Enhanced dynamic range analog filter topologieswith a notch/all-pass circuit example

Bilgin Metin Æ Shahram Minaei Æ Oguzhan Cicekoglu

Received: 12 March 2006 / Revised: 29 March 2007 / Accepted: 4 April 2007 / Published online: 27 July 2007

� Springer Science+Business Media, LLC 2007

Abstract The signal handling capability of the filters is

called dynamic range. In this paper, a topological form for

the synthesis of filters with high dynamic range is proposed.

A biquad notch/all-pass filter is shown in conformity with the

given topological form. It is shown that there is a trade-off

between dynamic range and high input impedance property.

The presented circuit is compared with other notch filters in

the literature. It has less number of components, better high-

frequency response and dynamic range compared to others.

Since the circuit includes a minimum number of resistors, it

can easily provide electronically tunable circuits through

resistor/controlled current conveyor replacement. Simula-

tions are performed to verify the theoretical results. Routh-

Hurwitz stability analyses are also given.

Keywords Current conveyors � All-pass filter �Notch filter � Dynamic range � First generation current

conveyor

1 Introduction

Recently there is a growing interest towards low voltage

low power analog filters. Reduced supply voltages however

limit the voltage swings of the input/output terminals of the

active building blocks. This in turn reduces the dynamic

range of the filter. Thus the signal processing quality is

deteriorated with associated signal to noise ratio reduction.

In this paper, a topological form for the synthesis of filters

with high dynamic range is proposed. A simple way to

provide high input impedance which is important for cas-

cading in voltage mode (VM) circuits, is to apply the input

signal source to the high input impedance terminal(s) of the

active component(s) without any other connection to this

terminal. For example the Y terminal of the second gen-

eration current conveyor (CCII) can be used for this pur-

pose. In this paper it is shown that there is a trade-off

between dynamic range and high input impedance property

for the analog filter.

Notch filters are needed to filter out the unwanted

frequencies of an electrical signal. In the literature, some

second order VM notch filters using current conveyor were

proposed [1–3]. One of them employs two capacitors, four

resistors and three current conveyors [1]. The circuits in

[2]–[3] use two capacitors, four resistors and a single current

conveyor. In a recently published paper, an operational

transresistance amplifier (OTRA) with two capacitors and

four resistors are employed for realizing second-order notch

active filter [4]. The first generation current conveyor (CCI)

[5] is also used in the implementation of second-order all-

pass filter employing four resistors and two capacitors [6],

but it is a current mode (CM) filter and so it is not in the scope

of this study.

