Lesson 1
COMMUNICATIONS CIRCUITS
1.1 Pad/Attenuator
 A passive circuit that variably reduces the amplitude or power of a signal
without considerably distorting its waveform.
 Fixed
attenuators
which
are
called
pads
are
used
to
lower
voltage, dissipate power and improve impedance matching in circuits.
Insertion Loss, (IL) – a measure of attenuation introduced by the system in dB
Pin
I 2 in Z in
I
IL  10 log
 10 log 2
 20 log in
Pout
I out
I out Z out
Power Ratio, N
N 
Pin
 IL  10 log N
Pout
k 
I in
 IL  20 log k
I out
Current Ratio, k
N k2
Decibel (dB) Notation
The dB does not express exact amounts; instead, it represents the ratio of
the signal level at one point in a circuit to the signal level at another point in a
circuit.
1
LESSON 1 Communications Circuits
Generally,
dB x  multiplier  log
actual value
reference value
Specifically,
AP (dB )  10 log
Pout
Pin
A positive (+) dB value indicates that the output power is greater than the
input power which indicates a power gain. However, a negative (-) dB value
indicates that the output power is less than the input power which indicates power
loss or attenuation. The decibel originated as the Bel, named after Sir Alexander
Graham Bell. The Bel is expressed mathematically as
Bel  log
Pout
Pin
A dBm is a unit of measurement used to indicate a power level with respect
to 1mW. The dBm unit is expressed mathematically as
dB m  10 log
P
0.001W
Some common dB units
dBk
with reference to 1 kW
dBmV
with reference to 1 mV
dBW
with reference to 1 W
dBV
with reference to 1 V
dBm
with reference to 1 mW
dBi
with reference to isotropic level
dB
with reference to 1 W
dBd
with reference to dipole
dBn
with reference 1 nW
dBf
with reference to 1 femtowatt
2
LESSON 1 Communications Circuits
Classifications of Pad/Attenuator
A) According to Configuration
L-Type
T-Type
Bridged-T
Pi-Type
O-Type
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LESSON 1 Communications Circuits
H-Type
Bridged-H
k-Derived Equations
Resistance values for a designed attenuator/pad
k 1

 k 
R 1  Z O k  1
R5  Z O 
 k 

k 1
 1 

k  1
R6  Z O 
k 1

k  1
R7 
k  1

k  1
R 8  2Z O 
R2  Z O 
R3  Z O 
ZO k 2  1


2  k 

R4  Z O 
k
k
2


 1
B) According to Symmetry
 Symmetrical
T-pad, Pi-pad, O-Pad, H- pad, Bridged-T, and Bridged- H are all symmetrical
networks.
 Asymmetrical
L-pad is an example of a asymmetrical network.
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LESSON 1 Communications Circuits
C) Balanced/Unbalanced
 Balanced
O-Pad, H- pad, and Bridged- H are examples of a balanced network.
 Unbalanced
L-pad, T-pad, Pi-Pad, and Bridged-T are examples of an unbalanced network.
Network Impedances
Iterative Impedance - the impedance which when used to terminate one end of a
two-port network will make the impedance seen on the other end equal.
Adjusting the source impedance or the load impedance, in general, is called
impedance matching.
Iterative Impedance
If Z in  Z L then, Z L  Z iterative
If Z out  Z s then, Z s  Z iterative
Characteristic Impedance
For a symmetrical network, the characteristic impedance can be calculated as
Z o  Z SC Z OC
where:
Zo
=
characteristic impedance, (Ω)
ZSC
=
short-circuit impedance, (Ω)
ZOC
=
open-circuit impedance, (Ω)
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LESSON 1 Communications Circuits
1.2 Filters
 A filter is a frequency-selective circuit designed to pass some frequencies and
reject others.
 In filters, the range of frequencies that have a high output is called a
passband, and the range of frequencies that are attenuated or rejected is
called a stopband. The boundary frequency between a passband and a stop
band is called the cut-off frequency. The rate of transition from passband to
stopband and vice versa, given in dB/decade or dB/octave, is called the roll-
off rate.
Cut-off Frequency
A cut-off frequency is also the frequency at which the output power is 50% of the
maximum or the output amplitude is 70.7% of the maximum. Other terms for cutoff are critical frequency, corner frequency, break frequency and half-power point
frequency.
fC 
1
2 
where:
fc

=
cut-off frequency, (Hz)
=
time constant, (sec)

=
R*C for RC network, (sec)

