conducted and radiated noise caused by an automobile
alternator can be suppressed by connecting the radio's power leads
directly to the battery and by installing Feed Through capacitors in
line with the alternator leads.
•
E4E04…
•
E4E05…
•
Noise from an electric motor can be suppressed by installing a
brute-force AC-line filter in series with the motor leads.
E6D08… Core permeability (for a given size core) is the property that
determines the inductance of a toroidal inductor with a 10-turn
winding.
Amateur Radio Extra Class
Circuits & Resonance for All!
The usable frequency range of inductors that use toroidal cores,
assuming a correct selection of core material for the frequency being
used is from less than 20 Hz to approximately 300 MHz.
•
E6D09…
•
E6D10…
One important reason for using powdered-iron toroids rather than
ferrite toroids in an inductor is that powdered-iron toroids generally
have better temperature stability.
Applications for powdered Iron toroids would be oscillator and filter
circuits where inductance stability with temperature is important.
•
A primary advantage of using a toroidal core instead of a
solenoidal core in an inductor is that toroidal cores contain most of the
magnetic field within the core material.
E6D12…
Amateur Radio Extra Class
Circuits & Resonance for All!
•
Forty three turns of wire will be required to produce a 1-mH
inductor using a ferrite toroidal core that has an inductance index
(AL) value of 523 millihenrys/1000 turns.
E6D13…
N turns = 1000 x (√ (L / AL))
N turns = 1000 x (√ (1 / 523))
•
43.7 turns
E6D14… Thirty five turns of wire will be required to produce a 5microhenry inductor using a powdered-iron toroidal core that has an
inductance index (A L) value of 40 microhenrys/100 turns.
N turns = 100 x (√ (L / AL))
N turns = 100 x (√ (5 / 40))
•
35.35 turns
E6D18… One reason for using ferrite toroids rather than powdered-iron
toroids in an inductor is that Ferrite toroids generally require fewer
turns to produce a given inductance value.
Element 4 Extra Class
Question Pool
Circuits & Resonance for All!
Valid July 1, 2008
Through
June 30, 2012
What can cause the voltage across reactances in
series to be larger than the voltage applied to them?
E5A01
A. Resonance
B. Capacitance
C. Conductance
D. Resistance
E5A02
What is resonance in an electrical circuit?
A. The highest frequency that will pass
current
B. The lowest frequency that will pass
current
C. The frequency at which the capacitive
reactance equals the inductive reactance
D. The frequency at which the reactive
impedance equals the resistive
impedance
What is the magnitude of the impedance
of a series R-L-C circuit at resonance?
E5A03
A. High, as compared to the circuit
resistance
B. Approximately equal to capacitive
reactance
C. Approximately equal to inductive
reactance
D. Approximately equal to circuit resistance
What is the magnitude of the impedance of a
circuit with a resistor, an inductor and a capacitor
all in parallel, at resonance?
E5A04
A. Approximately equal to circuit resistance
B. Approximately equal to inductive reactance
C. Low, as compared to the circuit resistance
D. Approximately equal to capacitive reactance
What is the magnitude of the current at the input
of a series R-L-C circuit as the frequency goes
through resonance?
E5A05
A. Minimum
B. Maximum
C. R/L
D. L/R
What is the magnitude of the circulating current
within the components of a parallel L-C circuit at
resonance?
E5A06
A. It is at a minimum
B. It is at a maximum
C. It equals 1 divided by the quantity [ 2
multiplied by Pi, multiplied by the square
root of ( inductance "L" multiplied by
capacitance "C" ) ]
D. It equals 2 multiplied by Pi, multiplied by
frequency "F", multiplied by inductance "L"
What is the magnitude of the current at the
input of a parallel R-L-C circuit at resonance?
E5A07
A. Minimum
B. Maximum
C.R/L
D.L/R
What is the phase relationship between the
current through and the voltage across a series
resonant circuit?
E5A08
A. The voltage leads the current by 90
degrees
B. The current leads the voltage by 90
degrees
C. The voltage and current are in phase
D. The voltage and current are 180
degrees out of phase
What is the phase relationship between the
current through and the voltage across a parallel
resonant circuit?
