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May 10, 1996 - The current feedback operational amplifiers (CFOAs) are receiving increasing attention as basic building blocks in analog circuit design.
Analog Integrated Circuits and Signal Processing, 11,265-302 (1996) 9 1996 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.

Applications of the Current Feedback Operational Amplifiers AHMED M. SOLIMAN Electronics and Comm. Engineering Dept., Cairo University, Egypt

Received April 6, 1995; Revised May 10, 1996

Abstract. The current feedback operational amplifiers (CFOAs) are receiving increasing attention as basic building blocks in analog circuit design. This paper gives an overview of the applications of the CFOAs, in particular several new circuits employing the CFOA as the active element are given. These circuits include differential voltage amplifiers, differential integrators, nonideal and ideal inductors, frequency dependent negative resistors and filters. The advantages of using the CFOAs in realizing low sensitivity universal filters with grounded elements will be demonstrated by several new circuits suitable for VLSI implementation. PSPICE simulations using the AD844-CFOA which indicate the frequency limitations of some of the proposed circuits are included. Key Words: current feedback op amps 1.

Introduction

The current feedback operational amplifiers (CFOAs) also known as the transimpedance operational amplitiers are now commercially available in bipolar integrated circuits form from several manufacturers. [12]. Very recently a CMOS circuit configuration derived from the bipolar CFOA was described [3]. The CFOAs are now recognized for their excellent performance in high speed and high slew rate analog signal processing [4]. Recently current mode and voltage mode filters implemented from a single CFOA were given [5]. In this paper several applications of the CFOAs in realizing voltage amplifiers, integrators, inductors, frequency dependent negative resistors and filters are proposed. PSPICE simulation results are given which demonstrate the frequency limitations of some of the reported circuits.

2.

The Current Feedback Op Amp

The CFOA is a very versatile four-terminal active building block represented symbolically as shown in Fig. 1 and described by the following matrix equation:

O lOO

Iy Iz Vo

=

01 00 00 i J 0 0 1

/

Vy VZ Io

(1)

The X terminal which is also defined as the inverting input terminal is characterized by a very low input

impedance. The Y terminal which is also defined as the noninverting input has a very high input impedance. The two outputs Z and O exhibit a very high and a very low output impedance respectively. The CFOA is considered to be a cascade of a second generation current conveyor (CC II+) [6] and a voltage buffer. This paper concentrates on the applications of the CFOA with the output terminal Z (also known as the compensating pin) being available. It has been demonstrated in [5] that the CFOAs including the terminal Z are much more versatile than other existing CFOAs topologies, this fact will be clearly recognized from the applications of the CFOAs described in this paper. All the simulations included in this paper are based on using the PSPICE model for the AD 844 A/ADCFOA in which the stray capacitance at the compensating pin Cz = 5.5 pF and Rz = 2.2 Mr2. The DC supply voltages used are -t-12v. In the following section the CFOA is used as the basic building block in realizing voltage amplifiers and integrators.

3. Voltage Amplifiers and Integrators The first building block considered here is the generalized three port voltage controlled voltage source (VCVS) shown in Fig. 2(a). The output voltage is given by: Vo = K ( V l - V2)

(2-a)

266

Soliman

Figs. 3(c), (d) represent similar simulations for the inverting amplifier of Fig. 2(c). It is seen that the phase is independent of R1 since the inverting input X is at virtual ground which eliminates the effect of the stray capacitance C x on the amplifier characteristics. The differential voltage integrator is shown in Fig. 4(a). The circuit has the advantage of using a single resistor and a single grounded capacitor, where as in the conventional op amp balanced time constant integrator two resistors and two capacitors are required. The output voltage Vo is given by: Vo ---- W~ (V~ - V2)

(3-a)

1 w0 = - CR

(3-b)

S

Fig. 1.

The symbolic representation of the CFOA.

where

where RE K = -R1

(2-b)

It is seen that the circuit provides equal gain for the noninverting input V1 and the inverting input Vz, besides this gain is controlled by varying the resistor R1 without affecting the bandwidth which is controlled by the grounded resistor R2. These properties are not achievable with the VCVS using conventional op amps in which both resistors are floating, the noninverting voltage gain equals the inverting voltage gain plus one and the bandwidth depends on the voltage gain and the gainbandwidth of the op amp. Fig. 2(b) represents the noninverting VCVS which has infinite input impedance and gain equals to K which can be less than one. The inverting VCVS shown in Fig. 2(c) has a finite input impedance given by R1 which must be taken much larger than the input resistance of the CFOA which is typically of the order of 65f2. Of course the realization of an inverting amplifier with infinite input impedance and with grounded resistors requires two CFOAs as shown in Fig. 2(d). Figs. 3(a), (b) represent the PSPICE simulations of the magnitude in db and the phase in degrees for the noninverting amplifier shown in Fig. 2(b) with Rz = 20 Kf2 and RI = 5,10,15 and 20 Kf2. From the simulations it is seen that the 3 db frequency is very close to the theoretical value which is given by f3 db = 1 1.447 MHz. At frequencies above 100 KHz, 27r R 2 C z - the phase characteristics depend on R1, this is due to the zero which resulted from the stray input capacitance at port X.

