CALIFORNIA STATE UNIVERSITY NORTHRIDGE
HIGH FREQUENCY NARROW
BAND-PASS ACTIVE RC FILTERS USING ALL-PASS ELEMENTS
A graduate proje~t submitted in partial satisfaction
of the requirements for the degree of Master of Science in
Electrical Engineering
by
Shahriar Sadeghi
May 1987
The graduate project of Shahriar Sadeghi is approved:
Robert-tenderson
Nagwa Bekir
CALIFORNIA STATE UNIVERSITY NORTHRIDGE
ii
)
DEDICATION
I would like to dedicate this graduate project to my
parents, Najiollah and Asieh, for without their love and
support this work may never have been completed.
s.s.
iii
p •
ACKNOWLEDGEMENT
I wish to acknowledge my graduate advisor, Professor
Yuh Sun, not only for providing me with insight into the
theory of high frequency active filters but also for his
guidance and encouragement. I am also grateful to Professor
Robert Henderson who read and edited the entire draft of
the project. Special thanks to Professor Edmund Gillespie
and his son, Stanley Gillespie, for providing the test
equipment used in this project. I am also indebted to
Professor Nagwa Bekir for reviewing the project in such a
short time.
s.s.
iv
TABLE OF CONTENTS
page
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . .. . . . . . . . . .. . . . . . . . . . . . . . ..
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iii
Acknowledgement.
iv
List of
vi
List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
Abstract. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
I .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
l
I I.
Theory of Operation ...••..••..•.•.•••.•..•..••
6
III. Review of Narrow Band-Pass Filters Using AllPas s E 1 e me n t s . • • • . . • . • • • • • • • • . . • • • • • • . • • • . • • • •
10
IV.
Analysis and Design.
14
v.
Experimental Design ..
24
VI.
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . .
29
VII. Conclu'sion....................................
33
References.........................................
34
v
LIST OF FIGURES
Figures
page
1.
Ideal second order band-pass filter...........
36
2.
Root-locus plot for the narrow band
configuration of Fig. 1.......................
37
3.
Op-amp realization of the narrow band filter..
38
4.
Comer's discrete transistor version of the
narrow band filter............................
39
5.
6.
7.
8.
9.
Ideal all-pass using current controlled
current source................................
40
Ideal all-pass using voltage controlled
current source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
All-pass realization using bipolar transistor
as a voltage controlled current source........
42
Narrow band filter using all-pass circuit of
of Fig.
43
7.....................................
Root-locus plot for all-pass structure of
Fig. 7......................... .. .. . . . . . . . . . . .
44
10. All-pass using voltage controlled current
source........................................
45
11. All-pass using voltage controlled voltage
source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
12. Phase response for ideal, Comer's, and
proposed all-pass structures..................
47
13. General transistor amplifier..................
48
14.
Hybrid~
model for transistor amplifier of
Fig. 13.......................................
49
15. Variation of the transfer unity short circuit
current gain, fT, with Ic and Vee.............
50
16. Narrow band filter using broadbanding
technique.....................................
51
vi
17. SPICE program for the filter of Fig. 8 for
c = 161 pF, R = 150 ohm . . • . • . . • . • • . . . • . . . . . • • .
52
18. SPICE program for the filter of Fig. 8 for
c = 100 pF, R = 150 ohm • .•••.••••••••••.•.••••
56
19. SPICE program for the filter of Fig. 8 for
c = 75 pf, R = 150 ohm . ••••••••••..•.•••••.•••
60
20. Gain loss and phase response for the filter of
Fig. 16 for a feedback capacitance of 16lpF •..
64
21. Gain loss and phase response for the filter of
Fig. 16 for a feedback capacitance of lOOpF .••
65
22. Gain loss and phase response for the filter of
Fig. 16 for a feedback capacitance of 7 5pF .•.•
66
23. Gain loss and phase response for the filter of
Fig. 16 for a feedback capacitance of 16lpF
and a compensating capacitor of 10 OpF ..••.••.•
67
24. Gain loss and phase response for the filter of
Fig. 16 for a feedback capacitance of lOOpF
and a compensating capacitor of lOOpF .•....•••
68
25. Gain loss and phase response for the filter of
Fig. 16 for a feedback capacitance of 89pF
and a compensating capacitor of 10 0 pF •••.••.••
69
vii
1-
LIST OF TABLES
page
Tables
[1]
[2]
[3]
[4]
[51
[61
D.C. bias voltages of transistors in the
filter of Fig. 8.............. .. . . . . .. . . . . . .
70
D.C. bias voltages of transistors in the
filter of Fig. 1 6 . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
High frequency parameters for the
transistors of filter configuration of
Fig. 8 used for SPICE models................
72
The ideal, estimated and SPICE values of
center frequency and Q for the filter of
Fig. 8 for three different values of
feedback capacitance........................
73
The ideal, estimated and measured values of
quality factor and center frequency for
filter of Fig. 16 for three different
feedback capacitor.........................
74
The ideal and measured values of the center
frequency of the filter of Fig. 16 when a
compensating capacitor is used in the
emitter lead of the last gain stage........
75
viii
ABSTRACT
HIGH FREQUENCY NARROW BAND-PASS
ACTIVE RC FILTERS USING ALL-PASS ELEMENTS
by
Shahriar Sadeghi
Master of Science in Engineering
This graduate project explores the use of bipolar
transistors in designing an integrable high frequency(1 - 15MHz) narrow band active RC filter. The feasibility
of using first order transistor all-pass blocks in a
feedback configuration for generating a pair of complex
poles close to the jW axis (high Q realization) will be
investigated. An ideal model for the filter is first
considered and then an integrable circuit that resembles
the model closely is designed. The limitations due to
transistor's parasitic elements is taken into account and
estimation of filter's center frequency and quality factor
shift due to these parasitic effects is evaluated. Based
on these estimations the design is carried out in such a
ix
way that the deviation of the ideal and designed filter
parameters are minimized. This filter was first simulated
with SPICE and then constructed, measured and compared to
the ideal case. The final design led to a high frequency
narrow band filter that operates at the desired center
frequency of 10.7 MHz.
X
I.
INTRODUCTION
The advent of integrated circuits (IC), technology has
caused remarkable changes in the philosophy of filter
design. These changes are responsible for many proposed
methods for constructing integrable narrow band active
filters. Even though these methods are successful in
eliminating the inductor from the filter, most are
limited to low frequency (i.e. 0-1 HHz) operation.
Inductors are impossible to manufacture in monolithic form
and are incompatible with any of the modern techniques for
assembling electronics systems. Therefore, there has been
considerable interest in finding filter realizations that
do not require an inductor and are operable at higher
frequencies (i.e. beyond 1 HHz). One of the major
applications of this type of filter is in the intermediate
frequency stages of radio receivers. For F.H. receivers,
this intermediate frequency stage is 10.7 MHz.
This project is concerned with the realization of an
integrable (inductorless) high frequency (1-15HHz) and
relatively high Q (40-300) narrow band RC active filter.
The primary cause of limitations to the high frequency
capability of active integrated filters is finite
gain-bandwidth product of the active element used in the
realization. The effect of the finite gain-bandwidth
1
2
product is to cause the filter poles to shift from their
desired locations. As the value of Q which is to be
realized increases, the frequency limit caused by the
finite gain-bandwidth product becomes more severe. The
finite gain-bandwidth product of active devices, such as
transistors and amplifiers, is due to the complex gain and
low pass behavior of the active device at high frequencies.
This is in turn due to the internal parasitic reactances
of the transistors. Achieving better high frequency filter
performance by minimizing the limitations caused by the
internal parasitic reactances, has long been the subject of
research by many workers in the field.
In a recent approach [1] these internal parasitic
reactances, instead of being considered undesirable, were
exploited to realize a low pass characteristic which
together with resistors were used to achieve a desired high
frequency response. These are the class of filters which
are called Active-R, and have been given particular
attention for high frequency filter realization in the
recent years. the main problem with active-R type of filter
reali~ations
is the extremely poor repeatability and
predictability of parasitic transistor parameters and their
dependence on temperature and bias condition.
In the face of these unpredictable parasitic effects,
Chiou and Schaumann (2] suggested that a single
(frequency-stabilizing) control loop would not be
3
sufficient for obtaining reliable high frequency integrated
filters. Rather, a tunning scheme with multiple control
loops would have to be devised so that parameters such as
bandwidth and gain could be stabilized in addition to pole
frequency. In this context, the deviation of the filter
parameters is automatically measured and used as the
control input for controlling the overall filter parameters
automatically. Chiou and Schaumann's approach has yielded
satisfactory results although it's high degree of
complexity draws our attention away from it.
A simpler approach, which is used in this project, is
the traditional embedding of amplifiers into a passive RC
network. In this approach special design techniques
is
used to minimize errors introduced by the frequency
dependent amplifier gain. In recent years varying degrees
of success has been reported using this second approach.
In particular a few of these recent designs, employing
op-amps as the active element, have shown remarkable filter
response in terms of sensitivity to finite gain-bandwidth
product (6],[8].