In this paper, we present a VM biquad notch/all-pass filter

that fits a certain topological form. It employs a single CCI,

two resistors and two capacitors and has an enhanced dy-

namic range. Since the number of the resistors can be re-

duced by one employing a controlled conveyor, we used a

current controlled CCI for realizations. The first beneficial

B. Metin (&) � O. Cicekoglu

Electrical and Electronic Engineering Department, Bogazici

University, Bebek, Istanbul 34342, Turkey

e-mail: bilginx@boun.edu.tr

O. Cicekoglu

e-mail: cicekogl@boun.edu.tr

S. Minaei

Department of Electronics and Communication Engineering,

Dogus University, Acibadem, Kadikoy, Istanbul 34722, Turkey

e-mail: sminaei@dogus.edu.tr

123

Analog Integr Circ Sig Process (2007) 51:181–189

DOI 10.1007/s10470-007-9054-8

property of the presented circuits is the use of the minimum

number of resistors, in other words three fewer resistors than

the circuits in [1]–[4] are used. The resistors can be replaced

by controlled current conveyors, as active resistors and an

electronically tunable circuit is obtained without a signifi-

cant increase in chip area since the number of resistors is

minimal. The second advantage of the proposed circuits is

electronic configurability which means that the element

matching condition can be controlled electronically with the

resistor in series to the X terminal to change the filtering

function as notch or all-pass operation, but the circuits re-

ported in [2]–[4] would need an additional active element to

be used as a resistor for changing element-matching condi-

tions for both notch and all-pass functions. The third

advantage of the proposed circuit is that it is suitable for high

frequency of operation since it uses a feed-forward capacitor

between its input and output. This capacitor short-circuits

the input to the output at high frequencies. This property is

important for notch and all-pass filters since in contrast to a

low-pass or a band-pass function, both require a flat fre-

quency response at the high frequency region. The fourth

advantage of the circuit is reduced total harmonic distortion

(THD) as a result of enhanced dynamic range. Moreover

there is another mechanism that is effective at high fre-

quencies. Due to the feed-forward capacitor the active ele-

ment is bypassed and very low THD is obtained. In this case

however one should ensure that the input signal source is

capable to drive the load at the output since the active filter is

bypassed and the load is driven directly by the input signal

source. SPICE simulations and Routh-Hurwitz stability

analysis are performed to illustrate the functionality of the

circuit. Furthermore the presented circuit is compared with

other VM notch/all-pass filter circuits [2]–[3] in terms of

frequency response and THD.

2 Dynamic range consideration of current conveyor

based filters

The THD performance of an analog filter is related to the

magnitude of the voltage swings at the terminals of the

active component. The allowed maximum voltage swings

are related to the magnitude of the supply voltages and to

the non-linearity of the active device. For analog voltage-

mode filters where high input impedance is desired the

input port is selected to be the Y terminal of the current

conveyor. This in turn fixes the voltage swings at the Y

terminal and at the X terminal independent of the voltage

gain of the overall circuit. For maximum performance, the

output node of the filter should be selected such that it has

the maximum voltage swing. For the second generation

current controlled conveyor (CCCII) given in Fig. 1 [7] as

an example, the Y terminal voltage swing is –VEE +

VEB + VCESAT < VY < VCC – VBE – VECSAT, that is around

± 1.6 V for ± 2.5 V power supply. One can derive

advantages about the dynamic range if the input signal

source is applied to a passive network rather than directly

to a terminal of the active element. In this case the input

signal may be voltage divided by the passive RC network

and then applied to the input terminals of the active block

as shown in Fig. 2. This property is strongly topology

dependent, thus the input range enhancement can be dif-

ferent for each topology. The output however is to be taken

directly from a terminal that has the largest signal swing.

For example for the current conveyor in Fig. 1, maximum

possible voltage swing at the Z terminal is slightly higher

than the Y terminal. In fact –VEE + VCESAT < VZ < VCC –

VECSAT which is around ± 2.3 V for the ± 2.5 V power

supply. In some cascadable topologies [2–3] the input

signal is applied directly to the high input impedance ter-

minal of the active component, therefore a trade-off exists

between the dynamic range and the high input impedance

property for the analog filter.

For an analog filter the resistor replacement by a minus type

CCCII (CCCII–) enables tunability, in this case the X terminal

behaves as one of the ports and the Y terminal connected to Z

behave as the other port of the realized resistor. However one

should note that unlike a passive resistor the CCCII– based

active resistor cannot be considered as a bilateral two-port

element. Rather it behaves as a resistor with different voltage

swing restrictions on both ends. From this view as a resistor

connection, the X terminal of the CCCII– should be connected

to the higher voltage swing node compared to its Y–Z terminal

connected node in the circuit. In case of Fig. 1 the voltage at

the X terminal will be VX = bVY + RXIX under the condition of

IX << 2IC. Here, b is the voltage transfer ratio and RX is the

parasitic resistor at the X terminal as defined in [7]. As long as

the condition of IX << 2IC is satisfied, RX active resistor values

should be selected to reduce the voltage swing effects on the X

terminal for the enhanced dynamic range.

Fig. 1 The current controlled current conveyor (CCCII)

182 Analog Integr Circ Sig Process (2007) 51:181–189

123

3 The presented notch/all-pass filter circuit

The CCI as an active element can be useful in realizing

single CCI-based high-output impedance CM filters since

the output current can be fed back without altering the high

impedance of the output port [6]. However, in this paper

we show the usability of the CCI in VM filters. The elec-

trical symbol of the first-generation current conveyor [5] is

shown in Fig. 3(a). A current controlled CCI (CCCI) can

be obtained from the Fabre’s CCCII [7] as shown in

Fig. 3(b). The terminal relationship of the CCCI can be

characterized with the following equations:

VX ¼ bVY þ RXIX; IY ¼ cIX ; IZ ¼ �aIX ð1Þ

where ideally b = 1, a = 1, c = 1 and they represent the

voltage or current transfer ratios of the current conveyor.