E5A09
A. The voltage leads the current by 90
degrees
B. The current leads the voltage by 90
degrees
C. The voltage and current are in phase
D. The voltage and current are 180
degrees out of phase
What is the phase angle between the voltage
across and the current through a series R-L-C circuit
if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms?
E5B07
A. 68.2 degrees with the voltage leading the
current
B. 14.0 degrees with the voltage leading the
current
C. 14.0 degrees with the voltage lagging the
current
D. 68.2 degrees with the voltage lagging the
current
What is the phase angle between the voltage
across and the current through a series R-L-C circuit
if XC is 100 ohms, R is 100 ohms, and XL is 75 ohms?
E5B08
A. 14 degrees with the voltage lagging the
current
B. 14 degrees with the voltage leading the
current
C. 76 degrees with the voltage leading the
current
D. 76 degrees with the voltage lagging the
current
What is the relationship between the current
through and the voltage across a capacitor?
E5B09
A. Voltage and current are in phase
B. Voltage and current are 180 degrees
out of phase
C.Voltage leads current by 90 degrees
D. Current leads voltage by 90 degrees
What is the relationship between the current
through an inductor and the voltage across an
inductor?
E5B10
A. Voltage leads current by 90 degrees
B. Current leads voltage by 90
degrees
C. Voltage and current are 180
degrees out of phase
D. Voltage and current are in phase
What is the phase angle between the voltage
across and the current through a series RLC circuit
if XC is 25 ohms, R is 100 ohms, and XL is 50 ohms?
E5B11
A. 14 degrees with the voltage lagging the
current
B. 14 degrees with the voltage leading the
current
C. 76 degrees with the voltage lagging the
current
D. 76 degrees with the voltage leading the
current
What is the phase angle between the voltage
across and the current through a series RLC circuit
if XC is 75 ohms, R is 100 ohms, and XL is 50 ohms?
E5B12
A. 76 degrees with the voltage lagging
the current
B. 14 degrees with the voltage leading
the current
C.14 degrees with the voltage lagging
the current
D. 76 degrees with the voltage leading
the current
What is the phase angle between the voltage
across and the current through a series RLC circuit if
XC is 250 ohms, R is 1 kilohm, and XL is 500 ohms?
E5B13
A. 81.47 degrees with the voltage
lagging the current
B. 81.47 degrees with the voltage
leading the current
C. 14.04 degrees with the voltage
lagging the current
D. 14.04 degrees with the voltage
leading the current
What coordinate system is often used to display
the resistive, inductive, and/or capacitive
reactance components of an impedance?
E5C13
A.
B.
C.
D.
Maidenhead grid
Faraday grid
Elliptical coordinates
Rectangular coordinates
When using rectangular coordinates to graph
the impedance of a circuit, what does the horizontal
axis represent?
E5C09
A. The voltage or current associated
with the resistive component
B. The voltage or current associated
with the reactive component
C. The sum of the reactive and resistive
components
D. The difference between the resistive
and reactive components
In rectangular coordinates, what is the impedance
of a network comprised of a 10-microhenry inductor in
series with a 40-ohm resistor at 500 MHz?
E5C22
A. 40 + j31,400
B. 40 - j31,400
C. 31,400 + j40
D. 31,400 - j40
In rectangular coordinates, what is the
impedance of a circuit that has an admittance of 5
millisiemens at -30 degrees?
E5C17
A. 173 - j100 ohms
B. 200 + j100 ohms
C. 173 + j100 ohms
D. 200 - j100 ohms
When using rectangular coordinates to
graph the impedance of a circuit, what does
the vertical axis represent?
E5C10
A. The voltage or current associated
with the resistive component
B. The voltage or current associated
with the reactive component
C. The sum of the reactive and resistive
components
D. The difference between the resistive
and reactive components
What do the two numbers represent that are
used to define a point on a graph using rectangular
coordinates?
E5C11
A. The magnitude and phase of the
point
B. The sine and cosine values
C. The coordinate values along the
horizontal and vertical axes
D. The tangent and cotangent
values
If you plot the impedance of a circuit using the
rectangular coordinate system and find the impedance
point falls on the right side of the graph on the horizontal
line, what do you know about the circuit?