Figs. 4(b) and 4(c) represent the noninverting and the inverting integrators which are obtainable from Fig. 4(a) by setting Va = 0 and V] = 0 respectively. Fig. 4(d) represents the infinite input impedance inverting integrator using a grounded resistor. Figs. 5(a), (b) represent the magnitude and phase for the noninverting integrator shown in Fig. 4(b) with R = 5, 10, 15 and 20 Kf2 and C = lnE The magnitude error is given approximately by C z / C and equals to 0.55%. Similar simulations for the inverting integrator of Fig. 4(c) are given in Figs. 5(c), (d). It should be noted that the phase for the inverting integrator equals to 90 ~ over a wide frequency range and is independent of the magnitude of R (due to the virtual ground at X). It is also possible to realize differential integrators with infinite input impedance at both inputs using two CFOAs as shown in Figs. 6(a) and 6(b) where Vo in both cases is given by eqn. (3). Of course replacing the capacitors in Fig. 6 by resistors, one obtains the voltage instrumentation amplifiers, based on their well known current conveyor version [7-8]. 4.

Inductor and FDNR Realizations

In this section the realizations of nonideal and ideal grounded inductors using the CFOA are considered.

4.1.

Series L-R Circuits

Fig. 7(a) represents a series L-R circuit based on the circuit given in [9].

Applications of the CFOAs

Vi .

267

Y

-vo Vl.

=% V2 o

R1

(b)

(a) RI Vi.,

-_Vo Y

Vi9

~

m

(c)

---. Vo

(d)

Fig. 2. (a) The differential VCVS. (b) The noninverting VCVS. (c) The inverting VCVS. (d) The infinite input impedance inverting VCVS.

The input impedance Zi is given by: Zi = sCR1R2 -I- (R1 + R2)

(4)

Thus it is seen that the circuit realizes a series L-R circuit, with L = CR1Rz and R = Rt + R2. Another circuit which employs also four resistors, a single capacitor together with the CFOA is shown in Fig. 7(b). Its input impedance is given by:

Zi =

sCR1R2 + R1 sC[R2 - R I ( K - 1)] + 1

(g-a)

Thus it is seen that the necessary condition to realize a series L-R circuit is given by:

R2 K = 1 + R--7

(5-b)

In this case L = CR1R2 and R = R1, that is for equal R1 and R2 this circuit has double the Q factor of the circuit of Fig. 7(a). Again this circuit is derived from the inductor circuit given in [ 10]. Fig. 8(a) shows the simulation results of the magnitude and the phase of the input impedance of the circuit of Fig. 7(a) with R1 = R2 = 1 KS2, C = 1 nF and R = 1 Kf2. Fig. 8(b) shows similar simulations for the circuit of Fig. 7(b) with R1 = R2 = 1Kf2, C = 1 nF, R = 10Kf2 and K = 2.

4.2.

Parallel L-R Circuits

In this section two new circuits are given, each circuit employs a single CFOA, a single capacitor and two

268

Soliman

20 T ..................................................................................................................

Gain in Db.

15 ~

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Rl=Sk

lo ~

. . . . . . . . .

:

Rl=10k

\

$' Rl=iSk

9

\

9

\

Rlw20k

I I R2=20k

-10 + ......................

9 ......................

lOOHz o

1.0KHz e

9 9

r ......................

IOKHz

r ......................

100KHz

9 ......................

1.0MHZ

IOMH:

vdb(5) Frequency

(a)

Od T

-2od ~

........

.

.

.

.

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.

\L\ -40d

~

Rl~20k

. . . . . . . . .

\

\\

\\

-6o~

~

Rl=lOk

. . . . . . . . .

\

R2-20k

Rl~Bk

IOOHz . o

I.OIC~Iz v

10KHz

100KHz

1.0MHz

* vp(5) Frequency

(b) Fig. 3. (a) The magnitude characteristicsof the VCVS of Fig. 2(b). (b) The phase characteristicsof the VCVS of Fig. 2(b).

Applications of the C F O A s

2O T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Gain in Db.

zs"

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. . . . . .

Rl=10k .

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\

\ .

: 100Hz

a

*

v

~

vdb(5)

.

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.

R2=20k

i. 0KHz

,, ",\

10KHz

100KHg

\

'~

\",i'\

"

\\

i. 0MHz

10MHI

Frequency

(c)

Phase

200d ~

............................................

RI= 5k,10k, 15k,20k

9

i6oa

7\

.... \

*,\ 9~,t\

\

% \\

12oa

R~=20k

\ \

10OHz

1.0KHZ

10KHz

IO0KHZ

1.0MHz

\ 10MHz

Frequency

(d) Fig. 3. (c) The magnitude characteristics of the VCVS of Fig. 2(c). (d) The phase characteristics of the VCVS of Fig. 2(c).

269

270

Soliman

Vi .