The plus or minus sign of a in (1) denotes a positive or

negative type CCCI, respectively. Also, RX is the parasitic

resistance at the X terminal of the conveyor [7].

The proposed circuit is shown in Fig. 4(a). The number of

the resistors can be reduced by one by using CCCI instead of

CCI as shown in Fig. 4(b). In this case R1 is replaced with the

RX of the CCCI. Since the number of resistors is minimal,

replacing the R2 with a CCCII– provides an electronically

tunable filter as shown in Fig. 4(c). The transfer functions are

given for the ideal case (a = 1 b = 1 and c = 1) as follows:

Vo

Vi¼ 2þ sC1ðR1 � R2Þ þ s2C1C2R1R2

2þ 2sC2R2 þ sC1ðR1 � R2Þ þ s2C1C2R1R2

ð2Þ

The quality factor (Q) and the angular pole frequency (x0)

for the filter can be given as follows: Q ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2R1R2C1C2

p=

ð2R2C2 þ ðR1 � R2ÞC1Þ, x0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2=ðR1R2C1C2Þp

. Sensiti-

vities of x0 with respect to the capacitors and resistors are

one half in magnitude. Sensitivities of the Q to the

capacitors and resistors are shown in Table 1. Equation (2)

yields the following notch response when the element

matching condition of R1 = R2 = R is fulfilled:

Vo

Vi¼ 2þ s2C1C2R2

2þ 2sC2Rþ s2C1C2R2ð3Þ

Considering the active element non-idealities as given in

(1), the transfer function in (3) becomes:

Vo

Vi¼ bð1þ aÞ þ sC1Rð1� bcÞ þ s2C1C2R2

ð1þ aÞ þ sRðC1ð1� bcÞ þ C2ð1þ aÞÞ þ s2C1C2R2

ð4Þ

Equation (4) shows that angular pole frequency and the Q

of the transfer function are

Fig. 2 The general topology for enhanced dynamic range

Y

X

CCCII+Z

+Z

Z

IY

IX

VY

VX

VZ

IZY

XCCI

IY

IX

VY

IZ VZVXIC

(a) (b)

Fig. 3 (a) Circuit symbol of the CCI (b) Obtaining current controlled

CCI from the CCCII

Fig. 4 (a) The proposed circuit with CCI (b) The proposed circuit

with current controlled CCI (c) Electronically tunable form of the

proposed circuit

Table 1 Sensitivities of Q to passive components

SQR1¼ �SQ

R2

12� C1R1

2C2R2þC1ðR1�R2Þ

SQC1

� 12þ 2C2R2

2C2R2þC1ðR1�R2Þ

SQC2

� 12þ C1ðR1�R2Þ

2C2R2þC1ðR1�R2Þ

Analog Integr Circ Sig Process (2007) 51:181–189 183

123

x0 ¼1

R

ffiffiffiffiffiffiffiffiffiffiffi

aþ 1

C1C2

r

and Q ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

C1C2ðaþ 1Þp

C1ð1� bcÞ þ C2ðaþ 1Þ :

Equation (2) can be converted to an all-pass response if the

element matching condition R2 = C1R1/(C1–C2) is fulfilled.

Vo

Vi¼ 2ðC1 � C2Þ � sC1C2R1 þ s2C2

1C2R21

2ðC1 � C2Þ þ sC1C2R1 þ s2C21C2R2

1

ð5Þ

Considering the active element non-idealities as shown in

(1), the transfer function in (5) can be given as follows:

Vo

Vi¼bðaþ1ÞðC1�C2Þ�sC1R1ðC2�C1þC1bcÞþs2C2

1C2R21

ðaþ1ÞðC1�C2ÞþsC1R1ðC2aþC1�C1bcÞþs2C21C2R2

1

ð6Þ

Equation (6) shows that angular pole frequency and the

quality factor of the transfer function are

x0 ¼ 1R1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðC1�C2Þðaþ1ÞC2

1C2

q

and Q ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðC1�C2ÞC2ðaþ1Þp

C1ð1�bcÞþC2a. Note that

the angular pole frequencies of the filters are independent

of the voltage gain b and the current gain c of the CCI.

