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January 7, 2009 10:51 WSPC/123-JCSC 00455
Journal of Circuits, Systems, and Computers
Vol. 17, No. 4 (2008) 637–658
c
World Scientific Publishing Company
HISTORY AND PROGRESS OF THE
KERWIN–HUELSMAN–NEWCOMB FILTER
GENERATION AND OP AMP REALIZATIONS
AHMED M. SOLIMAN
Electronics and Communication Engineering Department,
Faculty of Engineering, Cairo University, Egypt
asoliman@ieee.org
Revised 20 January 2008
The history of Kerwin–Huelsman–Newcomb (KHN) second-order filter is reviewed. A
generation method of the KHN filter from passive RLC filter is presented. Two alter-
native forms of the KHN circuit using operational amplifier are reviewed. The effect of
finite gain-bandwidth of the op amps is considered and expressions of the actual ω0and
Qare given. Two KHN circuits with inherently stable Qfactor are also included. Two
new partially compensated inverted KHN circuits are introduced. Active compensation
methods to improve the KHN and the inverted KHN circuit performance for high Q
designs are summarized. Spice simulation results are given. The progress of the KHN
realizations using the current conveyor is also summarized briefly.
Keywords: KHN circuit; active filters; op amps.
1. Introduction
The two most famous multiple output active filter circuits are the
Kerwin–Huelsman–Newcomb (KHN) bi-quadratic circuit1and the Tow–Thomas
bi-quadratic circuit (TT).2,3Both circuits are included almost in all textbooks in
Active filters,4–11 and are introduced in most universities to the undergraduate or
graduate students. Due to the great importance of these circuits and the progress in
their realizations it is desirable to collect such progress in review papers. Recently,
the progress in the TT circuit is summarized in a review paper.12 It is also desirable
to provide such a review paper for the KHN circuit, this is the objective of this
paper. In the original paper,1the theory started by considering a general trans-
fer function of order n, state variable flow graphs with negative gain integrators
are used then to develop the insensitive transfer function realization in terms of
integrated circuits. The operational amplifier (op amp) is then used to form the
integrators and summers needed for the signal flow graph realization. Based on the
fact that any polynomial with real coefficients can be factored into first- or second-
order degree terms that also have real coefficients, the generalized transfer function
can be realized as a cascade of first- and second-order sections. As a consequence,
637
January 7, 2009 10:51 WSPC/123-JCSC 00455
638 A. M. Soliman
the work in Ref. 1 concentrates on the realization of the general second-order trans-
fer function using two integrators and two summers. The resulting circuit has four
outputs and employs a total of four op amps, two capacitors, and 10 resistors. In
most textbooks and for simplicity the summer stage at the output is not included
and the three output KHN circuit with highpass, bandpass, lowpass outputs using
three op amps is the one that is given in Refs. 4–10. In the next section a gener-
ation method to obtain the KHN circuit from a second-order passive RLC circuit
is given. The generation method is differentfromthatusedinRef.12fortheTT
circuit in which the resistor and the inductor in the RLC circuit are combined as
one impedance unit. In the following generation method the three passive elements
in the RLC circuit are taken as separate elements.
2. Generation of KHN Circuit from Passive RLC Circuit
Figure 1(a) represents the passive series RLC filter which is described by the fol-
lowing equations:
I=Vi−V1
R1
,I=V1−V2
sL ,V
2=1
sC I. (1)
The above equations can be written in the following form:
Vi1=Vi−V1
a,−Vi1=−1
sτ1
(V1−V2),V
2=−1
sτ2
(−Vi1),(2)
C
L
R1
I
V1V2
Vi
(a)
-Vi1 V2
Vi
a
sτ1 sτ2
-1 -1
+ Σ
-
+
b
(b)
Fig. 1. (a) The passive RLC filter. (b) Block diagram of the passive RLC filter.
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 639
where
a=R1
R,V
i1=IR, τ1=L
R,τ
2=CR. (3)
The parameter Rhas the unit of resistor but has no physical existence in the circuit
of Fig. 1(a).