Y

-Vo

V1 9

--Vo

R

Tc

V2 "

• m

(a)

(b) vi 9

R

vi~

:v~ I

> -S

__%

__C

m

(d)

(c)

Fig. 4. (a) The differentialintegrator. (b) The noninvertingintegrator. (c) The invertingintegrator. (d) The infinite input impedanceinverting integrator. resistors only, that is two resistors less than the circuits of Fig. 7. For the circuit of Fig. 9(a) the input admittance is given by: 1

1

l

Yi -- sCR1R~ + ~ + R-2

(6)

It is seen that the circuit realizes L = CR1Rz in parallel with R = RIR~R2 This circuit is equivalent to the two well known circuits using the op amp and the CC II as the active building blocks [11-12]. This circuit however has the advantage of using a grounded capacitor. A second parallel L-R circuit is shown in Fig. 9(b). A necessary condition for this circuit is to have R2 = R1, in this case it is clear that the circuit realizes a parallel L-R circuit with L = CR1R2 and R = R1, that is it has double the Q factor of the inductor circuit of + R 2

"

Fig. 9(a), when equal resistors are used. This circuit however is very sensitive to the resistors ratio which must be unity (due to the cancellation of two terms in the denominator of the Yi). Practically R2 must be taken equals to R1 + Rx for proper operation of the circuit. Fig. 10(a) shows the simulation results of the magnitude and the phase of the input impedance of the circuit of Fig. 9(a) with R1 = R2 = 1 Kf2 and C = 1 nE Fig. 10(b) shows similar simulation results for the circuit of Fig. 9(b) with R1 = 0.935 K~2, R2 = R1 + Rx = 1 K~2 and C = 1 nF. It is worth noting that the input resistance of this circuit at DC equals to (R2 - R1), and a phase error of 180 ~ can be noticed in the simulations if R1 is taken equals to R2 without compensating the effect of Rx. As pointed out before the design equation for R2 should be modified to take the effect of Rx into account. The sim-

Applications of the CFOAs

R=SK

I

i i

R=20k

" ~

o~

C=lnf

100Hz o *

1. OKHz ,

10KHz

100KHz

1.0MHz

~ vdb(5) Frequency

(a~ -40d T ................................................................................................................

ii Phage

.

,,,

-fOOd "

.

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//y

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.

C=lnf

- 1 6 0 d

+

. . . . . . . . . . . . . . . . . . . . . .

100Hz

,. . . . . . . . . . . . . . . . . . . . . .

1.0KHZ *

9

*

T . . . . . . . . . . . . . . . . . . . . . .

10KHz

r

. . . . . . . . . . . . . . . . . . . . .

100KHz

~ . . . . . . . . . . . . . . . . . . . . .

1.0MHz

10MH:

vp{5) Frequency

(b) Fig. 5. (a) The magnitude characteristics of the integrator of Fig. 4(b). (b) The phase characteristics of the integrator of Fig. 4(b).

271

272

Soliman

Db

'

R=5k

r

I o~

c=Inf

lOOHz =

I. 0XHz 9 A

*

10KHz

100KHz

1.0MHz

vdb(5)

Frequency

(c/

~o~ T T-&U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

2

9

"

9

9

'\

:

\

~oo~-:'

.\\ ~ ,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

R=Sk,10k,15k,20k I

C=lnf

SOd ~

60d +

.

.

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100HZ

=

1.0KHz

*

9

A

~ . . . . . . . . . . . . . . . . . . . . . .

IOOKHz

10gHz

~ . . . . . . . . . . . . . . . . . . . . . .

1.0m~z

10HH

vp(S)

Frequency

(d) Fig. 5. (c) The magnitude characteristics of the integrator of Fig. 4(c). (d) The phase characteristics of the integrator of Fig. 4(c).

Applications of the C F O A s

Vl o.

Y X

Z

0

+

R

vo

V2 o, (a)

V1 9 Z O

_Vo v

C

C

-Vo

V2e (b)

Fig. 6. Two equivalent differential integrators with infinite input impedance at both inputs.

273

274

Soliman

R2

C

Zi

Zi

)-


>! Od ~ ...................... 0.0:LT, HZ = 180-ip(vl)

.

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.

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.

.

.

r ..................... 10.00:',Hz

.

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.

.

.

.

~ ...................... 20.00KHz

~ ...................... 30.00KHz

n ...................... 40.00KHz

50.00KH:

Frequency

(a) 8.0K T .................................................................................................................

Izll 4.oK~

i" .

9

o

"

1

*

:

--/._~.

........................... i........................... i.............................

= i/ilvl) 100d T .................................................................................................................. Phase

/

,f

,odil

I,

SEL>> 1 Od~ ........................... 0. I K H ~ o 180-ip(vl )

~ ............................ 50.0~z

r ........................... I00.0KBz

,. . . . . . . . . . . . . . . . . . . . . . . . . . . . 150,0KE'IZ

200.0F.H:

Frequency

~) Fig. 12. (a) The magnitude and phase of Zi of the inductor Of Fig. 1 l(a). (b) The magnitude and phase of Zi of the inductor of Fig. 11 (b).

280

Soliman

It?

iR

R

CI

> >

R2

(a)

6.0mA

T ................................................................................................................

,.~

. . . . . .

~.o~,i

.

.

.

i . . . ! . . . i . . .

.

OA

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

a

i(v3)

r ................................................................................................................ I

Phase

2o0a4

10oo~iS %;LS

...................

0Hz 180+ip(v3

~ ...................... 20KHz

~ ...................... 40KHz

r .....................

60~'tz

~ ...................... 80KHz 100KHI

) Frequency

(b) Fig. 13. (a)A parallelFDNR-R circuit.(b) The magnitude and phase of Yi of the circuitof Fig. 13(a).