=
L/R for RL network, (sec)
Frequency Response
 A graphical representation of the output with respect to frequency.
Ideal Frequency
6 Response Curve
LESSON 1 Communications Circuits
Practical Frequency Response Curve
Filter Construction
A) Based on Configuration
L-type
O-Type
T-Type
Pi-Type
B) Based on Order
 One method of creating a more selective filter is to cascade filter stages.
First Order
Second Order
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LESSON 1 Communications Circuits
C) Based on Materials Used
Passive
 Composed of only passive components (resistors, capacitors, and inductors),
and provides no amplification.
 At higher frequencies (above 100-kHz), it is more common to find LC filters
made of inductors and capacitors.
RC Passive Filter
RL Passive Filter
Active
 Typically employs RC networks and amplifiers with feedback and offers a
number of advantages
Active Filter Circuits
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LESSON 1 Communications Circuits
D) Based on Design
Butterworth
 Butterworth filters are termed maximally-flat-magnitude-response filters,
optimized for gain flatness in the pass-band and have slow transition.
Bessel
 Bessel filters are optimized for maximally-flat time delay (or constant-group
delay).
Chebyshev
 Chebyshev filters are designed to have a ripple in the passband, but they
have a steeper roll-off after the cut-off frequency.
Elliptic
 Has an almost perfect frequency response (very fast transition) but has
variations on both the passband and the stopband.
The Response Curves of the Major Families of Filters
Note
Consider high frequencies
Capacitive reactance
Inductive reactance
XC 
1
; f  ; XC  0
2fC
Consider low frequencies
XC 
1
; f  ; XC  
2fC
(shorted)
(open)
X L  2fL ; f  ; X L  
X L  2fL ; f  ; X L  0
(open)
(shorted)
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LESSON 1 Communications Circuits
E) Based on Frequency Response
Low-Pass Filter
 Passes frequencies below a critical frequency called the cut-off frequency and
attenuates those above.
Low-Pass Filter Frequency Response
High-Pass Filter
 Passes frequencies above critical frequency but rejects those below.
High-Pass Filter Frequency Response
Bandpass Filter
 Passes only frequencies in a narrow range between the upper and the lower
cut-off.
Bandpass Filter Frequency Response
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LESSON 1 Communications Circuits
Bandstop filter
 Rejects or stops frequencies in a narrow range but passes others.
Bandstop Filter Frequency Response
Interval is the ratio between the frequencies at two signals. An interval of 10:1 is
termed as decade while an interval of 2:1 is termed as octave.
 Audio Octaves with an interval of 2:1
10 Hz
fundamental
20 Hz
1st octave
40 Hz
2nd octave
80 Hz
3rd octave
 Audio Decades with an interval of 10:1
10 Hz
fundamental
100 Hz
1st decade
1 kHz
2nd decade
10 kHz
3rd decade
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LESSON 1 Communications Circuits
Low-Pass Filter Circuits
RC Low-Pass Filter
RL Low-Pass Filter
Notice the placement of the elements in the RC and the RL low-pass filters
 Consider the RC low-pass filter circuit and determine the following:
a) Output voltage, VO,
b) Voltage gain ratio, VO/VS,
c) Cut-off frequency, fC
Solution:
a) Using the voltage divider principle,
  jX C
 R  jX C
VO  V S 
VO




XC
 V S 
 R2  X 2
C





1
To simplify the equation, multiply a factor of 1 equivalent to
XC
1

 X 
C 

VO

XC
 V S 
 R2  X 2
C

12


1




XC



2

 
  1
  X C  


2
LESSON 1 Communications Circuits
VO



VS 




1
 R

 XC



2






1 

b) Voltage gain, Vo/VS becomes
AV 



 



VO
VS
1
 R

 XC



2






1 


c) To determine the cut-off frequency, remember that the gain at cut-off is
equal to 70.7% of the maximum so that
AVcutoff 
1
AV
2 max
The maximum gain for passive filter is 1, so the equation is reduced to
AVcutoff 
1
2
At cut-off, the voltage gain equation becomes



AV  



1
 R

 XC



2



 1

2

1 


Simplify and evaluate XC at the cut-off frequency.
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LESSON 1 Communications Circuits
 R
2  
 XC
2

  1

2
 R
2  
 XC

  1

 R
1  
 XC



2
The equation is reduced to X C  R
1
R
2 f C C
fC 
1
2 RC
High-Pass Filter Circuits
RC High-Pass Filter
RL High-Pass Filter
 Consider the RC high-pass filter circuit and determine the following:
a) Output voltage, VO,
b) Voltage gain ratio, VO/VS,
c) Cut-off frequency, fC
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LESSON 1 Communications Circuits
Solution:
a) Using the voltage divider principle,