Equation (3) can be represented by the block diagram shown in Fig. 1(b), where
the parameter bequals to 1 and is added for the purpose of realization of the KHN
circuit. It should be noted that although the passive RLC circuit has no feedback
paths the block diagram includes two negative feedback loops. The KHN circuit1
is realizable directly from this block diagram and is shown in Fig. 2(a), with the
block diagram parameters given by
a=2R3
R3+R4
,b=2R4
R3+R4
,τ
1=C1R1,τ
2=C2R2.(4)
The equivalent block diagram of the circuit of Fig. 2(a) is shown in Fig. 2(b).
R4
C1C2
R2
R1
A2
A1
A3
VHP
VBP
R
R
R3
VI
+
+
+
-
-
-
VLP
(a)
VBP
VHP VLP
VI
R3+R4
sC1R1 sC2R2
-1 -1
2R3
2R4 +
-
+
R3+R Σ
4
(b)
Fig. 2. (a) The KHN filter.1(b) Block diagram of the KHN filter.
January 7, 2009 10:51 WSPC/123-JCSC 00455
640 A. M. Soliman
The transfer functions of the three outputs at the circuit are given by
VHP
VI
=
2R4
R3+R4s2
s2+2R3
R3+R4
·s
R1C1+1
R1R2C1C2
,
VBP
VI
=
−2R4
R3+R4
s
R1C1
s2+2R3
R3+R4
·s
R1C1+1
R1R2C1C2
,
VLP
VI
=
2R4
R3+R4
1
R1R2C1C2
s2+2R3
R3+R4
·s
R1C1+1
R1R2C1C2
.
(5)
The circuit is usually designed by taking equal capacitors C1=C2=Cand the
design equations are given by
R1=R2=1
ω0C,R
4=(2Q−1)R3.(6)
It is seen that there is independent control on Qby adjusting the value of R4
without affecting ω0of the filter. The magnitude of the gain at ω0at any of the
three outputs of the filter is given by 2Q−1.
In this case the parameters a, b in the block diagram of Fig. 2(b) are given by
a=1
Q,b=2−1
Q.(7)
The filter polarities can be inverted as given by Geffe in the modified KHN circuit
published in Ref. 13.
3. Inverted KHN Circuit
In many cases it may be desirable to have a non-inverting bandpass response. The
circuit reported in Ref. 13 and shown hereinFig.3(a)isaninvertedversionof
the KHN circuit. The circuit can also be generated from the passive RLC block
diagram of Fig. 1(b) by taking:
a=1
Q,b=−1,τ
1=C1R1,τ
2=C2R2.(8)
The transfer functions at the circuit three outputs are given by:
VHP
VI
=−s2
s2+3R3
R3+R4
·s
R1C1+1
R1R2C1C2
,
VBP
VI
=
s
R1C1
s2+3R3
R3+R4
·s
R1C1+1
R1R2C1C2
,
VLP
VI
=
−1
R1R2C1C2
s2+3R3
R3+R4
·s
R1C1+1
R1R2C1C2
.
(9)
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 641
R4
C1C2
R2
R1
A2
A1
A3
VHP VBP
R
R
R3
+
+
+
-
-
-
VI
R
VLP
(a)
VBP
VHP VLP
VI
R3+R4
sC1R1sC2R2
-1 -1
3R3
- Σ
-
+
(b)
Fig. 3. (a) The inverting input Kerwin–Huelsman–Newcomb filter.13 (b) Block diagram of the
inverting input KHN filter.
Taking equal capacitors C1=C2=Cand the design equations are given by
R1=R2=1
ω0C,R
4=(3Q−1)R3.(10)
It is seen that there is an independent control on Qby adjusting the value of
R4without affecting ω0of the filter. The magnitude of the gain at ω0at any of the
three outputs of the filter is given by Q.