What is intended in this project is to use bipolar
transistor amplifiers, rather than op-amps, as the active
element. This choice is inevitable since for the frequency
ranges under consideration, 1-15 MHz, the poor frequency
capability of op-amps makes them hopeless. The choice of
bipolar transistor active unit, on the other hand, has
4
yielded some satisfactory results at higher frequencies as
was shown by Comer (3] recently. Comer's approach, which
will be applied for this project's design, is concerned
with employing all-pass networks in a feedback configuration
for generating a pair of complex poles close to the jw axis
(high Q realization). The op-amp version of this design,
shown in Fig. 3, was proposed by Comer and Mcdermid [4],[5]
in 1968, and later independently, by Tarmy and Ghausi [6].
This type of approach can produce very high values of
circuit Q (above 1000) while exhibiting low values of
sensitivity and temperature drift [5). Furthermore, the
potential for high frequency performance is quite good due
to the very low sensitivity to amplifier's gain-bandwidth
product [61,[8).
This project is therefore mainly concerned with
exploring the application of bipolar transistor active RC
networks for realization of the filter. In this realization
all-pass networks are used in a feedback configuration for
achieving an integrable high frequency narrow band active
filter. This choice of high frequency filter has the
advan~ages
of using high gain-bandwidth product bipolar
transistors. Also it employs a realization that minimizes
the dependency of filter's pole frequency and Q on the
finite gain-bandwidth product of the active element.
Minimization of this dependency and achieving maximum
gain-bandwidth product for the active unit to realize an
5
integrable (inductorless) high frequency (1-lSMHz) and
relatively high Q (40-300) narrow band RC active filter is
the goal of this project.
II.
THEORY OF OPERATION
The method of using all-pass structures in a feedback
configuration for realizing a narrow band response could
best be understood by first looking at the ideal version of
this configuration in terms of control and feedback
topology. Basically a second order narrow band filter can
be realized by a cascade of first order all-pass elements
and a near unity negative gain amplifier as shown in Fig. 1.
The operation of this filter for sinusoidal inputs can
be illustrated by considering the phase relationships of
the voltages at points A and B. The all-pass stages have a
frequency response which is constant in magnitude and a
phase response that changes from 180 degree to 0 degree
as the radian frequency W varies from zero to infinity.
If the frequency of the input signal applied at point A is
W=l/T, each all-pass network will shift the phase by 90
degree. The feedback loop will have a total phase shift of
360
d~gree
at point B. With this phase condition positive
feedback is present, and if the absolute value of the
negative gain block Ko is less than but near unity, the
output voltage will be a maximum. At other frequencies the
phase shift through the loop is different from 360 degree
and the overall gain will be considerably smaller than the
maximum value. In theory, very sharp band-pass
7
characteristics can be obtained by this filter, but in
practice the circuit Q is limited by many nonideal factors
such as drift in element values and complex gain structure
of the active devices.
The transfer function for any second order system can
be written as:
2
Vo
= Ko
+ CS + D
S
(1 )
X
Vi
2
S
+ AS + B
The resonant frequency and Q for the system are given by:
Wo
= JB"
(2)
and
(3)
The transfer function for the ideal configuration of Fig. 1
can be found as:
8
2
Vo
=
Vi
(S
Ko
1/T)
(4)
X
1-Ko
s
2
1-Ko
2
+
X
T
s
2
+ 1/T
l+Ko
In this case,
Wo
Q
1
=
=
(5)
T
1
1-Ko
(6)
X
2
1+Ko
It is interesting to note that for the ideal
configuration the factor determining the resonant frequency
is not related to Q. It can also be noted that as Ko
approaches -1, Q becomes very large. Unfortunately, as Ko
approaches -1 a very small drift in Ko causes a large
corresponding change in Q.
A root-locus plot with respect to the loop gain for
narrow band-pass characteristic of Fig. 1 is shown in
Fig. 2. In this root locus plot the closed loop complex
conjugate pole pairs giving the narrow band-pass
characteristic is marked with boxes.
9
Two distinct advantages of this configuration can be
readily seen by investigating this root locus plot. First,
with the transmission zero in the right half S plane, there
is a d.c. negative feedback loop round the circuit, which
stabilizes the bias point of all the active devices
employed in the realization. Second, the critical loop gain
Ko for high selectivity at the center frequency of the
passband is unity rather than 2 or 3 or higher which is the
requirement for some other types of selective filters such
as Wien bridge or a negative immitance converter
configuration. Therefore, with a unity gain requirement for
the amplifier a higher degree of gain and phase precision
can be realized rather than the non unity case.
The next step is to design an integrable circuit for
the all-pass structures and the negative unity gain block
that is not only practical but also closely resembles the
ideal model. However, before this new circuit is considered,
a brief review of what has already been proposed is given
so that a basis for comparison can be established.
III.
REVIEW OF
NARROW BAND-PASS FILTERS USING ALL-PASS ELEMENTS
The original op-amp version of the narrow band filter
proposed by Comer is shown in Fig. 3, [4]. the first two
op-amp stages in the feedback loop are all-pass stages
proposed by Ponsonby [7].
The transfer function for this op-amp version of narrow
band configuration shown in Fig. 3 is:
2
Vo
(S + 1/T)
R2
=
Vi
(7 )
X
R1(1+Ko)+R2
s
2
R1(1-Ko)+R2
2
+
X
T
s
2
+ 1/T
R2(1+Ko)+R2
3
where T=RC, Ko=[A/A+2J
and A is the gain of the op-amp.
The circuit Q is:
Q
=
R1(1+Ko)+R2
1
X
2
R1(1-Ko)+R2
R1
----(when Ko=1 and R1>>R2) (8)
R2
and the resonant frequency is given by:
10
11
Wo
1
=
2
1
= -·
( 9)
RC
T
Note that, as it was illustrated for the ideal model of
the narrow band filter, the selection of 0 is independent
of resonant frequency. Since Ko can approach a near unity
value, the circuit 0 can approach a value determined by the
ratio of Rl to R2.
This value can be very high and values
of 0 exceeding 1000 have been reported
[6].
The 0 sensitivity of this op-amp version of narrow
band filter to loop gain Ko is :
0
= KoO = 0 (when Ko=1).
S
(10)
Ko
Relating the 0 sensitivity to the individual amplifier
gain results in the following:
s
0
A
60
= --.
A
If a circuit 0 of 100 is required and an amplifier of
moderate capability is used (A=SOOOO), the sensitivity
(11)
12
factor is:
s
Q
= 0.012
A
A drift in A of +100% results in a Q change of +1.2%.
Therefore, this version of a narrow band filter can be
made almost insensitive to the amplifier gain by choosing
an amplifier with higher gain •
Fig. 4 shows a modified version of filter of Fig. 3
with transistor replacing op-amps. This circuit can
operate at quite high frequencies (i.e. beyond 1Mhz). This
results from the fact that all transistors in this filter
operate with unity voltage gain which maximizes the
bandwidth of each stage. This fact was also depicted in the
root-locus plot for the ideal model of previous section.
Similar to the op-amp version, the bipolar version of the
narrow band filter shown in Fig. 4, uses the transistor as
an unity gain voltage controlled voltage source.
In Fig. 4, the first stage provides an inverting gain.
The next four transistors make up all-pass stages, while
the emitter follower is used to minimize loading problems.
The transfer function for the transistor version of the
filter is as follows:
13
2
Vo
Vi
(S - 1/T)
-KoR2
=
• ( 12)
2
X
R1(l+Ko) + R2
s
2
2 Rl(l-Ko)+R2
+ -T Rl(l+Ko)+R2
s
+ 1/T
Equations (8) and (9) still apply to to this transistor
version of the filter, but the constant Ko is now given
by:
Ko
= Klo
K2o K3o K4o
(13)
where Klo is the absolute value of the gain of stage 1. K2o
and K3o are the gains of the all-pass stages and K4o is the
gain of the last emitter follower.
As can be seen, the bipolar version of the narrow band
filter shown in Fig. 4 is fully integrable and can produce
very high frequency filter operation.
IV.
ANALYSIS AND DESIGN
To design a high frequency integrated circuit it is
necessary to understand and model the parasitic elements
that will be present in the physical circuit, so that an
accurate model can be made.
In this project a controlled current source rather than
a controlled voltage source is used for designing an
all-pass circuit.
An ideal all-pass element can be constructed using a
current controlled current source (C.C.C.S.) as shown in
Fig. 5 [91. In Fig. 5
~,
the transfer current ratio, is
unity and the input and the output impedances of the
c.c.c.s.
are assumed to be zero and infinity respectively.
Analysis of Fig. 5 shows the transfer function to be :
Vo
Vi
=
1 - RCS
(14)
1 + RCS
It should be emphasized that in a practical realization
the input and output impedances of the C.C.C.S. are not zero
and infinity respectively. The input impedance for the ideal
realization of Fig. 5 is:
14
15
Zi
=
R(l + RCS)
•
(15)
(1 + 3RCS)
Alternatively, an ideal all-pass element can be
constructed using a voltage controlled current source
(V.C.C.S.) as shown in Fig. 6. In Fig. 6 the transfer
conductance ratio, is 1/R and the input and the output
impedances of the
v.c.c.s.
are assumed to be both infinity.