R
 R  jX C
VO  V S 
VO




R
 V S 
 R2  X 2
C





1
To simplify the equation, multiply a factor of 1 equivalent to
1R 
2




1



R

R

2 
2
2


R  XC   1  
  R  
 
 



1

2 
X 
1   C  
 R  

V O  V S 


VO
R



VS 




b) Voltage gain, Vo/VS becomes
AV 



1


2
 1   X C 

 R 

VO
VS








c) To determine the cut-off frequency, remember that the gain at cut-off is
equal to 70.7% of the maximum so that
AVcutoff 
1
2
15
AV
max
LESSON 1 Communications Circuits
The maximum gain for a passive filter is 1, so that the equation is reduced to
AVcutoff 
1
2
At cut-off, the voltage gain equation becomes



1
AV  

2
 1   X C 

 R 




 1

2



Simplify and evaluate XC at the cut-off frequency.
X 
2  1  C 
 R 
X 
2 1   C 
 R 
X 
1  C 
 R 
2
The equation is reduced to X C  R
1
R
2 f C C
fC 
1
2 RC
16
2
2
LESSON 1 Communications Circuits
Band Pass Filter Circuit
The band pass filter circuit frequency response as shown is a combination of a high
pass filter and a low pass filter frequency response where f1 and f2 are the cut-off
frequencies.
Assumption: C1>>C2
Consider frequencies that are very low, and since X C 
and the circuit is now a high pass filter.
The cut-off frequency becomes f 1 
1
2R1C 1
17
1
, C2 becomes open
2 fC
LESSON 1 Communications Circuits
Now, consider frequencies that are very high and since X C 
1
, C1 becomes
2 fC
shorted and the circuit is now a low pass filter.
The cut-off frequency becomes f 2 
1
2R 2C 2
Shape Factor
 The shape factor of a filter is the ratio of the –60 dB bandwidth to its –3 dB
bandwidth.
Shape Factor 
BW60dB
BW3dB
Band Reject Filter (Wien Bridge)
18
LESSON 1 Communications Circuits
1.3 Resonance
 At any given coil and capacitor, as the frequency increases, the reactance
of the coil increases and the reactance of the capacitor decreases.
Because of these opposite characteristics, any LC combination should
have a frequency at which the inductive reactance of a coil equals the
capacitive reactance of the capacitor. This condition in an ac circuit where
XL equals XC is called resonance.
 Resonant circuits are the basis of all transmitter, receiver, and antenna
operation. Without these resonant circuits, radio communication would
not be possible.
Resonant Frequency
 The frequency at which the opposite reactances are equal
XL  XC
2f R L 
2
fR 
fR 
1
2f R C
1
( 2  ) 2 LC
1
2  LC
where:
fR
=
Resonant Frequency, (Hz)
XL
=
Inductive reactance, (Ω)
XC
=
Capacitive reactance, (Ω)
L
=
Inductance, (H)
C
=
Capacitance, (F)
19
LESSON 1 Communications Circuits
Series Resonance
 The series-resonant circuit across an ac source
In any series circuit, the same value of current flows in all parts of the circuit
at any instance. However, the inductive reactance leads by 90O compared with the
zero reference angle of the resistance, and the capacitive reactance lags by 90O.
Therefore, XL and XC are 180O out of phase.
Vector Diagram of the Currents and the Voltages
in a Series Resonant Circuit
Minimum Impedance at Series Resonance
 Since reactances cancel at resonant frequency, the impedance of the
series circuit is minimum and equal to the low value of the series
resistance. This minimum impedance at resonance is resistive, resulting in
a zero phase angle.
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LESSON 1 Communications Circuits
Reactance Curve of a Series Resonant Circuit
Maximum Current at Series Resonance
 The amount of current is greatest at the resonant frequency since impedance
is at its lowest at resonance. The response curve of the series resonant circuit
shows that the current is small and below resonance, rises to its maximum
value at resonant frequency, and then drops off to small values above
resonance.
Frequency Response of a Series Resonant Circuit
Resonant Rise in Voltage across L or C
 Since the current is the same in all parts of a series circuit, the maximum
current at resonance produces the maximum voltage IXC across C and an
equal IXL voltage across L for the resonant frequency.
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LESSON 1 Communications Circuits
Unity Power Factor
 Since the circuit acts as a purely resistive (zero-reactance) load to the source
at resonance, power factor is therefore equal to 1.
Parallel Resonance
 The parallel-resonant circuit across an ac source
In the parallel tuned circuit, the same voltage is across both the coil and the
capacitor. In the inductive branch, the current lags the source voltage by 90 O. In
the capacitive branch, the current leads the source voltage by 90O.
Because the line current is ideally zero at resonance, it should be possible to
disconnect the source and the current should continue to oscillate back and forth
between the coil and the capacitor indefinitely. This exchange of energy between
the inductor and the capacitor is called the flywheel effect and produces a
damped sine wave at the resonant frequency. The primary purpose of the parallel
tuned circuit is to form a complete ac sine wave output.
Maximum Line Impedance at Parallel Resonance
 Since reactances are equal at resonance, it follows that susceptances are also
equal and they cancel at resonant frequency; the admittance of the parallel
circuit is therefore minimum and thus produces maximum impedance. The
maximum impedance at resonance is resistive, resulting in a zero phase
angle.
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LESSON 1 Communications Circuits
Susceptance Curve of a Parallel Resonant Circuit
Minimum Line Current at Parallel Resonance
 The amount of current is least at the resonant frequency since impedance is
at its maximum at resonance. The response curve of the parallel resonant
circuit shows that the current is high below resonance, drops to its lowest
value at resonant frequency, and then rises again above resonance.
Frequency Response of a Parallel Resonant Circuit
Resonant Rise in Current through L and C
 The current through each reactance is equal to I = V/X and will usually be
greater than the source current.
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LESSON 1 Communications Circuits
Unity Power Factor
 Since the circuit acts as a purely resistive (zero-reactance) load to the source
at resonance, power factor is therefore equal to 1.
Quality Factor
 Q of a circuit is defined as the ratio of reactive power to the true power or
Q 
PQ
PR
 Q is also a measure of the band pass filter’s selectivity. A high Q indicates
that a filter selects a smaller band of frequencies (more selective). The quality
factor Q is defined as the ratio of resonant frequency to bandwidth or
Q 
fR
B
Q of a Series Circuit
 When the resistance is in series with any reactance (like in the case of a
series resonant circuit), an increase in resistance produces a lower Q.
PQ
IX L