4. Effect of Finite Gain Bandwidth of the Op Amps
The finite gain bandwidth of the op amp limits the maximum frequency of operation
of the KHN circuit and the inverted KHN circuit as well. The frequency limitation
January 7, 2009 10:51 WSPC/123-JCSC 00455
642 A. M. Soliman
equation of the both circuits take the single pole model of the op amp into con-
sideration is given next. Assume matched op amps are used which are internally
compensated to have a single pole open loop response with a unity gain bandwidth
ωt. Thus, the op amp open loop gain is given by
A(s)= A0ω0
s+ω0
∼
=ωt
s.(11)
Taking the effect of the finite gain bandwidth into consideration the denominator
of the KHN circuit is given by
D(s)=s2+ω0
Qs+ω2
0+s
ωt4s2+ω0
Q+2ω0s+ω2
0
Q.(12)
Following Budak–Petrala method14 the fractional shifts in ω0and Qare given
approximately by
∆ω0
ω0
∼
=−ω0
ωt
,∆Q
Q
∼
=4ω0Q
ωt
.(13)
It is seen that the fractional shift in Qis 4Qtimes the fractional shift in ω0,which
sets an upper bound on the maximum frequency of operation for a given op amp
and for a specified Qand an allowable limit on the incremental change in Q.
For the inverted KHN, D(s)isgivenby
D(s)=s2+ω0
Qs+ω2
0+s
ωt5s2+ω0
Q+2ω0s+ω2
0
Q.(14)
Following Budak–Petrala method14 the fractional shifts in ω0and Qare given
approximately by
∆ω0
ω0
∼
=−ω0
ωt
,∆Q
Q
∼
=5ω0Q
ωt
.(15)
It is seen that the fractional shift in Qis 1.25 the shift in Qof the original KHN
circuit and is 5Qtimes the fractional shift in ω0. This sets an upper bound on the
maximum frequency of operation for a given op amp and for a specified Qand an
allowable limit on the incremental increase in Q.
5. Compensation of the KHN Circuit
As seen in the previous section the KHN circuit and the inverted KHN circuit both
suffer from a rather drastic Q-factor-enhancement effect due to the op amps finite
gain bandwidth. The Q-factor enhancement is due to the excess phase lag around
the loop and hence may be compensated for by the addition of an equal amount
of phase lead. The passive compensation methods are not satisfactory solutions as
there is no guarantee that the phase cancellation will be valid at different envi-
ronmental conditions.15 Before discussing the active compensation methods of the
KHN circuit, it is desirable to include here one of the attractive self-compensated
three amplifier circuits with stable Qfactor.15
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 643
R4= (2Q-1) R3
C1
C2
R2
R1
A2
A1
A3
VLP
VHP
R
R
R3
VI
-
+
+
+
-
-
VBP
(a)
R4= (2Q-1) R3
C1
C2
R2
R1
A2
A1
A3
VHP
VLP
R
R
R3
VI
-
+
+
+
-
-
VBP
(b)
Fig. 4. (a) Modified KHN circuit 1 with stable Qfactor.15 (b) Modified KHN circuit 2 with
stable Qfactor.
5.1. The modified KHN with stable Q factor
The circuit shown in Fig. 4(a) was introduced in Ref. 15 and is based on the
assumption that the three op amps used are matched. The actual Qexpression15
is given by
Qa ∼
=Q
1+Q2ω0
ωt1
−ω0
ωt2
−ω0
ωt3.(16)
For matched op amps it is seen that the circuit is almost free from Q-factor error.
The circuit shown in Fig. 4(b) is related to that shown in Fig. 4(a) by RC:CR
transformation6of the two integrator elements. It can also be generated from the
January 7, 2009 10:51 WSPC/123-JCSC 00455
644 A. M. Soliman
KHN circuit of Fig. 2(a) by representing the op amps by the nullators and norators
and exchanging the outputs of the two integrator stages. It is possible to generate
many more circuits based on the interchange of the two ports of the three nullors,16
however the circuit of Fig. 4(a) is the most attractive one.
5.2. Active compensation of the KHN circuit
Phase correction in the KHN circuit can be achieved if the phase lead integrator
reported in Ref. 17 is used in place of one of the two integrators as shown in
Fig. 5(a). The phase lead of the integrator that is used in Fig. 5(a) is given by
φ∼
=Kω0
ωt4a
K+1−1.(17)
Assuming matched op amps are used and taking K= 1; and to provide the
necessary phase lead of 3ω0/ωt, it is seen that ashould be taken equal to 8.