Analysis of Fig. 6 shows the transfer function to be:
1 - RCS
Vo
=
Vi
(16)
1 + RCS
A possible realization for the
v.c.c.s.
used in the
ideal all-pass structure of Fig. 6 is shown in Fig. 7.
In the circuit of Fig. 7 the collector current of the
transistor at low to mid-frequencies can be found as
follows:
Ic =
Ib
=
{3
(17)
Ib
Vi
(18)
( (3 +
1) (
re + R)
16
Ic
Ic
=
(3
Vi
( (3 +
N
(19)
1) ( re + R)
Vi
(when re<<R &(3 >>1) •
(20)
R
This derivation clearly shows that the transistor in
the circuit of Fig. 7 acts as a
v.c.c.s.
with a transfer
conductance of 1/R at least at low to mid-frequencies.
The complete narrow band filter configuration using
the all-pass circuit of Fig. 7 in a feedback configuration
is shown in Fig. 8, where 01 and 04 make up all-pass stages
and 06 provides the inverting gain stage. The emitter
followers are used for providing high input impedance and
low output impedance. The gain of the last inverting stage
is controlled by the potentiometer RE6.
This high frequency narrow band filter shown in Fig. 8
has the same transfer function as Comer's filter £31 given
in Eq.(12).
The center frequency and filter's 0 are
identical to Comer's given in Eq.s (9) and (8)
respectively. The constant Ko is now given by:
Ko
= Klo
K2o K3o K4o K5o K6o K7o.
(21)
\
\,
17
Klo, K3o, KSo, and K7o are the gains of the emitter
follower stages and are close to unity. K2o and K4o are the
gains of the all-pass structures and K6o is the absolute
value of the gain of the last inverting gain stage.
A major improvement of the proposed filter of Fig. 8 is
its improved frequency response of the all-pass blocks at
high frequencies. This improvement is due to the fact that
the feedback capacitor
c,
used in the realization of the
all-pass structure, dominates the frequency response and
pole locations. At the desired frequencies, 1-lSMHz, the
value of the feedback capacitor can be chosen much larger
than the transistor's parasitic capacitances. As a result
this large feedback capacitor dominates over the frequency
response and allows the parasitic capacitances of the
transistors to be neglected.
The feedback capacitor in effect acts as a Miller
compensator pole splitter; narrowbanding the transistor
dominant pole and broadbanding its nondominant pole. The
two root-locus plots shown in Fig. 9.a and 9.b depict this
pole splitting effect. In this figure Pl and P2 are the
poles of the transistor's response without compensation.
Pel and Pc2 are the poles of the all-pass structure using
feedback capacitor compensator.
In the filter of Fig. 8, deviation of the ideal
all-pass characteristics caused by the transistor's
parasitic elements can be evaluated using the dominant
18
pole approximation. At low frequencies, the collector
current of the transistor used in the all-pass structure
of Fig. 7, was shown to be Vi/R in Eq. (20). At high
frequencies this can be approximated by:
Ic
=
Vi
(22)
s
R(1 + ----)
Wh
as shown in Fig. 10.
Writing the node equation at the collector of the transistor in Fig. 10 and solving for the transfer function
yields:
2
RCS
\
1 - RCS Vo
Vi
=
Wh
•
(23)
S
(1 + RCS)(1 + ---)
Wh
Using a similar technique, The deviation of the ideal
all-pass structure of Comer's filter [3] shown in Fig. 4
19
can be evaluated . This all-pass structure is shown in
Fig. 11. In like manner, the collector voltage of transistor Ql and therefore the output voltage of emitter follower
can be approximated by:
Vc
Vi
=
(24)
s
1 +
Wh
At high frequencies, going through a similar derivation,
the transfer function is found to be:
s
1 - RCS +
Vo
Vi
Wh
=
(1 + RCS) ( 1 +
s
•
(25)
--)
Wh
Now a simple, yet reliable, way of comparing the
closeness of the two deviated all-pass transfer functions,
20
given by Eq.s (23) and (25), to the ideal case, is to plot
them. This can be done by assuming the same dominant pole
affects both characteristics and plotting the phase for
each transfer function at the desired frequency ranges.
Fig. 12 shows these plots for a dominant pole of SOMHz,
frequency range of 7 - 16MHz, and a RC time constant of
-8
l.SXlO (i.e. 1/2~ 10.6MHz). In these plots, the negative
sign of the proposed transfer function in Eq.
(23) is
neglected.
From these phase plots it is evident that the phase
characteristics of Comer's all-pass circuit are closer
to the ideal case at frequencies below the resonant
frequency (i.e. 10.6MHz). At frequencies above the resonant
frequency, however, the proposed all-pass circuit shows
less deviation from the ideal case than Comer's all-pass
circuit.
Assuming that the main high frequency limitations of
the proposed narrow band filter of Fig. 8 is due to the
last inverting gain stage, the high frequency loop gain K
for the filter of Fig. 8 becomes:
K
Ko
=
1 +
s
Wh
(26)
21
In Eq.
(26) Ko is the d.c. loop gain given by Eq.
(21) and
Wh is the dominant pole for the gain of the last inverting
transistor stage Q6. Replacing Ko in Eq.
(12) by the high
frequency loop gain approximation given in Eq. (26) , the
approximate transter function for the filter of Fig. 8 at
high frequencies becomes:
2
-Ko R2(S - Wp)
Vo
(27)
=
Vi
3
E3 S
2
Wp
+ ( 1 + E2) S +
Wp
2
(1 + E1) S + Wp
Q
where
\
E3
E2
=
=
R1 + R2
1
(28)
X
Rl(1 + Ko) + R2
T Wh
R1 + R2
2
(29)
X
R1(1 + Ko) + R2
T Wh
\
22
El
=
R1 + R2
1
(30)
X
Rl(l - Ko) + R2
Wp
R1(1 - Ko) + R2
2
=
2T Wh
(31)
X
T
0
Rl(l + Ko) + R2
and
1
Wp
As
=
(32)
T
it can be seen in Eq. (27), because of the dominant
pole approximation for loop gain K, the degree of the
denominator of the transfer function is raised by one.
Having the approximate transfer function in Eq. (27) in
mind, the next step is to estimate the shifted location of
the center frequency and quality factor. In this project
Sun's method [101 is used for this estimation. The shifted
center frequency and quality factor are given by:
23
2
E3(1 + E1)
1 + E2 -
Q
(E3)
+
2
"'*
Q
E3 Q
=
(E3)
( 34)
E3 Q
1 + E1 E3
where
E3
=
E3
1 + E2 -
(35)
Q
and
Q
=
Rl(1 + Ko) + R2
1
•
X
2
(36)
R1(1 - Ko) + R2
Investigation of the shifted center frequency, Wp and
the Quality factor, Q
in Eq.s (33),(34) shows that the
perturbation of the desired Wp and Q can be minimized by
maintaining a high dominant pole frequency Wh for the last
inverting stage.
Therefore having this objective in mind
the experimental design for the high frequency narrow band
filter can be started.
\
V.
EXPERIMENTAL DESIGN
Design of a high frequency active RC integrated
circuit using transistors is much more involved than one
using op-amps. This is due to the d.c. biasing and the
finite input and output impedances of the transistor.
Therefore, to design a reliable high frequency filter it
is necessary to understand the effect of d.c. biasing and
finite input-output impedance on the operation of the
filter.
The definition of "high frequencies" is a relative
term. In this project "high frequencies" is meant to be in
the range of 1 to 15 MHz. At these frequencies a general
transistor amplifier of Fig. 13 can be modeled by a high
frequency hybr id-1i model as shown in Fig. 14. This model
is not an exact model of the transistor at the higher
frequency ranges under consideration. However, it will be
used in this project in order to obtain approximate
predictions.
The gain of this amplifier can be approximated by a
dominant pole as:
A(S)
=
Ao
(37)
1 +
s
Wh
24
25
where Ao is the low frequency gain and Wh is high frequency
dominant pole given by [111:
Wh
=
1
(38)
RuoCu + R Tr oC Tr
where
1
(gm +
Ruo
}{RE {RB + RC) + RB RC) + RC + RB
rrr
=
{39)
1
{RB + RE)
1 + gmRE +
rrr
and
R]TO
=
RB + RE
I I rlf ·
(40)
1 + gm RE
Equations (38),(39),and {40) show that broadbanding can be
achieved by decreasing RC, RB, C1f ,and Cu and increasing
RE. To minimize Cu and
C~,
consider their relationship to
fT, the transfer unity short-circuit current gain bandwidth
product:
26
gm
C1i + Cu =
(41)
2rr fT
where
gm
=
IC
(42)
VT
and VT is the electron thermal voltage.
fT depends on collector current Ic and the collector to
emitter voltage Vee as shown in Fig. 15. It can be seen
from Fig. 15 that to minimize C1T and Cu, it is necessary to
have a large collector to emitter voltage.