Applications of the CFOAs

T

C

----~ I --tl C1

< Yi

>

R1

<
> R2

>

(c) C2

Yi

> CI-

(a) Fig. 13. (c) A grounded R, ideal FDNR circuit. (d) A canonic ideal FDNR circuit.

281

Soliman

282

4.01~A T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.0mA ~

SEL>>: r

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

OA

ilv3) ................................................................................................................ Phase

2ood!~ lood

Od

+ . . . . . . . . . . . . . . . . . . . . .

Onz D 180+ip{v3}

~ . . . . . . . . . . . . . . . . . . . . . .

, . . . . . . . . . . . . . . . . . . . . . .

20KHz

r . . . . . . . . . . . . . . . . . . . . .

40KHz

60KHz

1 . . . . . . . . . . . . . . . . . . . . . .

80KHz

100KHI

Frequency

(e) Fig. 13. (e) The magnitude and phase of Yi of the circuit of Fig. 13(d).

Vi

Vi

=

--

Y

1

-Vo

w

• a

1--

1 b K

(a)

b

I

T Co)

Fig. 14. Two equivalent realizations of the first order noninverting transfer function.

1 Ka

Applications of the CFOAs

i

R3

vo

Vi

9

~

(b)

R3

R3 vi

ra

/

R

(a)

283

:Vo

~

Vi

II

O~

9

--vo

R2

c

> > R5

>

CI - ~

(c)

RI

i >>R5

(d)

Vi *

R3 i

:Vo

(e) Fig. 15. (a) A single CFOA generalized configuration. (b), (c) First order all-pass circuits. (d), (e) Second order all-pass and notch circuits.

Fig. 16 shows the frequency response of the notch filter of Fig. 15(e) designed for fo = 15.915 KHz, taking

Cl = C2 = 1 nF, R1 = R2 = 10 Kf2, R3 = 10 Kf2,

284

Soliman

io

T .................................................................................................................

I

Gain D b

o"

-1o"

-2o

-30

-40

f0=15.813Khz -50 + ...................... 100Hz . vdb(ul:5)

r ......................

1.0KHz

r ...................... 10KHz

r ...................... 100KHz

r ...................... 1.0MHz

10MHI

Frequency

Fig. 16. The frequencyresponseof the notch filterof Fig. 15(e). R4 = 20 Kf2 and R5 = 40 KfL From the simulations the actual fo equals to 15.813 KI-Iz, which is very close to its theoretical value. In order to have independent control on the gain factor and on the zeros, R5 should be used to control the gain factor and R3 should be used to control the zeros. In this respect the circuit of Fig. 10d is better than that of Fig. 10e since the tuning is achieved by the two grounded resistors R5 and R4.

5.3.

The Noninverting Single-CFOA Filters

The CFOA is a very practical building block in realizing the second order filter circuits based on the positive feedback topology shown in Fig. 17(a). The Iowpass, highpass and bandpass Sallen-Key filters [ 18] using the CFOA are shown in Figs. 17(b), (c) and (d) respectively, and they have the same equations as in the classical op amp cases. An attractive application of the CFOA in the positive feedback topology is in the realization of a notch filter using a VCVS of gain K < 1 as shown in Fig. 17(e). The transfer function of this noninverting notch circuit is given by:

T(s) = K

s2 C2 R 2 "Jr-1 s2C2R 2 +4(1 - K ) s C R + 1

(14-a)

The Wo and the Q are given by: 1 CR'

COo -

1 Q - - 4(1 -

K)

(14-b)

It is seen that the circuit realizes complex poles and can be easily modified to realize lowpass and highpass notch responses. Fig. 18 shows the simulated frequency response of the notch filter of Fig. 17(e) designed for fo = 100 KHz, taking K = 0.95, C = 1 nF, R = 1.5915 Kf2 and R1 = 10 Kf2. It is seen that the theoretical f0 is in close agreement with its simulation value.

5.4.

The Inverting Single-CFOA Bandpass Filter

The general configuration shown in Fig. 19(a) has a transfer function given by: V 0

--

V/

--Z2(Z

=

3 -~- Z 4 )

Zl (Z3 + Z4) - Z2Z4

(15)

This configuration is suitable for realizing a bandpass filter as shown in Fig. 19(b). Its transfer function is

Applications of the CFOAs

Vi

o>

vo

~KR >

(a)

C1 Vi ; RI

Rix

R2

C2

vo

(b) RI Vi

-CI

I c:

o~

-vo

> )KR

(c) Fig. 17. (a) The general positive feedback topology using the CFOA. (b) LP filter using the CFOA. (c) HP filter using the CFOA.

285

286

Soliman

R2

I

Vi ~, R1

C2

R3

vo

I

(a) C

C

Vi 9

o~-----~,Vo

....X~2 >1 -3GOd

J

- 5 0 +

. . . . . . . . . . . . . . . . . . . . . . . . .

100Hz [ ] D vp(ul:5)

[]

~ . . . . . . . . . . . . . . . . . . . . . . . . . .

1 90KHz 9 vdb(ul:5)

~ . . . . . . . . . . . . . . . . . . . . . . . . . .