Another active compensated KHN circuit is shown in Fig. 5(b) which is based on
adding the phase corrector consisting of op amp number 4 and two resistors.18 The
phase lead of the summer stage is adjusted to 2ω0/ωtto cancel the two integrators
phase lag.
It should be noted that the circuits of Fig. 5 are better than the self-compensated
circuits of Fig. 4 as they can be used with mismatched op amps.
6. Compensation of the Inverted KHN Circuit
Figure 6(a) represents a partially compensated inverted KHN circuit obtained by
interchanging the two integrator outputs. Five more new circuits can be obtained
from Fig. 3(a) based on the interchange of the two ports of the three nullors.16
The circuit shown in Fig. 6(b) is related to that shown in Fig. 6(a) by RC:CR
transformation6of the two integrator elements. It can be proved that for the circuit
in Fig. 6(a), the fractional shift in Qis one fifth of its value for the circuit in Fig. 3(a).
It can also be proved that for the circuit in Fig. 6(b) the fractional shift in Qis the
negative of one fifth of its value for the circuit in Fig. 3(a).
Phase correction in the inverted KHN circuit can be achieved if the phase lead
integrator reported in Ref. 17 is used in place of one of the two integrators as shown
in Fig. 7(a).
Assuming matched op amps are used and taking K= 1; and to provide the
necessary phase lead of 4ω0/ωt, and using Eq. (17) it is seen that ashould be taken
equal to 10.
Another active compensated inverted KHN circuit is shown in Fig. 6(b) which
is based on adding the phase corrector consisting of op amp number 4 and two
resistors.18 The phase lead of the summer stage is adjusted to 2ω0/ωtin order to
cancel the two integrators phase lag.
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 645
(2Q-1) R
C
C
(K+1)R
R
A2
A1
A3
VHP
VBP
R
R
R
VI
+
+
+
-
-
-
VLP
A4
+
-
R/a
KR
R
(a)
(2Q-1) R
C C
R
R
A2
A1
A3
VHP VBP
R
R
R
VI
+
+
+
-
-
-
VLP
A4
R
3R
+
-
(b)
Fig. 5. (a) Active compensated KHN circuit using phase lead inverting integrator.17 (b) Active
compensated KHN circuit using phase corrector.18
7. Spice Simulations
In this section, spice simulations are carried out using the op amp µA 741 from
Analog Devices with ft= 1 MHz and using supply voltages of ±15 V. The KHN
circuitofFig.2(a)isdesignedforQ=5andf0=10kHztakingC1=C2= 500 pF,
R1=R2=31.9kΩ, R=10kΩ,R3=10kΩ,R4= 90 kΩ and using sinusoidal input
voltage source of 1 V magnitude.
January 7, 2009 10:51 WSPC/123-JCSC 00455
646 A. M. Soliman
R
R
R
R1
R2
R
(3Q-1)R
VHP
VLP VBP
VI
A1
A2
A3
C1
C2
+
+
+
-
-
-
(a)
R
R
R
R1
R2
R
(3Q-1)R
VLP
VHP VBP
VI
A1
A2
A3
C1
C2
+
+
+
-
-
-
(b)
Fig. 6. (a) The first partially compensated inverted KHN circuit. (b) The second partially
compensated inverted KHN circuit.
Figure 8(a) represents the spice simulation results of the magnitude and phase
of the KHN circuit together with the ideal response. Since the gain at the center
frequency equals to 2Q−1, and from the linear scale simulated magnitude it is seen
that the center frequency gain= 11, hence it is seen that Qhas increased from its
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 647
(3Q-1) R
C
C
2R
R
A
2
A
1
A
3
V
HP
V
BP
R
R
R
V
I
+
+
+
-
-
-
V
LP
A
4
+
-
R/10
R
R
R
(a)
(3Q-1) R
C C
R
R
A
2
A
1
A
3
V
HP
V
BP
R
R
RV
I
+
+
+
-
-
-
V
LP
A
4
R
4R
+
-
R
(b)
Fig. 7. (a) Active compensated inverted KHN circuit using phase lead inverting integrator. (b)
Active compensated inverted KHN circuit using phase corrector.