Motorola 2N2222 and high frequency RCA 2N40894 were
used for constructing emitter followers and all-pass
filters respectively. RCA 2N40894 was also used for the
inverting gain control stage since this stage must be as
broadband as possible.
Choosing a d.c. supply voltage of 10.0V and assuming
R2
= 0,
the d.c. bias voltages of all transistors in the
narrow band filter of Fig. 8 are calculated and shown in
table [1]. Where VB, VC, VE refer to the d.c. base,
collector, and emitter voltages of the transistors in the
narrow band filter of Fig. 8 respectively.
In the filter of Fig. 8, if a high center frequency is
desired, the RC product must be small. However C must be
27
larger than the parasitic capacitances to allow these
elements to be neglected. The emitter resistance of all the
emitter followers in the filter of Fig. 8 was chosen to be:
RE1
= RE3 = RES = RE7 =
470 ohms.
Since, according to table [11, the d.c. bias voltages of
all the emitter followers in the filter of Fig. 8 are close,
the output resistance of each emitter follower was found to
be approximately in the range of 5 - 20 ohms. Correspondingly R was chosen to be 150 ohms and C was selected
to have a range of 70 - 150 pF in order to realize a center
frequency in the range of 7 - 15 MHz.
According to the broadbanding conditions discussed
earlier a high frequency improvement can be achieved by
maintaining higher collector to emitter voltages, Vee, for
the all-pass and inverting gain stages. This can be done by
self biasing techniques, however, a more integrable
approach can be undertaken by using zenor diodes in the
emitter lead of the emitter followers as shown in Fig. 16.
The zenor diodes act as a level shifter, decreasing the
base voltages of the all-pass and inverting gain stage
which in effect increases their collector to emitter
voltage. 1N4372 zenor diodes with a zenor voltage of 3.0 V
are used for this purpose. Again for a center frequency in
the range of 7 - 15 MHz, R, the collector resistance of the
all-pass transistors selected to be 150 ohm and C to be in
28
the range of 70 - 150 pF. The emitter resistance of the
all-pass transistor, however, was selected to be 100 ohm.
To further improve the high frequency response, the emitter
and collector resistance of the last inverting stage was
reduced to 100 ohm.
Choosing a d.c. supply voltage of 10.0V and assuming
R2
= 0,
the d.c. bias voltages of all the transistors in
the improved narrow band filter of Fig. 16 are shown in
Table [2]. Where VB, VC, and VE refer to the base,
collector, and emitter voltages of the transistors in the
filter of Fig. 16.
VI.
EXPERIMENTAL RESULTS
The circuit of Fig. 8 was simulated with SPICE [121
for three different values of the feedback capacitance of
161 pF, 100 pF, and 75 pF. R was 150 ohm and Rl and R2 was
chosen to be 150 Kohm and 150 ohm respectively. The emitter
resistance of all emitter followers were 470 ohm. The high
frequency transistor parameters used in spice were derived
for RCA 2N40894 and Motorola 2N2222 according to the
transistor's specification sheets and d.c. bias voltages of
table [1]. These parameters are tabulated in table [3].
Using trial and error, the required emitter resistance,
REG, of the last inverting stage for achieving a unity
voltage gain at the center frequency was found to be 136
ohm. As a result the approximate dominant pole for this
last inverting stage, using Eq.s (38), (39), and (40), was
evaluated to be 55.8 MHz.
The results of this simulation for three different
values of the feedback capacitor of 161 pF, 100 pF, and
75 pF is shown in Fig.s 17,18,and 19 respectively. Based
on these results, the estimation formulas given in Eq.s
(33), and (34) and the approximate dominant pole, the
ideal, estimated, and SPICE values of center frequency and
quality factor are tabulated as is shown in table (4].
From these tables it is evident that the ideal results
29
30
are in good agreement with the estimated and SPICE results.
As the expected center frequency increases,
the SPICE and
estimated center frequency and quality factor have more
deviation from their ideal value. This is expected since at
higher frequencies the effect of parasitic capacitances is
more severe.
Next the improved filter of Fig. 16 was actually
constructed for three different values of the feedback
capacitance of 161 pF, 100 pF, and 75 pF. R was 150 ohm and
Rl and R2 were chosen to be 100 kohm and 220 ohm
respectively. The emitter follower's emitter resistances
REl, RE3, and RES were 100 ohm while RE7 was 470 ohm.
1N4372 Zenor diodes were inserted in the emitter lead of
emitter followers Ql, Q3, and Q5 as shown in Fig. 16. Also
RCA 2N40894 and Motorola 2N2222 were selected for the allpass structure and inverting gain structure as in the SPICE
analysis considerations. The high frequency transistor
parameters for the RCA 2N40894 transistor of the last
inverting gain stage was evaluated using the d.c. bias
voltages of table [21 and transistor specification sheets
as follows:
gm
Ic
=
=
Vt
80
=
.69 mho
ft = 800 MHz
ru
= 115.0
ohm
31
C J.L =
c "1\ =
1 pF
gm
- CJA.= 136.3 pF
Wt
The zenor resistance for 1N4372 at the selected zenor
current was found from specification sheets to be 275
ohm. The required emitter resistance, REG, of the last
inverting stage for achieving unity voltage gain at the
center frequency was measured to be 55 ohm. Using this
value of emitter resistance, the dominant pole of the last
inverting stage according to Eq.s (38),
(39), and (40) was
evaluated to be 90 MHz.
The circuit was tested with a Hewlett Packard Network
analyzer (Model # 8754- A
).
The plot of frequency and
phase response of this improved circuit for the three
feedback capacitances of 161 pF, 100 pF and 75 pF are shown
in Fig.s 20, 21, and 22 respectively. Based on these plots,
the estimation formulas given in Eq.s (33),
(34) and the
dominant pole location, the ideal, estimated, and actual
values of center frequency and quality factor are as shown
in table [51 •
From these results, it can be seen that as the center
frequency increases the deviation of ideal and actual
values becomes more severe as expected.
The actual quality
factor is much lower than estimated and expected quality
factors. Reason for this might be the fact that in actual
circuit the loop gain K is not unity. This can be seen by
32
noting that in actual gain characteristics of the filter in
Fig.s 20, 21, and 22, the gain at the center frequency is
not unity.
Finally, to compensate for the dominant pole of the
last inverting gain stage, which was believed to be the
source of all discrepancies, a 100 pF capacitor was placed
in parallel with the emitter resistance of the last
inverting stage. The frequency and phase response plots for
the compensated case for three different values of feedback
capacitance of 161pF, 100pF and 89pF are shown in Fig.s
23, 24, and 25 and the results are tabulated in table [6).
The results show that a center frequency of 10.6 HHz is
achieved when a 89pF feedback capacitor is used in the
compensated circuit. Also the ideal center frequencies and
actual center frequencies agree to a high extent.
This
shows the last inverting stage is responsible for much of
the discrepancies in terms of the center frequency and Q
shift.
VII.
CONCLUSION
Employing all-pass networks in a feedback loop is an
efficient way of achieving high frequency narrow band
filters. This method can be used in the design of selective
filters for center frequencies of up to and beyond 15 MHz
and quality factors in the range of 40 - 300. In this
project high frequency narrow band filters were build that
employed transistor all-pass blocks in a feedback loop. A
new transistor all-pass circuit was designed that used a
feedback capacitor for achieving all-pass characteristics.
New techniques were used to minimize filter parameter
deviation from desired values. Good agreement was shown
between measured and estimated filter parameters especially
at lower frequencies.
Finally, using compensation
techniques, the designed filter parameters were
demonstrated to have excellent agreement with the ideal
values.
33
REFERENCES
[1]
J.R. Brand and R. Schaumann, "Active R filters: Review
of theory and practice," IEE J. Electron. Circuits and
Systems, vol. 2, pp. 89-101, 1978.
[2]
C. Chiou and R. Schaumann, "Design and performance of
a fully integrated bipolar 10.7-MHz analog bandpass
filter," IEEE J. Solid-State Circuits vol. SC-21,
No. 1, pp. 6-14, Feb. 1986.
[3]
D.J. Comer, "High frequency narrow-band active
filters," IEEE Trans. on Circuits and Systems, vol.
CAS-33, No. 8, pp. 838-840, August 1986.
[4]
D.J. Comer and J.E. McDermid, "Inductorless bandpass
characteristics using all-pass networks," IEEE Trans.
Circuit Theory, vol. CT-15, pp. 501-503, Dec. 1968.
[5]
D.J. Comer and J.E. McDermid, "A sensitivity study of
bandpass filters using all-pass networks," in Proc.
Second Asilomar Conf. on Circuits and systems, Nov.
1968, pp. 202-207.
[6]
R. Tarmy and M.S. Ghausi, "Very high-Q insensitive
active RC networks," IEEE Trans. Circuit Theory,
vol. CT-17, pp. 358-366, Aug. 1970.