10KHz

,. . . . . . . . . . . . . . . . . . . . . . . . . .

100KHz

i. 0MH~

Frequency

Fig. 21. The magnitude and phase of the bandpass filter of Fig. 20(d). [

1

/

COO-- ~/C1C2R2R3,

6.2.

C1

Q = RI~/ C2R2R3

R1

The bandpass gain at COo= T(jCOo) = - - -

R3 The lowpass DC gain ----T(0) = - - R

R

(21-a)

(21-b)

It is seen that the Wo and the Q sensitivities to all circuit components are very low (< 1). For a specified COo and Q, there are many posible choices for the element values of the filter. Taking C1 = C2 = C, R2 = R3, the design equations are given by: R] = R2 =

Q cooC 1 R3--

co0C

(22-a) (22-b)

R1 R3 - orR=-IT(jCOo) l IT(0) I

The circuit of Fig 20(b) has the advantage of having an infinite input impedance. The transfer functions of this circuit are given by: s ~ 0+-~) Vo~ _ C7R3 (1 + -~) and Vo2 = ClC2R2R3 Vi D(s) Vi D(s) (24) where D(s) is the same as given by equation (19), and of course wo and the Q are the same as given by equation (20). The design equations can be taken as given by (22). The grounded resistor R controls the gain of the filter as seen from the following equations: R1

R1

T ( j coo) = -~3 -6 --~ T(O) =

i+

R3 -

-

R

The grounded resistor R 1 controls Q without affecting COo. The resistor R controls the gain, and for a specified T(jCOo), or T(0), the design equation of R is given by: R=

The Noninverting BP-Noninverting LP Filters

(20)

(23)

(25-a)

(25-b)

If the magnitude of the gain is not one of the specified parameters, then R can be taken as open circuitresulting in a unity mc gain and a bandpass gain at coo equals

to a. It is worth noting that the filter based on the two CFOAs gyrator circuit [14] has one of the capacitors floating.

292

Soliman

R

Vi -~ *Vol

,r,Vo2

RI

-~CI

% Ca) Vi 9 *'col ;vo2

(b)

Fig. 22. (a) Inverting BP- inverting LP filter using three CFOAs. Another noninverting BP-noninverting LP filter is shown in Fig. 20(c). The circuit has the same w0 and Q as given by equation (20). The gain at COoand the DC gain are given by: T(jwo) = T(0) =

gl

1 + -R3

(26-a)

1 + __R3

(26-b)

R1 For a specified 090, Q, T(jcoo) or (T(0)) and taking C1 = C2 = C, the design equations are given by: R1 = R3

Q

(27-a)

cooC

R1 -

-

R2 =

T(jwo) - 1 1 (woC)2R3

or R3 = RI(T(0) - 1)

(27-b) (27-c)

(b) Noninverting BP- noninverting LP filter using three CFOAs.

For a specified w0 and Q only, the design equations can be taken as in equation (22), and in this case 1 T(jwo) = Q + 1 and T(O) = 1 +-~.

6.3. The Inverting BP-Noninverting LP Filter Fig. 20(d) represents another BP-LP filter using the same number of circuit components and employs an inverting integrator in the second stage instead of a noninverting one as in the previous three cases. The transfer functions in this case are given by:

Yo1

cSR3

V02

Vi

D(s) '

Vi

1

C,C2R2R3 D(s)

(28)

'

where D(s) is given by equation (19). The design equations can be taken as given by equation (22). For

Applications of the CFOAs

P h a

Od

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(d) Fig. 22. (c) The magnitude and phase of the bandpass filter of Fig. 22(a). (d) The magnitude and phase of the bandpass filter of Fig. 22(b).

294

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R3 Ri

!

_ _

~ ~ ~ ' ~

kvo~

(a) Vi

9 RI

C

2

'VV~ (6) Fig. 23. (a) Inverting HP-BP-LP filter using three CFOAs. (b) Noninverting HP-BP-LP filter using three CFOAs.

Ri

Vi Ii

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(a) Fig. 24. (a) Inverting HP-BP-LP filter using five CFOAs.

V~

Applications o f the C F O A s

4oT .................................................................................................................

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(b) Fig. 24. (b) The magnitude and phase of the bandpass filter of Fig. 24(a).

Vi

Vol

(c) Fig. 24. (c) Noninverting HP-BP-LP filter using five CFOAs.

1.OMh

lOHh

296

Soliman

this circuit the DC gain equals to unity, and T(jwo) =

Q. Fig. 21 shows the magnitude and phase simulation results of this bandpass filter designed for f0 = 31.83 KHz and Q = 40, taking C~ = Cz = 1 nF, R1 = 200 Kf2 and R2 : R3 = 5 Kf2.

ues. It should be noted that although the magnitude response is identical to that of Fig. 22(c), the phase response deviates at frequencies above 1 MHz due to the capacitance Cx of the first CFOA.

7.2.

7.

The Multiple-CFOA Filters

In this section several novel multiple-CFOA second order filters are introduced.

7.1.