E5C12
A. It has to be a direct current circuit
B. It contains resistance and capacitive
reactance
C. It contains resistance and inductive
reactance
D. It is equivalent to a pure resistance
Which point on Figure E5-2 best represents that
impedance of a series circuit consisting of a 400 ohm
resistor and a 38 picofarad capacitor at 14 MHz?
E5C19
Figure E5-2
A. Point 2
B. Point 4
C. Point 5
D. Point 6
Point 3
Point 2
Point 8
Point 5
Point 6
Point 4
Point 7
Point 1
Which point in Figure E5-2 best represents the
impedance of a series circuit consisting of a 300 ohm
resistor and an 18 microhenry inductor at 3.505 MHz?
E5C20
Figure E5-2
A. Point 1
B. Point 3
C. Point 7
D. Point 8
Point 3
Point 2
Point 8
Point 5
Point 6
Point 4
Point 7
Point 1
Which point on Figure E5-2 best represents the
impedance of a series circuit consisting of a 300 ohm
resistor and a 19 picofarad capacitor at 21.200 MHz?
E5C21
A. Point 1
B. Point 3
C. Point 7
D. Point 8
Figure E5-2
Point 3
Point 2
Point 8
Point 5
Point 6
Point 4
Point 7
Point 1
Which point on Figure E5-2 best represents the impedance
of a series circuit consisting of a 300-ohm resistor, a 0.64-microhenry inductor and an 85-picofarad capacitor at 24.900 MHz?
E5C23
A. Point 1
B. Point 3
C. Point 5
D. Point 8
Figure E5-2
Point 3
Point 2
Point 8
Point 5
Point 6
Point 4
Point 7
Point 1
What coordinate system is often used to display
the phase angle of a circuit containing resistance,
inductive and/or capacitive reactance?
E5C14
A. Maidenhead grid
B. Faraday grid
C. Elliptical coordinates
D. Polar coordinates
In polar coordinates, what is the impedance of a
network consisting of a 400-ohm-reactance
capacitor in series with a 300-ohm resistor?
E5C04
A.
B.
C.
D.
240 ohms at an angle of 36.9 degrees
240 ohms at an angle of -36.9 degrees
500 ohms at an angle of 53.1 degrees
500 ohms at an angle of -53.1 degrees
In polar coordinates, what is the impedance of a
network consisting of a 100-ohm-reactance
inductor in series with a 100-ohm resistor?
E5C01
A. 121 ohms at an angle of 35 degrees
B. 141 ohms at an angle of 45 degrees
C. 161 ohms at an angle of 55 degrees
D. 181 ohms at an angle of 65 degrees
In polar coordinates, what is the impedance of a
network consisting of a 400-ohm-reactance
inductor in parallel with a 300-ohm resistor?
E5C05
A.
B.
C.
D.
240 ohms at an angle of 36.9 degrees
240 ohms at an angle of -36.9 degrees
500 ohms at an angle of 53.1 degrees
500 ohms at an angle of -53.1 degrees
In polar coordinates, what is the impedance of a net-work
consisting of a 100-ohm-reactance inductor, a 100-ohm-reactance
capacitor, and a 100-ohm resistor, all connected in series?
E5C02
A. 100 ohms at an angle of 90 degrees
B. 10 ohms at an angle of 0 degrees
C.10 ohms at an angle of 90 degrees
D. 100 ohms at an angle of 0 degrees
In polar coordinates, what is the impedance of a net-work
consisting of a 300-ohm-reactance capacitor, a 600-ohm-reactance
inductor, and a 400-ohm resistor, all connected in series?
E5C03
A.
B.
C.
D.
500 ohms at an angle of 37 degrees
900 ohms at an angle of 53 degrees
400 ohms at an angle of 0 degrees
1300 ohms at an angle of 180 degrees
In polar coordinates, what is the impedance of a
network consisting of a 100-ohm-reactance
capacitor in series with a 100-ohm resistor?