PR
IR
X
2f R L
QS  L 
R
R
2L
QS 
R * 2 LC
QS 
QS 
L /C
R
24
LESSON 1 Communications Circuits
Q of a Parallel Circuit
 When a resistor is connected across a coil or capacitor reactance (like in the
case of a parallel resonant circuit), the effective Q of the circuit will vary
directly with the value of the resistance.
PQ V 2 / X L

PR V 2 / R
R
R
QP 

X L 2 f R L
Qp 
R * 2  LC
2 L
R
QP 
L/C
QP 
 A shunt resistor is often connected across a parallel LC circuit to lower its Q.
This makes the circuit less sensitive to being resonant at any one frequency
and broadens the frequency response.
Bandwidth

The frequency range over which a signal is transmitted or which a receiver or
other electronic circuit operates. One method of measuring the bandwidth is
to measure the width of either the voltage or the current response curve
between points at 0.707 maximum. Since power is proportional to voltage or
current squared, the 0.707 point is also the half-power point (0.7072 = 0.5)
or down 3 dB.
Thus, the bandwidth is normally measured between half-
power points, or –3 dB points.
BW 
fR
Q
Where:
fR
=
Resonant Frequency, (Hz)
Q
=
Quality Factor
BW
=
Bandwidth, (Hz)
25
LESSON 1 Communications Circuits
1.4 Review on Amplifiers
AF and RF Amplifiers
 The fundamental difference between the audio frequency amplifier and the
radio frequency amplifier is the band of frequencies they are expected to
amplify. True “high-fidelity” sounds would require circuits capable of handling
audio frequencies from as low as 15 to over 15000 Hz without distortion.
Most RF amplifiers amplify only a relatively narrow portion of the RF
spectrum, attenuating all other frequencies.
Power Amplifiers
 One or more low-level (low power) amplifiers may be required to drive the
input of a power amplifier adequately.
The first stage of an amplifying
system showed a low-noise type because all following stages will be
amplifying any noise that the system generates.
Class A
 A Class A amplifier is biased so that it conducts continuously for 360° of an
input sine wave. The bias is set so that the output never saturates or cuts-off.
In this way, its output is an amplified linear reproduction of the input. The
Class A amplifier is used primarily as small-signal voltage amplifiers or for
low-power amplifiers.
Class A Power Amplifier Input/ Output Signal
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LESSON 1 Communications Circuits
Class AB
 A Class AB amplifier is biased near cut-off. It will conduct for more than 180°
but for less than 360° of the input. It is used primarily in push-pull amplifiers
and provides better linearity than a Class B amplifier but with less efficiency.
Class B
 A Class B amplifier is biased at cut-off and conducts only one-half of the sine
wave input. This means that only one-half of the sine wave is amplified.
Normally, two Class B amplifiers are connected in a push-pull arrangement so
that both positive and negative alternations of the input are amplified
simultaneously.
Class B Power Amplifier Input/ Output Signal
Class C
 A Class C amplifier is one whose output conducts load current during less
than one-half cycle of an input sine wave.
The total angle during which
current flows is less than 180O. The Class C amplifier, being the most
efficient, makes a good power amplifier.
Class C Power Amplifier Input/ Output Signal
27
LESSON 1 Communications Circuits
Summary of Power Amplifier Characteristics
Class
Degree of Conduction
Maximum Efficiency
Distortion
A
360°
25%
low
AB
Greater than 180°but
less than 360°
Between 25% to
79%
medium
B
180°
79%
high
C
Less than 180°
100%
highest
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LESSON 1 Communications Circuits
1.5 Practice Problems
1) Convert an absolute power ratio of 100 to a power gain in dB.
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2) Convert a power level of 200mW to dBm.