[7]
J.E.B. Posonby, "Active all-pass filter using a
differential operational amplifier," Electron. Lett.,
vol. 2, pp. 134-135, April 1966.
[8]
G.S. Moschytz, "High-Q factor insensitive active RC
network, similar to Tarmy-Ghausi circuit but using
single-ended operational amplifiers," Electron.
Letters, vol. 8, No. 18, pp. 458-459, Sept. 1972.
[9]
A. Fabre and P. Rochegude, "Allpass filters using a
current-controlled current source," Electron. Letters,
vol. 21, No. 25/26, pp. 1205-1207, Dec. 1985.
34
35
[101 Y. Sun, "Formulas for pole-Q and resonance frequency
shifts in RC active circuits due to amplifier finite
gain bandwidth", Department of E.C.E., University of
Wisconsin, Madison, June 1974.
[111 Y. Sun, Lecture notes, Electronics 1, C.S.U.N ..
[12] L.W. Nagle and D.O. Pederson,"Simulation program with
integrated circuit emphasis (SPICE)", Electron. Res.
Lab. Report ERLM382, University of California,
Berkeley, USA, April 1973.
36
Fig. 1
Ideal Second Order Band-Pass Filter
37
~K=I
0
~K=I
0
Fig. 2
Root-Locus Plot For The Narrow Band Configuration of Fig. 1
38
v;
R,
I
Fig. 3
Op-Amp Realization of The Narrow Band Filter
39
ll.·O Volts
- 6.o
Fig. 4
Comer's Discrete Transistor
Version of The Narrow Band Filter
40
c
V;
Vo
oc:r
R
=l.
l
Fig. 5
Ideal All-Pass Using Current Controlled Current Source
41
c.
v;
I:
Vi
"R
~
-
'R
l
-
Fig. 6
Ideal All-Pass Using Voltage Controlled Current Source
42
Vcc
R
c
Vo
Y .Ic
-~1
l.b
r
Fig. 7
All-Pass Realization Using
Bipolar Transistor as A Voltage Controlled Current Source
43
Vee
Vi
1
o. 0
1/tJff.s
1<,
01,03,05,07--- Motorala 2N2222
02,04,06------ RCA
2N40894
Rl=l50K ohm
R2=150 ohm
R=l50 ohm
REl=RE3=RE5=RE7=470 ohm
RE6=136 ohm
C=l61 pF, 100 pF, 75 pF
Fig.S
Narrow Band Filter Using
Al~pass
Circuit of Fig. 7
,, .
44
,JW
a) Root-Locus plots
For Response Without
Compensation.
P.":.------
i.)
I
c.z
b) Root-Locus Plot
For Response With
Compensation.
Fig. 9
Root-Locus Plots For All-Pass Structure of Fig. 7
45
Vc.c.
v.
r
A
) Ic =
Fig. 10
All-Pass Using Voltage Controlled Current Source
46
Vee
- v,·
v,·
-p
-
If
S
Wh
Fig. 11
All-Pass Using Voltage Controlled Voltage Source
47
FRE:GUENCY I MH1:
,..
15
lb
10
II
8
7
-45r---------------------------------------------~
w
w
a:
1.5
w
D
Fig. 12
Phase Response For Ideal, Comer's, and Proposed All-Pass
Structures
48
V,·
Fig. 13
General Transistor Amplifier
49
Vo
t---~-----
"Rc
Fig. 14
HybridTr Model For The Transistor Amplifier of Fig. 13
50
Vee
Vo\ts
rY'I.A
Fig. 15
Variation of The Transfer
Unity Short Circuit Current Gain, fT, With Ic and Vee.
51
Vee.
I
o·0
Vo 1-fs
Va
Q1,Q3,Q5,Q7--- Motorala 2N2222
2N40894
Q2,Q4,Q6------ RCA
1N4372
DZ1,DZ2,DZ3--Rl = 100 Kohm
R2 = 220 ohm
R = 150 ohm
RE1=RE2=RE3=RE4=RE5=100 ohm
REG= 55 ohm
RE7= 470 ohm
R' = 100 ohm
C=161 pF, 100 pF, 75 pF
Fig. 16
Narrow Band Filter Using Broadbanding Techniques
52
OHIGH FREQUENCY NftRROW BftND FILTER
I NF'UT LISTING
TEMPERATURE =
27.000 IIEG C
0***********************************************************************
•loiiiiTH OUT = 80
0 10.0
3
0 ftC 1 0
VIN 1
2 150K
R1
1
QMOlll
lH
3 2 4
RE1 4
,...J0 470
150
RC2 3
4 161f'
C1
5
Q2
4 6 QMOD2
0 150
RE2 6
Q3
QMOD3
3 5 7
0 470
RE3 7
8 150
RC4 3
7 161F'
C2
8
QMOD4
Q4
8 7 9
RE4 9
0 150
Q5
3 8 10 QMOD1
0 470
RE5 10
RC6 3 12 150
Q6 12 10 11 QMOD2
RE61 11 14 135.00
RE62 14 0 15.00
C6
14 0
.lU
Q7 3 12 13 QMOD3
RE7 13 0 470
R2
13 2 150
.MODEL QMODl NPNCBF=100 RB=18.75 CJC=BP CJE=246.8Pl
.MODEL QMOD2 NPNCBF=BO RB=20 CJC=1P CJE=210Pl
.MODEL QMOD3 NPNCBF=100 RB=18.75 CJC=BP CJE=278.6Pl
,MODEL QMOD4 NPNCBF=BO RB=20 CJC=1P CJE=243,8PJ
,ftC LIN 40 5.586MEG 5.666MEG
*ftC DEC 20 8.466E+5 8.466Et7
.PLOT ftC VDBC13l
oPLOT ftC Vf'C13l
.END
vee
•
Fig.l7
SPICE Program For
The Filter of Fig. 8 For C=16lpF, R=150ohm
53
OHIGH FREQUENCY NARROW BAND FILTER
AC I'INALYSIS
0****
=
TEMPERATURE
27.000 IIEG
c
0***********************************************************************
X
FREG
X
VDB<13l
..
..
.
...
..
..
..
..
.
..
.
-3.006E+Ol
5.586Et06 -2,371Et01
5.588E.+06 -2.326E+Ol
5.590Et06 -2.278Et01
5.592E+06 -2.227E+01
5.594E+06 -2.173Et01
5.596Et06 -2.116Et01
5.598E.t06 -2.054Et01
5.600Et06 -1.989Et01
5.602E+06 -1,918Et01
5.604E+06 -1.840E+Ol
5.607E+06 -1.756E+Ol
5.609E+06 -1.663Et01
5.611E+06 -1.560Et01
5.613Et06 -1.443E+Ol
5.615Et06 -1.311Et01
5.617Et06 -1.159E+01
5.619E+06 -9,818EtOO ,
5.621E+06.-7.783Et00
5.623E+06 -5.617E+OO
5.625E+06 -4.009E+OO
5.627E+06 -4,181E.+OO
5.629E+06 -5.965EtOO
5.631Et06·-8,133Et00
5.633E+06 -1.012Et01
5.635E+06 -1.185Et01
5.637E+06 -1.333E+Ol
5.639Et06 -1.462Et01
5.641Et06 -1.576E+Ol
5.643Et06 -1.677Et01
5.645E+06 -1.769Et01
5.648Et06 -1.851E+Ol
5.650Et06 -1.927E+01
5.652E+06 -1,997Et01
5.654Et06 -2.062E+Ol
5.656Et06 -2.123Et01
5.65BE+06 -2.179Et01
5.660Et06 -2.232Et01
5.662E+06 -2.282Et01
5.664Et06 -2.330Et01
5.666E+06 -2.375E+01
-
*
*
*
*
-
-
-
e.-
-1T090Et61
..
*·
*
·*
.
*
*
*
*
*
*
*
.
*
*
*
*
*
*
*
*
*
*
*
*
.
-
--·1. eoeE+Ol
*
*
.
..
.
..
..
..
..
-
--~.eoeE+ot
. **
*
·*
- -
*·*.
***
*
**
-
- - -
-------
Fig.17 (Continued)
Gain Response
- - -
---
-
---
54
y
1******* 87/05/05, *******
SPICE 2F.l C25FEB80)
******* 15.24.59.*****
OHIGH FREQUENCY NI'IRROW BI'IND FILTER
I'IC I'INI'ILYSIS
0****
TEHPERI'ITURE
=
27,000 DEG C
0***********************************************************************
X
FREQ
X
!5.586E+06
5.58BE+06
5.590Et06
5.592E+06
5.594Et06
5.596E+06
5o598E+Ob
5.600E+06
5o602Et06
5.604Et06
5.607E+06
5.609Et06
5.611E+06
5.613Et06
5.615E+06
5.617E+06
5.619E+06
5.621Et06
5.623£+06
5.625Et06
s.627E+06
5.629Et06
5.631E.t06
5.633E+06
5.635Et06
5.637Et06
5.639Et06
5.641E+06
5.643E+06
5.645Et06
5.648E.+06
5.650Et06
5.652Et06
5.654Et06
5.656E+06
5.658Et06
5o66QEt06
S.662Et06
5o664Et06
5.666Et06
VPC13)
..