E5C06
A. 121 ohms at an angle of -25 degrees
B. 191 ohms at an angle of -85 degrees
C.161 ohms at an angle of -65 degrees
D. 141 ohms at an angle of -45 degrees
In polar coordinates, what is the impedance of a
network comprised of a 100-ohm-reactance
capacitor in parallel with a 100-ohm resistor?
E5C07
A. 31 ohms at an angle of -15 degrees
B. 51 ohms at an angle of -25 degrees
C. 71 ohms at an angle of -45 degrees
D. 91 ohms at an angle of -65 degrees
In polar coordinates, what is the impedance of a
network comprised of a 300-ohm-reactance
inductor in series with a 400-ohm resistor?
E5C08
A. 400 ohms at an angle of 27 degrees
B. 500 ohms at an angle of 37 degrees
C. 500 ohms at an angle of 47 degrees
D. 700 ohms at an angle of 57 degrees
In polar coordinates, what is the impedance of a
circuit of 100 -j100 ohms impedance?
E5C15
A. 141 ohms at an angle of -45 degrees
B. 100 ohms at an angle of 45 degrees
C. 100 ohms at an angle of -45 degrees
D. 141 ohms at an angle of 45 degrees
In polar coordinates, what is the impedance of a
circuit that has an admittance of 7.09 millisiemens
at 45 degrees?
E5C16
A. 5.03 x 10 –E05 ohms at an angle of 45 degrees
B. 141 ohms at an angle of -45 degrees
C. 19,900 ohms at an angle of -45 degrees
D. 141 ohms at an angle of 45 degrees
In polar coordinates, what is the impedance of a series
circuit consisting of a resistance of 4 ohms, an inductive
reactance of 4 ohms, and a capacitive reactance of 1 ohm?
E5C18
A.
B.
C.
D.
6.4 ohms at an angle of 53 degrees
5 ohms at an angle of 37 degrees
5 ohms at an angle of 45 degrees
10 ohms at an angle of -51 degrees
Which of the following can be used as a
relative measurement of the Q for a seriestuned circuit?
E4B17
A. The inductance to capacitance ratio
B. The frequency shift
C. The bandwidth of the circuit's frequency
response
D. The resonant frequency of the circuit
What is the half-power bandwidth of a parallel
resonant circuit that has a resonant frequency of 1.8
MHz and a Q of 95?
E5A10
A. 18.9 kHz
B. 1.89 kHz
C. 94.5 kHz
D. 9.45 kHz
What is the half-power bandwidth of a parallel
resonant circuit that has a resonant frequency of 7.1
MHz and a Q of 150?
E5A11
A. 157.8 Hz
B. 315.6 Hz
C.47.3 kHz
D.23.67 kHz
What is the half-power bandwidth of a parallel
resonant circuit that has a resonant frequency of 3.7
MHz and a Q of 118?
E5A12
A.
B.
C.
D.
436.6 kHz
218.3 kHz
31.4 kHz
15.7 kHz
What is the half-power bandwidth of a parallel
resonant circuit that has a resonant frequency of
14.25 MHz and a Q of 187?
E5A13
A. 38.1 kHz
B. 76.2 kHz
C. 1.332 kHz
D. 2.665 kHz
What is the resonant frequency of a series RLC
circuit if R is 22 ohms, L is 50 microhenrys and C is
40 picofarads?
E5A14
A. 44.72 MHz
B. 22.36 MHz
C. 3.56 MHz
D. 1.78 MHz
What is the resonant frequency of a series RLC
circuit if R is 56 ohms, L is 40 microhenrys and C is
200 picofarads?
E5A15
A.
B.
C.
D.
3.76 MHz
1.78 MHz
11.18 MHz
22.36 MHz
What is the resonant frequency of a parallel RLC
circuit if R is 33 ohms, L is 50 microhenrys and C is
10 picofarads?
E5A16
A. 23.5 MHz
B. 23.5 kHz
C. 7.12 kHz
D. 7.12 MHz
What is the resonant frequency of a parallel RLC
circuit if R is 47 ohms, L is 25 microhenrys and C is
10 picofarads?
E5A17
A. 10.1 MHz
B. 63.2 MHz
C. 10.1 kHz
D. 63.2 kHz
What is the term for the time required for the
capacitor in an RC circuit to be charged to 63.2% of
the supply voltage?