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3) Determine the iterative impedance of the T-Pad and the H-pad.
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LESSON 1 Communications Circuits
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4) What is the insertion loss, IL, in dB of a symmetrical T-network whose series
arm is 50  and whose shunt arm is 200  when inserted in a circuit, whose
impedance is equal to the characteristic impedance of the network?
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LESSON 1 Communications Circuits
5) Design an H-pad with an iterative impedance of 300  and an insertion loss of
26 dB.
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6) Determine the iterative impedance of the Pi-Pad and the O- pad.
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LESSON 1 Communications Circuits
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7) Compute for the resistance values of an O-network for an iterative impedance
of 600  and an insertion loss of 35 dB.
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32
LESSON 1 Communications Circuits
8) What resistor value, R, will produce a cut-off frequency of 3.4 kHz with a
.047µF capacitor?
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9) Suppose that a low-pass filter has a cut-off frequency of 1 kHz. If the input
voltage for a signal at this frequency is 30 mV, what is the output voltage?
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10) Calculate the cut-off frequency, fc, and Vout at fc. Assume Vin = 10Vpp for all
frequencies.
R  10 k
Input voltage,
Vin
C  0.01F
Output voltage,
V out
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33
LESSON 1 Communications Circuits
11) Calculate the cut-off frequency, fc, and Vout at fc. Assume Vin = 10Vpp for all
frequencies.
L  50mH
Input voltage,
Vin
R  1k
Output voltage,
V out
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12) Calculate the resonant frequency for a 2µH inductance and a 3pF capacitance.
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13) What value of inductance, L, resonates with a 106pF capacitor at 1000 kHz?
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34
LESSON 1 Communications Circuits
14) If C is increased from 100 to 400pF, L should be decreased from 800µH to
________ for the same fR?
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15) For an fr of 500 kHz and a bandwidth of 10kHz, calculate Q.
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35
LESSON 1 Communications Circuits
1.6 Multiple Choice Questions
1) The phase angle of an LC circuit at resonance is
a. 0°
b. + 90°
c. 180°
d. -90°
2) Below resonance, a series LC circuit appears
a. inductive
b. resistive
c. capacitive
d. none of the above
3) Above resonance , a parallel LC circuit appears
a. inductive
b. resistive
c. capacitive
d. none of the above
4) A parallel LC circuit has a resonant frequency of 3.75 MHz and a Q of 125.
What is the bandwidth?
a. 15 kHz
b. 30 kHz
c. 60 kHz
d. none of the above
5) What is the resonant frequency of an LC circuit with values L=100  H and
C=63.3 pF?
a. 1 MHz

b. 8 MHz
c. 2 MHz
d. 20 MHz
36
LESSON 1 Communications Circuits
6) In an RC low-pass filter, the output is taken across the
a. resistor
b. inductor
c. capacitor
d. none of the above
7) On logarithmic graph paper, a 10 to 1 range of frequencies is called a (n)
a. octave
b. decibel
c. harmonic
d. decade
8) The cut-off frequency, fc, of a filter is the frequency at which the output is
a. reduced to 50% of its maximum
b. reduced to 70.7% of its maximum
c. practically zero
d. exactly equal to the input voltage
9) The decibel attenuation of a passive filter at the cut-off frequency is
a. -3 dB
b. 0 dB
c. -20 dB
d. -6 dB
10) To increase the cut-off frequency of an RL high-pass filter, one can
a. decrease the value of R
b. decrease the value of L
c. increase the value of R
d. both B and C
37