..
.
...
.
.
..
..
..
...
..
.
-2.006Et0>!
9,940Et01
9.970Et01
l.OOOEt02
l.004Et02
l.OOBE+02
1.013Et02
1.019Et02
1.025Et02
1.033E+02
1.042E+02
1,053E+02
1.066Et02
1.083Et02
1.105Et02
l.l34E+02
1.174E+02
1.234Et02
1.326Et02
1.476E+02
1.713E+02
-1.604Et02
-1.382E+02
-1.244Et02
-1.158Et02
-1.103E+02
-1,065Et02
-1.037Et02
-1.016Et02
-9.999Et01
-9,870E+Ol
-9.764Et01
-9.676Et01
-9.602Et01
-9,540E+01
-9.485Et01
-9,438E+01
-9.397Et01
-9,361Et01
-9.329E+01
-9.300Et01
.
...
..
..
..
-
--t.eoeE+O~
- - e.- - - - - - i.eoeEtO>! -2TOeOE+ez
*
*
**
**
**
*·*
·*
·*
·*
·*
.*
.*
**
*
*
*
*
*·
*·
*·
*
*
*
*
*
·*
·*
·*
·*
·*
·*
·*
·*
Fig.l7 (Continued)
Phase Response
* *
55
OHIGH FREQUENCY NARROW BAND FILTER
AC ANALYSIS
TEMPERATURE
=
27,000 IIEG C
0***********************************************************************
X
FREQ
VDBC13>
-6,000Et0l
-8.000E+01
X
5.625Et05
6.311Et05
7.081Et05
7,946Et05
8,915Et05
1.000Et06
1.122Et06
1.259Et06
1.413Et06
1.585Et06
1.7791::+06
1.996Et06
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3.163Et06
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3.982E+06
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1.000E+07
1.122E+07
1.259Et07
1.413£+07
1,585Et07
1.779Et07
1.996Et07
2.239Et07
2.513Et07
2.819Et07
3 .163Et07
3,549Et07
3,982E+07
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5.013E+07
5.625E+07
-6,607Et01
-6.602Et01
-6,595Et01
-6.588E+01
-6.578Et01
-6.566E+01
-6.551Et01
-6,532E+Ol
-6,508E+01
-6.479Et01
-6.4421::+01
-6,395Et01
-6.337Et01
-6,263E+01
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-6.491E+01
-6.589Et01
-6.669Et01
-6,732E+Ol
-6.781E+Ol
-6.817E+01
-6,842Et01
-6.856Et01
-6.862Et01
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.
.
.
.
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-
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- - -
o.
*
*
*
*
*
*
*
*
*
*
*
*
*
*
.
*·
*
·*
.
*
*
*
*
.
.
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
-------
-
----
- -
Fig.17 (Continued)
Gain Response
- - - - - - - -
-
56
/1******* 87/05/05. *******
SPICE 2F.1 C25FEB801
******* 15.10.38·*****
OHIGH FREQUENCY NARROW BAND FILTER
0****
INPUT LISTING
TEMPERATURE =
27.000 DEG e
0***********************************************************************
•WIDTH OUT = 80
vee 3
o 10.0
VIN 1
0 Ae 1 0
R1
1
2
150K
Gl
3 2 4
0110111
RE1 4
0 470
RC2 3
5 150
e1
5
4
lOOP
G2
5 4 6 GI10D2
RE2 6
0
150
G3
3 5 7 OHOD3
RE3 7
0 470
Re4 3
8 150
e2
8
7
lOOP
G4
8 7 9
GHOD4
RE4 9
0
150
G5
3 8 10 GHODl
RE5 10
0 470
Re6 3 12 150
G6 12 10 11 GHOD2
RE61 11 14 136.00
RE62 14 0 14.00
e6
14 0 .lU
G7 3 12 13 GHOD3
RE7 13 0 470
R2
13 2 150
.HODEL GHODl NPNCBF•lOO RB=18.75 eJC=8P eJE=246.8PJ
.MODEL OMOD2 NPNCBF=BO RB=20 CJC•1P CJE=210PJ
.MODEL GHOD3 NPNCBF=100 RB=18.75 CJC=8P eJE=278.6PJ
.MODEL QHOD4 NPNCBF=BO RB=20 eJe=lP eJE=243.8P)
.Ae LIN 40 8.455HEG 8o475MEG
*Ae bEe 20 8.46Et5 8.46Et7
• F'LOT Ae VIIB C13 I
.F'LOT Ae VPC131
,END
Fig.18
SPICE Program For
.
8 For C=lOO pF, R= 150ohm
The Filter of F1g.
57
OHIGH FREQUENCY NftRROW BftND FILTER
1'\C 1'\NALYSIS
0****
TEMPERATURE
=
27.000 DEG C
0***********************************************************************
X
FREQ
X
VDfJ< 13 l
-1.206Et0l - --1. eoeEto-1 - --o.eoeEtoe
8.455Et06 -1.142Et01
*
8.4!:.6Et06 -1.11BEt01
*
B.456Et06 -1.094Et01
*
8.457E+06--1.070Et01
*
8.457Et06 -1.046Et01
*
B.458Et06 -l.022Et01
*
8.45BE+06 -9.978Et00
*
8.459Et06 -9.743Et00
*
8.459Et06 -9.512E+OO
*
8.460Et06 -9.287Et00
*
e.460E+06 -9,069Et00
*
8.461Et06 -8.860Et00
*
8.461Et06 -8.663Et00
*
8.462£::+06 -8.479Et00
*
8.462E+06 -8.310EtOO
*
8.463Et06 -8.159E+OO
*·
8.463Et06 -8.028Et00
8.464Et06 -7,918E+OO
·*
8.464Et06 -7.831E.t00
·*
8.465E+06 -7.770E+OO
*
8.465Et06 -'7.7351::.+00
*
8.466Et06 -7.726EtOO
*
8.466Et06 -7.744EtOO
*
8.467E+06 -7.78BEt00
·*
8.467Et06 -7.858E+OO
·*
8.468Et06 -7,953Et00
*
8.468Et06 -8.070Et00
*
8.469Et06 -8.209EtOO
*·
8.469Et06 -8,366E+OO
*
8.470Et06 -8.540Et00
*
8.470Et06 -8.729Et00
*
8.471E+06 -8.930E+OO
*
8.471Et06 -9.142Et00
*
8.472E+06 -9.363Et00
*
8.472E+06 -9.590Et00
*
8.473Et06 -9.822Et00
·*
8.473Et06 -1.006Et01
*
8.4~4E+06 -1.030E+Ol
*
8,474E+06 -1,054Et01
*
8.475E+06--1.078E+Ol
*
..
..
...
.
..
.
..
.
..
..
..
..
..
..
..
..
..
..
- -
-
--.:..eoeEtoe -4T060Et60
.
.
.
*
..
.
.
--
-
- - ---- - -
Fig.18 (Continued)
Gain Response
- -
- - - --- - - - - -
58
y
1******* 87/05/05. *******
SPICE 2F.1 <25FEB801
******* 15.10.38·*****
OHIGH FREQUENCY NARROW BAND FILTER
AC ANI"'LYSlS
0****
TEMF'ERI"'TURE.