E5B01
A. An exponential rate of one
B. One time constant
C. One exponential period
D. A time factor of one
What is the term for the time it takes for a
charged capacitor in an RC circuit to discharge to
36.8% of its initial value of stored charge?
E5B02
A. One discharge period
B. An exponential discharge rate of one
C. A discharge factor of one
D. One time constant
The capacitor in an RC circuit is discharged to
what percentage of the starting voltage after two
time constants?
E5B03
A. 86.5%
B. 63.2%
C. 36.8%
D. 13.5%
What is the time constant of a circuit having two
220-microfarad capacitors and two 1-megohm
resistors all in parallel?
E5B04
A. 55 seconds
B. 110 seconds
C. 440 seconds
D. 220 seconds
How long does it take for an initial charge of 20 V DC to
decrease to 7.36 V DC in a 0.01-microfarad capacitor when a
2-megohm resistor is connected across it?
E5B05
A. 0.02 seconds
B. 0.04 seconds
C.20 seconds
D.40 seconds
How long does it take for an initial charge of 800 V DC to
decrease to 294 V DC in a 450-microfarad capacitor when a
1-megohm resistor is connected across it?
E5B06
A. 4.50 seconds
B. 9 seconds
C. 450 seconds
D. 900 seconds
E5D01
What is the result of skin effect?
A. As frequency increases, RF current flows
in a thinner layer of the conductor, closer
to the surface
B. As frequency decreases, RF current flows
in a thinner layer of the conductor, closer
to the surface
C. Thermal effects on the surface of the
conductor increase the impedance
D. Thermal effects on the surface of the
conductor decrease the impedance
Why is the resistance of a conductor different
for RF currents than for direct currents?
E5D02
A. Because the insulation conducts
current at high frequencies
B. Because of the Heisenburg Effect
C. Because of skin effect
D. Because conductors are nonlinear devices
What device is used to store electrical
energy in an electrostatic field?
E5D03
A. A battery
B. A transformer
C. A capacitor
D. An inductor
What unit measures electrical energy
stored in an electrostatic field?
E5D04
A. Coulomb
B. Joule
C. Watt
D. Volt
E5D05
What is a magnetic field?
A. Electric current through the space around
a permanent magnet
B. The region surrounding a magnet
through which a magnetic force acts
C. The space between the plates of a
charged capacitor, through which a
magnetic force acts
D. The force that drives current through a
resistor
In what direction is the magnetic field
oriented about a conductor in relation to the
direction of electron flow?
E5D06
A. In the same direction as the current
B. In a direction opposite to the current
C. In all directions; omnidirectional
D. In a direction determined by the lefthand rule
What determines the strength of a
magnetic field around a conductor?
E5D07
A. The resistance divided by the
current
B. The ratio of the current to the
resistance
C. The diameter of the conductor
D. The amount of current
What is the term for energy that is stored
in an electromagnetic or electrostatic field?
E5D08
A. Amperes-joules
B. Potential energy
C.Joules-coulombs
D.Kinetic energy
What is the term for an out-of-phase, nonproductive power associated with inductors and
capacitors?
E5D09
A. Effective power
B. True power
C. Peak envelope power
D. Reactive power
In a circuit that has both inductors and
capacitors, what happens to reactive power?
E5D10
A. It is dissipated as heat in the circuit
B. It is repeatedly exchanged between
the associated magnetic and electric
fields, but is not dissipated
C. It is dissipated as kinetic energy in
the circuit
D. It is dissipated in the formation of
inductive and capacitive fields
How can the true power be determined in
an AC circuit where the voltage and current
are out of phase?
E5D11
A. By multiplying the apparent power
times the power factor
B. By dividing the reactive power by
the power factor
C. By dividing the apparent power by
the power factor
D. By multiplying the reactive power
times the power factor
What is the power factor of an R-L circuit having
a 60 degree phase angle between the voltage and
the current?
E5D12
A. 1.414
B. 0.866
C. 0.5
D. 1.73
How many watts are consumed in a circuit
having a power factor of 0.2 if the input is
100-V AC at 4 amperes?