4 Stability

Since the X and the Y terminals of the CCI behave as a

negative impedance converter (NIC), the stability of CCI

based circuits should be taken into consideration more

carefully. Thus, we apply Routh-Hurwitz stability criteria to

examine the effects of the frequency dependent non-ideal

current gains; a(s), c(s) and the voltage gain, b(s). We assume

that the current gains and the voltage gain have only a single

corner angular frequency which are denoted as xa, xc and xb

respectively. Therefore, these gains can be modeled as,

aðsÞ ¼ a0

1þ sxa

cðsÞ ¼ c0

1þ sxc

bðsÞ ¼ b0

1þ sxb

ð7Þ

where a0, c0 are the value of current gains and b0 is the value

of voltage gain at low frequencies. This one-pole model can

give only a rough idea about stability of the circuit, since the

active components have other poles and possibly zeroes at

higher frequencies that may affect the stability. For

simplification, we assume that the pole frequency of the

voltage gain is the k times of the pole frequencies of the

current gains, i.e. xb � kxa � kxc � kxp, where xp is the

corner angular frequency of current gains. For example,

the pole frequency fb of the voltage gain, and the pole

frequency fa of the current gain are respectively 3 MHz and

2.5 MHz for 2 lA, 10 MHz and 6 MHz for 4 lA, and

53 MHz and 23 MHz for 25 lA control currents (here, the

pole frequency fc of the current gain is close to the fa due to

duplicated current mirrors in the CCCI implementation as

shown in Fig. 3(b), although not the same because of

different loading effects, we assumed them to be equal for

simplicity). Frequency dependent non-ideal transfer

functions are obtained by substituting (7) into (4) for the

notch filter as:

TFN ¼Vo

Vi¼ a0 þ a1sþ a2s2 þ a3s3 þ a4s4

b0 þ b1sþ b2s2 þ b3s3 þ b4s4ð8Þ

where a0 = (1 + a0)b0xP2k, a1 = xPk(b0 + C1RxP (1 – b0c0)),

a2 = C1RxP (1 + k + kC2RxP), a3 = C1R(1 + C2RxP (1 + k)),

a4 = C1C2R2, b0 = xP

2k(1 + a0), b1 = xP (1 + k + a0 + RxP

k(C2 (1 + a0) + C1 (1 – b0 c0))), b2 = 1 + RxP (C2

(1 + k + a0) + C1 (1 + k + RC2 xPk)), b3 = R(C2 + C1

(1 + C2RxP (1 + k))), b4 = C1C2R2 and similarly substituting

(7) into (6) for the all-pass filter as:

TFAP ¼Vo

Vi¼ c0 þ c1sþ c2s2 þ c3s3 þ c4s4

d0 þ d1sþ d2s2 þ d3s3 þ d4s4ð9Þ

where c0 = (C1 – C2)(1 + a0)b0xP2k, c1 = kxP ((C1 – C2)

b0 – C1R1xP (C2 – C1 (1 – b0c0))), c2 = C1R1xP ((C1 – C2)

(1 + k) + kC1C2R1xP), c3 = C1R1 (C1– C2 + C1C2R1xP

(1 + k)), c4 = C12C2R1

2, d0 = (C1– C2)(1 + a0)xP2k, d1 = xP

((C1 – C2)k + (C1 – C2)(1 + a0) + C1R1xP k(C2a0 + C1

(1 – b0c0))), d2 = C1 – C2 + C1R1xP (C1 (1 + k) + C2a0) +

C12C2R1

2xP2k, d3 = C1

2R1 (1 + C2R1xP (1 + k)), d4 = C12C2R1

2

The Routh-Hurwitz criteria is applied on (8) and (9) to

investigate the stability of the circuit. Also, the nominal

values of voltage and current gains at low frequencies are

assumed to be approximately equal to unity for simplifi-

cation (a0 � b0 � c0 � 1).