=
27.000 DEG C
0***********************************************************************
X
FREQ
VP<131
-2,006Et0~
X
8o455Et06
8.456E+06
a.456E+06
a.457E+06
a.457E+06
a.45BE+06
a.45SE+06
a.459Et06
a.459E+06
8.460Et06
a.460Et06
a.461Eto6
a.461Et06
a.462E+06
8.462Et06
8.463Et06
a.463E+06
a.464E+06
8.464Et06
8.465Et06
a.465Eto6
a.466Et06
a.466E+06
a.467Et06
8o467Et06
a.46SE+06
a.46SE+06
a.469E+06
s.469E+06
a.470E+06
a.470E+06
a.471E+06
a.471E+06
8o472Et06
a.472E+06
a.473E+06
8.473Et06
a.474E+06
a.474Et06
a.475E+06
1.355Et02
1.369Et02
1.384Et02
1o400E+02
1.416Et02
1.434Et02
1.452Et02
1.471E+02
1.492E+02
1.514Et02
1.536Et02
1.560Et02
1.585E+02
1.612Et02
lo639Ei02
1,667Et02
lo697Et02
1.727Et02
1. 757Et02
1.789Et02
-1. 780E-t02
-1. 748E+02
-1.716E-t02
-1,685Et02
-1.653Et02
-1,623Et02
-1.593E+02
-1.564Et02
-1,536E+02
-1,509Et02
-1.484Et02
-1,459Et02
-1.435Et02
-1.413E+02
-1.392Et02
-1.372Et02
-1,352Et02
-1,334Et02
-1.317Et02
-1.301Et02
-
--1.606Et0~
- - e.- - - - - -
•
,
,
*
**
,
*
*
**
*
*
*
*
*
•
,
o
o
,
,
*
*
,
,
,
,
•
,
,
,
,
,
•
-2T090Et92
*
*
*
**
**
*
,
,
•
,
,
,
,
1.609Et0~
*
**
*
*
*
*
*
**
*
*
*
**
**
*
Fig.l8 (Continued)
Phase Response
59
OHIGH FREQUENCY NARROW BAND FILTER
AC ANALYSIS
0****
TEMPERATURE
=
27,000 I•EG C
0***********************************************************************
X
FRECl
VDB< 13>
-S,OOOE+Ol
X
-6.609Et01
-6,604Et01
-6.59BE+Ol
-6.590E+Ol
-6.581Et01
-6.569Et01
-6.554E+Ol
-6,535Et01
-6.512E+Ol
-6.483E+Ol
-6.447Et01
-6.401E+Ol
-6.343Et01
-6.271Et01
-6.179Et01
-6.060E+01
-5.903E+01
-5.688Et01
-5.367Et01
-4.794E+Ol
-7,731E+OO
-4.844Et01
-5,467Et01
-5.837E+01
-6.103E+Ol
-6.309Et01
-6.475E+Ol
-6.613E+Ol
-6.728E+01
-6,821Et01
-6.897Et01
-6.954Et01
-6.994Et01
-7,01BE+01
-7.028[+01
-7,030E+01
-7.02BE+01
5.9~3E+07 -7.031Et01
6.725Et07 -7,04BE+01
7.545E+07 -7.085E+01
8.466Et07 -7.144E.+01
8.466Et05
9.499E+05
1.066E+06
1.196Et06
1.342E+06
1.505Et06
1.689Et06
1.895E+06
2.127Et06
2.386Et06
2.677E+06
3.004E+06
3.370E+06
3.782Et06
4.243E+06
4.761E+06
5.342Et06
5.993E+06
6.725Et06
7.545Et06
8.466E+06
9.499Et06
1.066Et07
1.196Et07
1.342E+07
1,505E+07
1.689Et07
1.895Et07
2.127Et07
2.386E+07
2.677E+07
3.004E+07
3.370E+07
3.782Et07
4.243Et07
4.761E+07
5.342E+07
-6.000E+Ol
-. - - -
-4.000Et01
-
-
-2.000Et01
- - -
-
o.
*
*
*
*
*
*
*
*
*
..
.
...
..
...
.
..
..
..
..
..
..
..
..
..
..
.
- - -
- -
*
*
*
*
*
..
*·
*
·*
.
.
*
*
*
.
*
*
*
·*
*
*
.
*·
*
*
*
*
*
*
*
*
*
*
*
**
*
-
--------
- -
Fig.l8 (Continued)
Gain Response
-- --- -
- -
- - - -
60
11******* 87/05/05. *******
SPICE 2F.1 C25FEB80)
******* 13.59.24·*****
OHIGH FREQUENCY NARROW BAND FILTER
0****
INPUT LISTING
TEMPERATURE =
27.000 I•EG C
0***********************************************************************
•I.IIDTH OUT = 80
3
o 10.0
VIN 1
0 AC 1 0
R1
1
2 150K
Q1
3 2 4 DMODl
RE1 4
0 470
RC2 3
5 150
C1
5
4
75P
Q2
5 4 6 QMOD2
RE2 6
0 150
QMOD3
D3
3 5 7
RE3 7
0 470
RC4 3
8 150
C2
8
7
75P
QMOD4
Q4
8 7 9
RE4 9
0 150
Q5
3 8 10 QMOD1
RE5 10
0 470
RC6 3 12 150
Q6 12 10 11 QMOD2
RE61 11 14 136,9
RE62 14 0 13.1
C6
14 0
.lU
Q7 3 12 13 QMOD~
RE7 13 0 470
R2
13 2 150
.MODEL DMOD1 NPNIBF=100 RB=18.75 CJC=BP CJE=246,8P>
.MODEL QMOD2 NPNCBF=80 RB=20 CJC=1P CJE=210P>
.MODEL QMOD3 NPNCBF=lOO RB=18.75 CJC=8P CJE=278.6P>
.MODEL QMOD4 NPNCBF=80 RB=20 CJC=1P CJE=243,8P>
.I'IC LIN 40 10.6MEG lO.BMEG
*AC DEC 20 8.46E+5 8.46E+7
,PLOT AC VI1BI13)
.PLOT AC VPI13>
.END
vee
Fig.l9
SPICE Program For
The Filter of Fig. 8 For C=75 pF, R= 150 ohm
61
OHIGH FREQUENCY NARROW BAND FILTER
TEMPERATURE
AC ANALYSIS
0****
=
27,000 [lEG C
0***********************************************************************
X
FREQ
X
VIIB ( 13)
-
-
--i'. eoeEtO·l: - --·1:. eoeE to:~:
-3. ooeE +O·l:
- e.1.060Et07 -2.611Et01
*
1.061Et07 -2.562E+Ol
*
l.061Et07 -2.'511Et01
*
-2.456Et01
lo062E+07
*
-2.397Et01
lo062Et07
*
lo063Et07 -2.334Et01
*
lo063E+07 -2.267Et01
*
lo064E+07 -2.193Et01
*
lo064Et07 -2.113Et01
*
lo06'5Et07 -2.025E+01
*
lo06'5Et07 -1.927E+Ol
·*
lo066E+07 -1.817Et01
*
lo066E+07 -1.690E.t01
*
1.067Et07 -1.543Et01
*
1.067Et07 -1.365Et01
*
lo068Et07 -l.143Et01
1.068Et07 -8.483EtOO
*
lo069E.t07--4.192Et00
*
l.069Et07 2.072Et00
1.070Et07--1.527E-Ol
*
1.070Et07 -5.877E+OO
*
1.071E+07 -9,601Et00
·*
1.071Et07 -1.225E+01
*
1.072Et07 -1.429Et01
*
1.072Et07 -1. '595E+Ol
*
lo073E+07 -1.73'5Et01
*
1.073Et07 -1,8'55Et01
*
1.074Et07 -1.961Et01
·*
lo074E+07 -2.055E+Ol
*·
lo07'5Et07 -2.140Et01
*
lo07'5E+07 -2.217Et01
*
lo076Et07 -2.288Et01
*
lo076Et07 -2.354Et01
*
lo077E+07 -2,415Et01
*
1.077E+07 -2,472Et01
*
1.078Et07 -2.526Et01
*
l.078Et07 -2.576Et01
*
1.079Et07 -2.624Et01
*
lo079E+07 -2,669E+Ol
*
l.OBOE+07 -2.712E+Ol
*
..
..
..
.
-1T060Et61
.
..
..
* ..
..
.
.
..
..
..
..
..
*
.
.
..
..
- - -
-
- -
-
- - - - - -- - - - - - - - - - -- -
Fig.l9 (Continued)
Gain Response
62
OHIGH FREQUENCY NARROW BAND FILTER
AC ANALYSIS
TEMPERATURE = 27, 000 II E.G C
0****
0***********************************************************************
X
FREO
VP<l3)
..
..
-2.00eEtO~
X
lo060E+07
lo061E+07
lo061E+07
1.062Et07
lo062E.t07
lo063Et07
1.063Et07
lo064Et07
lo064Et07
1.065Et07
lo065E.t07
1.066Et07
lo066Et07
lo067E+07
lo067E+07
lo068Et07
lo068E.t07
1.069Et07
1.069Et07
lo070E+07
lo070Et07
lo071Et07
l.071E.t07
lo072E+07
1.072Et07
lo073E+07
lo073E+07
lo074Et07
1.074Et07
1.075Et07
1.075Et07
1.076Et07
lo076Et07
lo077Et07
lo077Et07
1.078Et07
lo078Et07
lo079Et07
lo079Et07
lo080Et07
9.831E+Ol
9.840E+01
9.850Et01
9.862Et01
9.876Et01
9.892Et01
9.912Et01
9,935Et01
9.964Et01
9.999Et01
l.004Et02
1.010E+02
1.017Et02
1.02BE+02
1.043E+02
1.067Et02
l.l12Et02
1.215Et02
1.586Et02
-1.276Et02
-1.051E+02
-9,764Et01
-9.410Et01
-9,205Et01
-9.072Et01
-8,979Et01
-8,911E+Ol
-8.859E+01
-8.819Et01
-8.786Et01
-8,760Et01
-8.738E+Ol
-8,719Et01
-8,704E+01
-8.691Et01
-8.679Et01
-8.670Et01
-8.661Et01
-8,654Et01
-8.648E+01
..
..
..
..
..
.
..
.
...
..
..
...
..