E5D13
A. 400 watts
B. 80 watts
C. 2000 watts
D. 50 watts
How much power is consumed in a circuit
consisting of a 100 ohm resistor in series with a 100
ohm inductive reactance drawing 1 ampere?
E5D14
A.
B.
C.
D.
70.7 Watts
100 Watts
141.4 Watts
200 Watts
E5D15
What is reactive power?
A. Wattless, nonproductive power
B. Power consumed in wire
resistance in an inductor
C. Power lost because of capacitor
leakage
D. Power consumed in circuit Q
What is the power factor of an RL circuit having
a 45 degree phase angle between the voltage and
the current?
E5D16
A. 0.866
B. 1.0
C. 0.5
D. 0.707
What is the power factor of an RL circuit having
a 30 degree phase angle between the voltage and
the current?
E5D17
A.
B.
C.
D.
1.73
0.5
0.866
0.577
How many watts are consumed in a circuit
having a power factor of 0.6 if the input is 200V AC
at 5 amperes?
E5D18
A.
B.
C.
D.
200 watts
1000 watts
1600 watts
600 watts
How many watts are consumed in a circuit
having a power factor of 0.71 if the apparent
power is 500 watts?
E5D19
A.
B.
C.
D.
704 W
355 W
252 W
1.42 mW
How can conducted and radiated noise
caused by an automobile alternator be
suppressed?
E4E04
A. By installing filter capacitors in series with the
DC power lead and by installing a blocking
capacitor in the field lead
B. By connecting the radio to the battery by the
longest possible path and installing a blocking
capacitor in both leads
C. By installing a high-pass filter in series with the
radio's power lead and a low-pass filter in
parallel with the field lead
D. By connecting the radio's power leads directly to
the battery and by installing coaxial capacitors
in line with the alternator leads
How can noise from an electric motor
be suppressed?
E4E05
A. By installing a ferrite bead on the AC line
used to power the motor
B. By installing a brute-force AC-line filter in
series with the motor leads
C. By installing a bypass capacitor in series
with the motor leads
D. By using a ground-fault current
interrupter in the circuit used to power the
motor
What material property determines the
inductance of a toroidal inductor with a 10turn winding?
E6D08
A.
B.
C.
D.
Core load current
Core resistance
Core reactivity
Core permeability
What is the usable frequency range of inductors
that use toroidal cores, assuming a correct selection
of core material for the frequency being used?
E6D09
A.
From a few kHz to no more than 30 MHz
B.
From less than 20 Hz to approximately 300 MHz
C.
From approximately 1000 Hz to no more than
3000 kHz
D.
From about 100 kHz to at least 1000 GHz
What is one important reason for using
powdered-iron toroids rather than ferrite
toroids in an inductor?
E6D10
A. Powdered-iron toroids generally have
greater initial permeabilities
B. Powdered-iron toroids generally have
better temperature stability
C. Powdered-iron toroids generally require
fewer turns to produce a given inductance
value
D. Powdered-iron toroids have the highest
power handling capacity
What is a primary advantage of using a
toroidal core instead of a solenoidal core in
an inductor?
E6D12
A. Toroidal cores contain most of the
magnetic field within the core material
B. Toroidal cores make it easier to couple
the magnetic energy into other
components
C. Toroidal cores exhibit greater hysteresis
D. Toroidal cores have lower Q
characteristics
How many turns will be required to produce a 1-mH
inductor using a ferrite toroidal core that has an inductance
index (A L) value of 523 millihenrys/1000 turns?
E6D13
A. 2 turns
B. 4 turns
C. 43 turns
D. 229 turns
How many turns will be required to produce a 5microhenry inductor using a powdered-iron toroidal core
that has an inductance index (A L) value of 40
microhenrys/100 turns?
E6D14
A. 35 turns
B. 13 turns
C. 79 turns
D. 141 turns
What is one reason for using ferrite
toroids rather than powdered-iron toroids in
an inductor?
E6D18
A. Ferrite toroids generally have lower initial
permeabilities
B. Ferrite toroids generally have better
temperature stability
C. Ferrite toroids generally require fewer
turns to produce a given inductance value
D. Ferrite toroids are easier to use with
surface mount technology