The Bandpass-Lowpass Filters

Fig. 22(a) represents an inverting BP-inverting LP filter which is generated from the circuit of Fig. 20(a) using a third CFOA acting as a voltage to current converter feeding-back the current ~ to terminal X of the first CFOA. The circuit has the same equations as that of Fig. 20(a), it has the advantage however of using a grounded resistor R3. This circuit is suitable for current excitation and in this case it will be classified as a mixed mode (current excitation and voltage responses) bandpass-lowpass tilter. Fig. 22(b) represents a very attractive noninverting BP-noninverting LP filter with infinite input impedance and with all resistors and capacitors being grounded. The circuit is generated from that of Fig. 20(b) using a third CFOA to act as a voltage to current converter. The equations for this circuit however are different from those of the circuit of Fig. 20(b), and are given by: s

VO1 --

Vi

CI"~

The Inverting HP-BP-LP Filter

The filter circuit shown in Fig. 23(a) realizes an inverting highpass, inverting bandpass and inverting lowpass response at the three-CFOA outputs. The transfer functions are given by: RS2

Vol Vi

~ D(s) '

R

Vo2 Vi

C,R~R,'s D(s)

R

and Vo3 Vi

_

(30)

CIC2R1R2Ri

D(s)

'

where D(s) = s 2 +

R

cI~S/~IK4

R + C1C2R1R2R3

(31)

From the above equation the cOoand the Q of the filter are given by:

cOo =

R

and Q = R4

CtC2R1R2R3

C2R2R3R

(32)

For a specified wo and Q the design equations may be taken as:

1

V02 -

D(s) and ~

C1C2R2R

D(s)

(29)

where D(s) is the same as given by equation (19). It is seen that the circuit has the same magnitudes of T(0) and T(jcOo) as the circuits of Figs. 20(a) and 22(a), thus the design equations (22) and (23) apply also to this circuit. Similarly the circuit of Fig. 20(c) may be modified using two more CFOAs to provide the necessary feedback currents, resulting in an alternative noninverting BP-noninverting LP filter with grounded elements and using four CFOAs. Fig. 22(c) shows the magnitude and phase responses of the bandpass filter of Fig. 22(a) with C1 = C2 = 0.2 nF, R1 ~-- 200 Kf2 and R = R2 = R3 : 10 Kf2. Fig. 22(d) shows similar results for the bandpass circuit of Fig. 22(b) designed with the same circuit val-

c h o o s e C 1 = C2 ~-- C ,

Ra = R2, R3 = R

(33)

Thus, R1 = R 2 -

1 o o C ' R4 = QR3

(34)

The resistor R4 controls Q without affecting COo. Ri controls the magnitude of the gain without affecting coo or Q and for the chosen design it can be easily seen that the magnitude of the gain at coo at any of the three outputs-- ~.R4

7.3. The Noninverting HP-BP-LP Filter

Fig. 23(b) represents an infinite input impedance threeCFOA noninverting highpass, bandpass and lowpass

Applications of the CFOAs

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(a)

Fig. 25. The magnitude and phase characteristics of the uncompensated and the compensated noninverting VCVS. (a) R1 = 10 K ~ , R2 = 20 K ~ .

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Fig. 25. (c) R1 = 2 Kf2, Rz = 20 Kf2. combinations of the three output currents may be taken to a current summer circuit. Fig. 24(b) shows the magnitude and phase of the bandpass circuit of Fig. 24(a) designed for Q = 50 and f0 = 31.83 KHz, taking C1 = C2 = 1 nF, R1 = R2 = R3 = Ri = R = 5 Kf2 and R 4 = 250 Kg2

filter. The transfer functions are given by: R(R3+R4) ~2 R3R4 ~

go1

VO2

R(R~+R4)S CIR1R3R4

Vi

D(s)

m

Vi

D(s)

'

and go3

Vi

-

R(R~-FR4) C1C2R1R2R3R4

D(s)

(35)

where D(s) is the same as given by equation (31). The design equations are the same as given by equations (33) and (34). For this design the gain at o~0 at any of the filter three outputs is given by Q + 1.

7.4.

The Inverting Universal Filter

Fig. 24(a) represents a five-CFOA inverting universal filter. The circuit has the same equations as that of Fig. 23(a). This circuit is also suitable to be driven by a current signal and as such it can be considered as a mixed mode inverting filter. Of course the circuit can also serve as a current mode universal filter by taking the currents in Rb R2 and R3 as the HP, BP and LP output currents respectively. It is worth noting that if a generalized second order response is required, the

7.5.

The Noninverting Universal Filter

The modified version of the filter circuit of Fig. 23(b) using two more CFOAs to realize voltage to current converters is given in Fig. 24(c). The numerators of the equations for this filter circuit however are different from those of the circuit of Fig. 23(b) and are the same as those of the circuits of Figs. 23(a) and 24(a) except for the polarities which are all positive in this case. This circuit is considered to be a very attractive voltage mode universal filter, with infinite input impedance, very low output impedances [19], and all the four resistors and the two capacitors being grounded.

8.

Frequency Limitations and Compensation Methods

Like the conventional op amp, the CFOA has frequency limitations caused by Rx, Cx, Rz and Cz.

Applications

of the CFOAs

299

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.........

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9 ........

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r .................. 1.0KHz

..................

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~ ..................

lOOKHz

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1.0MHz

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r ..................