January 7, 2009 10:51 WSPC/123-JCSC 00455
648 A. M. Soliman
(a)
(b)
Fig. 8. Simulation results of the magnitude and phase characteristics of KHN circuit of Fig. 2(a)
at (a) 10 kHz and at (b) 50 kHz.
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 649
theoretical value of 5 to Qa= 6. From the simulation results ∆Q/Q =0.2whichis
the same as the theoretical expected value obtained from Eq. (13).
Figure 8(b) represents the spice simulation results of the magnitude and phase
of the KHN circuit designed with the same Qvalue as the previous circuit and with
f0=50kHztakingC1=C2= 100 pF and all resistors the same as before. It is seen
that the center frequency gain = 19, hence Qa= 10 which is double the ideal value
of 5, and ∆Q/Q = 1 which is the same as the theoretical expected value obtained
from Eq. (13).
The inverted KHN circuit of Fig. 3(a) is designed for Q=5andf0=10kHz
taking C1=C2= 500 pF, R1=R2=31.9kΩ, R=10kΩ,R3=10kΩ,R4=
140 kΩ and using sinusoidal input voltage source of 1 V magnitude.
Figure 9(a) represents the spice simulation results of the magnitude and phase
of the KHN circuit together with the ideal response. Since the gain at the center
frequency equals to Q, and from the linear scale simulated magnitude it is seen
that the center frequency gain = 6.4, hence it is seen that Qhas increased from its
theoretical value of 5 to Qa=6.4. From the simulation results ∆Q/Q =0.28 which
is very close to the theoretical value of 0.25 obtained from Eq. (15).
Figure 9(b) represents the spice simulation results of the magnitude and phase
of the inverted KHN circuit designed with the same Qvalue as the previous circuit
and with f0=50kHztakingC1=C2= 100 pF and all resistors the same as b efore.
It is seen that the center frequency gain= 10, hence ∆Q/Q = 1 which is smaller
than the theoretical expected value of ∆Q/Q =1.25 obtained from Eq. (15).
Figure 10(a) represents the spice simulation results of the magnitude and phase
of the modified KHN circuit of Fig. 4(a) designed for Q=5andf0=10kHzand
taking same circuit values as for the KHN circuit of Fig. 2(a). From the simulations
it is seen that the simulated Qis 5 as its theoretical value.
Figure 10(b) represents the spice simulation results of the magnitude and phase
of the modified KHN circuit of Fig. 4(b) designed for Q=5andf0=10kHzand
taking same circuit values as for the KHN circuit of Fig. 2(a). From the simulations
it is seen that the simulated Qis 5 as its theoretical value.
Figures 11(a) and 11(b) represent the simulation results of the two active com-
pensated KHN circuits of Figs. 5(a) and 5(b) for Q=5andf0=50kHz.
Figures 12(a) and 12(b) represent the simulation results of the two new inverted
KHN circuits of Figs. 6(a) and 6(b) for Q=5andf0=50kHz.Fromthesimulations
of Fig. 12(a) it is seen that Qis slightly higher than its ideal value, and from
Fig. 12(b) it is slightly lower than its ideal value of 5 as expected.
Figures 13(a) and 13(b) represent the simulation results of the two active com-
pensated inverted KHN circuits of Figs. 7(a) and 7(b) for Q=5and f0=50kHz.
8. KHN Circuit Using Current Conveyors
Due to the frequency limitation of the KHN circuit using op amps it is desirable to
increase the frequency range of operation using the current conveyors (CCII). The
January 7, 2009 10:51 WSPC/123-JCSC 00455
650 A. M. Soliman
(a)
(b)
Fig. 9. Simulation results of the magnitude and phase characteristics of the circuit of Fig. 3(a)
at (a) 10 kHz and at (b) 50 kHz.
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 651
(a)
(b)
Fig. 10. (a) Simulation results of the magnitude and phase characteristics of the circuit of
Fig. 4(a) at 50 kHz. (b) Simulation results of the magnitude and phase characteristics of the
circuit of Fig. 4(b) at 50 kHz.