-
--t.eoeEto~
- - e.- - - - - -
t.eoeE+o~
-2ToeoEte2
*
*
**
*
*
*
*
**
*
**
*·*
·*
.*
*
* *·
*·*
·*
·*
·*
.*
.. **
.*
.. **
.*
.*
.*
.*
.*
.*
.. **
Fig.l9 (Continued)
Phase Response
*
63
OHIGH FREQUENCY NfiRROW SfiND FILTER
fiC fiNfiLYSIS
TEMf'ERfiTURE =
27 .ooo m::G c
0****
0***********************************************************************
X
FREQ
VDB<13l
-S.OOOE+Ol
X
1.070Et06
1.201Et06
1.347E+06
1.511E+06
1.696Et06
1.903Et06
2.135Et06
2.395E+06
2.688Et06
3.016Et06
3.384Et06
3.797E+06
4.260Et06
4.780E.t06
5.363Et06
6.017E+06
6.751E+06
7.575Et06
8.499E+06
9.536Et06
1.070E+07
1.201Et07
1.347E+07
1.511Et07
1.696Et07
1.903Et07
2.135E+07
2.395Et07
2.688E+07
3.016Et07
3.384Et07
3.797Et07
4.260E+07
4.780E+07
5.363E+07
6.017E+07
6.751E+07
7.575Et07
8.499E+07
9.536E+07
1.070Et08
-6.611Et01
-6.606E+01
-6.600Et01
-6.593Et01
-6.583Et01
-6.572Et01
-6.557E+Ol
-6.539Et01
-6.515E+Ol
-6.487Et01
-6.450Et01
-6.405Et01
-6.348Et01
-6.276E+Ol
-6.185Et01
-6.067Et01
-5.912E+Ol
-5.698E.t01
-5.380E+Ol
-4.809Et01
-3.326Et00
-4.877E.t01
-5.S05Et01
-5.884Et01
-6.159Et01
-6.378Et01
-6.559Et01
-6.713Et01
-6.845Et01
-6.956Et01
-7.046E+01
-7.115E+01
-7.160E+01
-7.185E+01
-7.194E+01
-7.196E+01
-7.202Et01
-7.221Et01
-7.258Et01
-7.314Et01
-7.382E+01
...
..
..
.
.
..
.
...
..
..
..
..
..
..
.
...
...
-6.000Et01
-4.000E+01
-2.000E+01
0.
**
*
*
*
**
*
**
*
*
** .
*·
*·*
.*
*
*
*
*
*
*
*
**
*
***
**
*
**
*
Fig.19 (Continued)
Gain Response
*.
,, .
64
521
57
riL.C•160
rREQ-STEP• .1 MHz
180
53
150
419
120
415
90
411
60
37
30
33
0
z
29
-30
t:l
fTl
a:
25
-s0
.....
21
-90
17
-120
13
-150
9
-180
,....
m
"'C
~
:::0
w
Cl
:J
tH
l!l
l:.
-u
I
*
(J)
fTl
+ ,....
G)
5
6.2
7.41
8.6
9.8
11
12.2
13.41
141.6
FREQ ( .4 MHz/DlVISION)
Fig.
20
Gain loss and Phase Response for The
Filter of Fig. 16 For a Feedback Capacitance of 161pF.
65
521
54
riL.C•11210P
rREQ-STEP• .1 MHz
18121
s121
150
46
12121
42
9121
38
6121
34
3121
3121
121
z
26
-3121
a:
22
-6121
18
-9121
14
-12121
10
-15121
6
-18121
IIl
"'C
"1J
I
:0
"-J
w
r:::l
:J
~
H
l?
:I:
*
Ul
r1
+ ,....
0
r1
G)
5
6.2
7.4
8.6
9.8
11
12.2
13.4
14.6
FREQ ( .4 MHz/DIVISION)
Fig. 21
Gain Loss and Phase Response for The
Filter of Fig. 16 For a Feedback Capacitance of 100 pF
"-J
66
521
55
riL.C•75
rREQ-STEP• .1 MHz
180
51
150
47
120
43
90
.._,
39
60
w
35
30
31
0
27
-30
23
-60
19
-90
15
-120
11
-150
7
-180
""'
m
"'0
0
:J
1H
zl:)
a:
:I:
*
"'0
:::c
:D
U'J
f'Tl
+ ,...,
t::l
f'Tl
C)
5
6.2
7.4
8.6
9.8
11
12.2
13.4
14.6
FREQ ( .4 MHz/DIVISION)
Fig. 22
Gain Loss and Phase Response for The
Filter of Fig. 16 For a Feedback Capacitance of 75 pF
67
49
521
riL.C•161-CC•120
rREQ-STEP• .05 MHz
180
45
150
41
120
37
90
"'D
....,
33
60
w
29
30
25
0
1-1
21
-30
a:
17
-60
13
-90
,...,
IIl
0
:::::>
r-
z
(!l
l:
'"0
:I:
J)
*
Ul
1"'1
+ ,...
t:l
M
C)
9
-120
5
-150
....,
-180
4.5
5.1
5.7
6.3
6.9
7.5
8.1
8.7
9.3
FREQ ( .2 MHz/DIVISION)
Fig. 23
Gain loss and Phase Response for
The Filter of Fig. 16 For a Feedback
Capacitance of 16lpF and a Compensating Capacitor of lOOpF
68
521
51
fiL.C•100.-CC•120
fREO-STEP• .1 MHz
180
47
150
43
120
,...,
39
90
"'C
35
60
31
30
27
0
23
-30
19
-60
15
-90
11
-120
7
-150
3
-180
co
'-J
w
0
::J
1H
zt!)
cr:
:L
*
"tl
:r
J)
U'l
JT1
+ ,...,
0
JT1
G)
5
6.2
7.4
8.6
9.8
11
12.2
13.4
......
14.6
FREQ C .4 MHz/DIVISION)
Fig. 24
Gain loss and Phase Response for
The Filter of Fig. 16 For a Feedback
Capacitance of lOOpF and a Compensating Capacitor of lOOpF
69
521
51
riL.C•89.CC•120
rREQ-STEP• .1 MHz
180
-47
150
-43
120
39
90
"C
....,
35
60
w
31
30
:::::1
27
0
23
-30
19
-60
15
-s0
11
-120
7
-150
3
-180
,...,
Ill
Cl
1-
H
z
(.!)
a:
~
*
'"0
I
:n
Ul
1"'1
+ ,....
t:l
1"'1
(;')
5
6.2
7.-4
8.6
9.8
11
12.2
13.-4
14.6
FREQ ( .4 MHz/DIVISION)
Fig. 25
Gain loss and Phase Response for
The Filter of Fig. 16 For a Feedback
Capacitance of 89pF and a Compensating Capacitor of lOOpF
70
Transistor
VB(volts)
VC(volts)
VE(volts)
01
5.4
10.0
4.7
02
4.7
6.0
4.0
03
6.0
10.0
5.3
04
5.3
5.4
4.6
05
5.4
10.0
4.7
06
4.7
6.0
4.0
07
6.0
10.0
5.3
TABLE
[1]
d.c. Bias Voltages of Transistors in the Filter of Fig. 8
Q
71
Transiator
VB(volts)
VC(volts)
VE(volts)
01
6.8
10.0
6.1
02
3.1
6.4
2.4
03
6.4
10.0
5.7
04
2.7
7.0
2.0
05
7.0
10.0
6.3
06
3.3
7.4
2.6
07
7.4
10.0
6.8
Table
[ 21
d.c. Bias Voltages of Transistors in the Filter Fig. 16
'
72
IC
Transistor
grn
=
fT
C.l(.
Cn'
MHZ
pF
pF
100
250
8
246.8
VT
01
•4
02
1.06
80
800
1
210.0
03
.45
100
250
8
278.6
04
1.23
80
800
1
243.8
05
•4
100
250
8
246.8
06
1.06
80
800
1
210.0
07
.45
100
250
8
276.8
Table
[ 31
High Frequency Parameters For The Transistors of
Filter Configuration of Fig. 8 used for SPICE Models.
73
c
Ideal Q
Estimated Q
from Eq.
( 3 4)
pF
SPICE Q
161
1000.5
904
560
100
1000.5
909
470
75
1000.5
884
450
c
Ideal fo
Estimated fo
from Eq.(33)
MHZ
SPICE fo
pF
MHz
161
6.6
6.2
5.6
100
10.6
9.7
8.5
75
14.1
12.5
10.7
MHZ
Table [41
The Ideal, Estimated and
SPICE Values of Center Frequency And Q For The Filter of
Fig. 8 For Three Different Values of Feedback CapacitanceS.
74
c
Ideal Q
pF
Estimated Q
uaing Eq.
( 34)
Actual
Meaaured Q
161
455
435
88.5
100
455
420
83.0
75
455
408
74.5
c
Ideal fo
pF
MHz
Estimated fo
using Eq.(33)
MHZ
Actual
Meaaured fo
MHZ
161
6.6
6.4
5.9
100
10.6
10.2
8.3
75
14.1
13.5
10.06
Table (5]
Ideal Estimated and Measured Values of
Quality Factor and Center Frequency for
Filter of Fig. 16. For Three Different Feedback Capacitors.
75
c
Ideal fo
Actual Measured fo
pF
MHZ
MHZ
161
6.6
6.5
100
10.6
9.9
89
11.9
10.6
Table [6)
The Ideal And Measured Values of
the Center Frequency of the Filter of Figure 16 when a
Compensating Capacitor is used in the Emitter Lead of the
Last Gain Stage.