10MHz

100MHZ

vp(5)

Frequency

(a)

[ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

o"

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lp.~

........ i ........ i

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vdb(5)

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.......

vpI5) o

i, O K H Z

10Fddz

100KHz

i

i. 0/4Hz

IOMHz

lOOMHz

i. 0 G H z

Frequency

(b) Fig. 26. The m a g n i t u d e a n d p h a s e characteristics o f the u n c o m p e n s a t e d and the c o m p e n s a t e d inverting V C V S . (a) R1 = 10 K~2, R2 = 20 K~2. (b) RI = 2 K~2, R2 = 4 K~2.

300

Soliman

_.o~~ ......................... ........ : ........: ........ : ........ ~ i.....~... \ !: ........ . : :\ ........ ii -40 ~ .......................................................................................................

s

~ ........

O vdb(5)

180d

~.ooJ

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l~od~

........

100Hz

.

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........

1 90 K t t z *

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........

10KHZ

i

........

1001r

c-o

\ ......................

1 90 Y ~ z

10~z

100/fflz

1.0GH=

vp(5) Frequency

(c)

Fig. 26.

(c) R1 = 2 K f 2 , R2 = 2 0 K~2.

40~ .....................................................................................................................

n

20;

/ / -0

/

/

I

-20"

-40 9

>>I ....................... lOOh [1

. vp{u2:5]

,. . . . . . . . . . . . . . . . . . . . . . . 1,OKh [2

9 vdb(u2:5)

~....................... lOKh

~....................... lOOKh

, ....................... 1.OMh

Frequency

Fig. 27. The magnitude and phase characteristics of the compensated bandpass filter of Fig. 24(a).

lOMh

Applications of the CFOAs

Although the effect of Rx can be minimized in most cases by taking the resistor connected to port X much larger than Rx, there are few circuits which require compensation for the effect of Rx, examples are the inductor circuits of Figs. 9(b) and ll(b). It has been demonstrated in Sections 4.2 and 4.3, that the compensation for the effect of Rx can be easily achieved, leading to simulation results that are very close to the theoretical expected ones. The effect of Cz on limiting the high frequency range of operation and passive compensation methods are discussed next. From the simulation results, it is seen that all the circuits with a resistor connected between port Z and ground are frequency limited by the pole which results due to the parasitic capacitance Cz at port Z. Well known passive compensation methods [20-21] can be applied to this class of circuits in order to extend the frequency range of the circuit. As an example, Wilson's passive compensation method [20] can be applied to the noninverting VCVS shown in Fig. 2(b) by adding a capacitor C of magnitude given by C = (Rz/R1)Cz, in parallel with R1, this will result in a pole-zero cancellation. Fig. 25(a) shows the magnitude and phase of a noninverting VCVS of gain 2, realized by taking RI = 10 Kf2, R2 = 20 K~2 and C = 11 PE It is seen that f3db has been extended from 1.5 MHz for the uncompensated VCVS to about 44.9 MHz. Fig. 25(b) shows similar simulations for the VCVS with same gain of 2, by taking R1 = 2 Kf2 and R2 = 4 K~2. It should be noted that although the uncompensated f3ab for this VCVS which is about 5 times larger than that of the previous case (since f3db = 1/2Jr R2Cz), the f3db of the compensated VCVS is almost the same as in Fig. 25(a). This is due to the fact that bandwidth of the compensated amplifier is limited by C, Rx, Cx and the voltage follower action from port Z to the output port of the CFOA. Fig. 25(c) shows similar simulations for the noninverting VCVS with gain of 10, realized with R~ = 2 Kf2 and R2 = 20 Kf2 For the inverting VCVS shown in Fig. 2(c), passive compensation is achieved using a single capacitor C, in parallel with R1 in the same way as was done for the conventional op amp VCVS circuits [21]. For pole-zero cancellation, the magnitude of C should also be taken equal to KC z, where K = R2/R1. Fig. 26(a), (b) show the magnitude and phase for the

301

case K = 2 taking Ra = 10 Kf2, R2 = 20 Kf2 and R1 = 2 Kf2, R2 = 4 Kf2 respectively. From the simulation results it is seen that f3db is approximately the same in both cases and is given by 48.4 MHz which is higher than that of the noninverting VCVS of the same gain. This is due to the fact that Cx has no effect on the frequency response since port Y is grounded. Fig. 26(c) shows similar simulations for the inverting VCVS with gain of 10, realized with R1 = 2 Kf2 and R2 = 20 Kf2. The same method of compensation can be applied to some of the filter circuits reported in this paper. As an example consider the filter of Fig. 24(a). Improvement in both the phase and the magnitude response can be achieved as shown in Fig. 27 by adding a capacitor C of magnitude 5.5 pF in parallel with Ri. The effect of Rz (typically 2.2 Mr2) on the circuits which employ a capacitor C connected between port Z and ground is observed at very low frequencies, since the pole produced by Rz and C is at 72 Hz (assuming C = lnF). Of course this effect is observed on the phase of the integrators at low frequencies. For filter applications however which are intended for frequencies >> 100 Hz, the effect of Rz can be minimized by using capacitors in the nano-Farads range.

9.