January 7, 2009 10:51 WSPC/123-JCSC 00455
652 A. M. Soliman
(a)
(b)
Fig. 11. (a) Simulation results of the magnitude and phase characteristics of the circuit of
Fig. 5(a) at 50 kHz. (b) Simulation results of the magnitude and phase characteristics of the
circuitofFig.5(b)at50kHz.
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 653
(a)
(b)
Fig. 12. (a) Simulation results of the magnitude and phase characteristics of the circuit of
Fig. 6(a) at 50 kHz. (b) Simulation results of the magnitude and phase characteristics of the
circuit of Fig. 6(b) at 50 kHz.
January 7, 2009 10:51 WSPC/123-JCSC 00455
654 A. M. Soliman
(a)
(b)
Fig. 13. (a) Simulation results of the magnitude and phase characteristics of the circuit of
Fig. 7(a) at 50 kHz. (b) Simulation results of the magnitude and phase characteristics of the
circuitofFig.7(b)at50kHz.
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 655
R3
R
R1
R2
R4
2R
C1C2
CCII
CCII
CCII
CCII
VI
VHP
VBP
VLP
Y
Y
Y
Y
Y
X
X
X
X
Z
Z+
Z-
Z-
X
Z
CCII
(a)
R3
R
R1
R2
R4= (3Q-1) R3
2R
C1C2
CCII
CCII
CCII
CCII
VI
VHP
VBP
VLP
Y
Y
Y
Y
X
X
X
X
Z
Z+
Z-
Z-
X
Z
CCII
R
Y
(b)
Fig. 14. (a) The grounded capacitor KHN circuit using current conveyors.19 (b) The grounded
capacitor inverted KHN using current conveyors. (c) The grounded resistor grounded capacitor
KHN circuit using five CCII+.20
January 7, 2009 10:51 WSPC/123-JCSC 00455
656 A. M. Soliman
Ri R1
R2C2
R4
R
C1
CCII
CCII
CCII
VIVHP
VBP
VLP
X
Y
Y
Y
Y
X
X
X
Z+
Z+
Z+
Z+
X
Z+
CCII
R3
CCII
Y
(c)
Fig. 14. (Continued)
first KHN circuit using CCII was introduced in Ref. 19 and is shown in Fig. 14(a).
This circuit has identical equations to the KHN circuit of Fig. 2(a) and it has the
advantage of using two grounded capacitors.
Figure 14(b) represents a new grounded capacitor realization of the inverted
KHN circuit using current conveyors. It has the same equations as the inverted
KHN circuit of Fig. 3(a) and is also represented by the block diagram of Fig. 3(b).
A further progress in the KHN circuit was achieved by the introduction of the
grounded resister grounded capacitor circuit shown in Fig. 14(c).20 This circuit
can realize all the eight sign polarities combinations of the three output voltages
by proper choice of the CCII polarities as explained in Ref. 20. The circuit can
employ five CCII+ as shown to realize three non-inverting filter responses. It has
the additional advantages of very high input impedance; the gain can be adjusted
by varying Riwithout affecting ω0or Qof the filter. Also the Qof the filter can
be adjusted by R4independent of ω0and the gain.
Further progress in universal filters was achieved by the introduction of the
MOS-C current mode circuit in Ref. 21 which employs three balanced output
modified differential current conveyors (MDCC), six MOS transistors and two
grounded capacitors.
January 7, 2009 10:51 WSPC/123-JCSC 00455
History and Progress of the Kerwin–Huelsman–Newcomb Filter 657
9. Conclusions
The KHN circuit and the inverted KHN circuit are generated from the passive
RLC filter circuit. The effect of the finite gain bandwidth on both the KHN and
the inverted KHN is summarized. The self-compensated KHN circuit is reviewed as
well as the modified KHN circuit obtained by interchanging the op amp outputs of
the two integrators. Simulation results are included to demonstrate the practicality
of both circuits as well the active compensated KHN circuits. Two new partially
compensated inverted KHN circuits are reported together with their simulation
results. The active compensation methods are also applied to the inverted KHN
circuit to provide stable Quniversal filters.
The progress of the KHN realizations using the current conveyor is also sum-
marized very briefly. Further progress in the KHN realization using the operational
transresistance amplifier (OTRA) has also been introduced in the literature22,23
and is not included here to limit the paper length.
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