Conclusions

The versatility of the current feedback op amp (CFOA) with an available Z terminal [2] in realizing analog circuits is demonstrated by numerous applications. These applications include the realization of voltage amplitiers, voltage integrators, inductors, FDNRs and filters. One of the major objectives of the paper is to give an overview of the second order filter circuits realized using the CFOAs. PSPICE simulations indicating the frequency limitations of some of the reported circuits using the AD 844-CFOA are given. Passive compensation methods for the noninverting and the inverting VCVS structures have been considered in this paper. Although the direct compensation methods can be applied to some of the circuits reported in this paper, other circuits may require special methods of compensation. I t is not the intention of this paper however to concentrate on the compensation of filter circuits.

302

Soliman

Acknowledgements The author would like to thank the reviewers for their useful comments. The author would like also to thank his graduate student A.S. Elwakil for his assistance with the PSPICE simulations included in this paper.

19. A. M. Soliman, "Current conveyors steer universal filter." IEEE Circuits and Devices Magazine. 11, pp. 45-46, March 1995. 20. G. Wilson, "Compensation of some operational amplifier based RC active networks?' IEEE Trans. Orcuits and Systems. CAS-23, pp. 443-446, July 1976. 21. A.M. Soliman and M. Ismail, "Passive compensation of Op Amp VCVS and weighted summer building blocks?' 1EEE Trans. Orcuits and Systems. CAS-26, pp. 898-900, Oct. 197~,

References 1. S. Evans, Current Feedback Op Amp Applications Circuit Guide. Complinear Corporation, Fort Collins, CO., 1988, pp. 11.20-11.26. 2. Analog Devices, Linear Products Data Book. Norwood, MA., 1990. 3. E. Bruun, "A dual current feedback op amp in CMOS technology." Analog Integrated Orcuits and Signal Processing. 5, pp. 213-217, 1994. 4. C. Toumazou, J. Lidgey and A. Payne, "Emerging Techniques For High Frequency BJT Amplifier Design: A Current Mode Perspective" in First Intentional Conference on Electronics Circuits and Systems, Cairo, 1994. 5. A. Fabre, "Insensitive voltage mode and current mode filters from commercially available transimpedance op amps?' lEE Proceedings-G, 140, pp. 319-321, 1993. 6. A. S. Sedra and K. C. Smith, "A second generation current conveyor and its applications?' IEEE Trans. on Circuit Theory. CT-17, pp. 132-134, 1970. 7. B. Wilson, "Universal conveyor instrumentation amplifier." Electronics Letters. 25, pp. 470-471, 1989. 8. B. Wilson, "Recent developments in current conveyor and current mode circuits?' IEEProceedings-G. 137, pp. 63-77, 1990. 9. A. J. Prescott, "Loss compensated active gyrator using differential input operational amplifier." Electronics Letters. 2, pp. 283-284, 1966. 10. A.C. Caggiano, "Operational amplifier simulates inductance?' Electronics. 41, p. 99, 1968. 11. R.L. Ford and F. E. J. Girling, "Active filters and oscillators." Electronics Letters, 2, p. 52, 1966. 12. A.M. Soliman, "Ford-Girling equivalent circuit using CC II?' Electronics Letters. 14, pp. 721-722, 1978. 13. A.M. Soliman and S. S. Awad, 'A tunable active inductance using a single operational amplifier." AEU (Electronics and Communications). 32, pp. 44 48, 1978. 14. A. Fabre, "A gyrator implementation from commercially available transimpedance operational amplifiers?' Electronics Letters. 28, pp. 263-264, 1992. 15. H.J. Orchard and A. N. Wilson, "New active-gyrator circuit?' Electronics Letters. 10, pp. 261-262, 1974. 16. A.M. Soliman, "New active-gyrator circuit using a single current conveyor." Proceedings IEEE. 66, pp. 1580-1581, 1978. 17. A.M. Soliman and S. S. Awad, "Canonical high selectivity parallel resonator using a single operational amplifier and its applications in filters?' lEE Electronic Circuits and Systems. 1, pp. 145-148, July 1977. 18. A. Budak, Passive and Active Network Analysis and Synthesis. Houghton Mifflin, 1974.

Ahmed M. Soliman was born in Cairo Egypt, on November 22, 1943. He received the B.S. degree from Cairo University, Egypt, in 1964, and the M.S. and Ph.D. degrees from the University of Pittsburgh, PA., U.S.A. in 1967 and 1970, respectively, all in electrical engineering. He is currently Professor and Head Electronics Group, Electronics and Communications Engineering Department, Cairo University, Egypt. Dr. Soliman served as Professor and Chairman of the Electrical Engineering Department, United Arab Emirates University (1985-1987), and as the Associate Dean of Engineering at the same University (19871991). He has held visiting academic appointments at the American University of Cairo (1982-1983), Florida Atlantic University, FL. (1979-1980) and San Francisco State University, CA. (1978-1979). Dr. Soliman served also as Associate Professor of Electrical Engineering at Florida Atlantic University, U.S.A. (1980-1981). He was a visiting scholar at the Technical University of Wien, Austria (Summer 1987) and at Bochum University, Germany (Summer 1985). He was a Research Analyst at the Central Research, Rockwell Manufacturing Company, Pittsburgh, PA., U.S.A. (Summer 1970). Dr. Soliman received the First Class Science Medal from the President of Egypt in 1977, for his services to the field of Engineering and Engineering Education.