For the notch realization:

R2C1C2 >0; RðC1ð1þð1þ kÞRC2xpþC2Þ>0; 2kx2p >0

ð10aÞ

C2þð2þ kÞRC22xpþRC2

1xpð1þ kþ kRC2xpÞð1þð1þ kÞRC2xpÞþC1ð1þRC2xpð2ð1þ kÞþ ð2þ kð2þ kÞÞRC2xpÞÞC2þC1ð1þð1þ kÞRC2xpÞ

>0

ð10bÞ

184 Analog Integr Circ Sig Process (2007) 51:181–189

123

and for the all-pass realization:

C21C2R2

1>0; C21R1ð1þC2R1xpðkþ1ÞÞ>0; 2kðC1�C2Þx2

p>0

ð11aÞ

Since all terms in (10) are positive and all terms in (11) are

positive for C1 > C2, the filters can be assumed stable. Note

that the above calculations are first order approaches to the

stability problem and do not guarantee stability. However

they give an idea to the designer.

5 Electronic configurability and tunability

Electronic configurability permits changing the filter

function simply by an external current. This is achieved by

changing the element matching condition by an electroni-

cally tunable resistor. As an example consider the follow-

ing case. Assume C1 = 2 C2 = C and 2R1 = R2 = 2R is

applied to (2) to obtain an all-pass response whereas again

C1 = 2C2 = C and with R1 = R2 = R, one obtains a notch

response with the following transfer function

Vo

Vi¼ 4þ s2C2R2

4þ 2sCRþ s2C2R2ð12Þ

Therefore, with C1 = 2C2 = C, the resistor R1 in Fig. 4(a) can

be adjusted to obtain an all-pass response or a notch response.

Note that if R1 is realized with the CCCI as in Fig. 4(b), it is

possible to configure the filtering function of the circuit

electronically through control current of the current conveyor.

Since the number of resistors is only two, controlled

conveyors can be used to replace them without a significant

increase in chip area as shown in Fig. 4(c). For example the

number of resistors in circuits proposed in [2]–[3] is four

that makes such a replacement difficult and costly.

6 Simulation results

6.1 The transient and frequency response analysis

To verify the theoretical analyses, we simulated the circuits

proposed in Fig. 4 using the SPICE circuit simulation pro-

gram employing the CCCI implementation based on Fig. 1.

The CCCI was implemented by using AT&T ALA400 BJT

transistors [8]. SPICE parameters of the transistors are tab-

ulated in Table 2. DC supply voltages of ± 2.5 V are used.

The presented circuit in Fig. 4(b) is designed with the pas-

sive element values R1 = 4 kW (IC = 3.25 lA), R2 = 4 kW,

C1 = 400 pF, and C2 = 200 pF to obtain notch filter with a

center frequency of f0 � 199 kHz. For realizing all-pass

filtering function, the circuit in Fig. 4(b) is simulated using

passive element values R1 = 2 kW (IC = 6.5 lA), R2 = 4

kW, C1 = 400 pF, C2 = 200 pF resulting in a center

frequency of f0 � 281 kHz. Theoretical and simulation

results of the AC analysis are depicted in Fig. 5(a) and (b) for

ðxpðð2þkÞC2ð1þ2RC2xpÞð1þkRC2xpÞþRC21xpð1þð1þkÞRC2xpÞð2þkþk2þkRC2xpð2þkþ2kRC2xpÞÞþ

C1ð2þkþð2þkð2þkÞÞRC2xpð2þRC2xpð2þkþ2kRC2xpÞÞÞÞÞðC2þð2þkÞRC2

2xpþRC21xpð1þkþkRC2xpÞð1þð1þkÞRC2xpÞþC1ð1þRC2xpð2ð1þkÞþð2þkð2þkÞÞRC2xpÞÞÞ

>0

ð10cÞ

C1 � C2 þ R1xpðC22 þ C2

1ð1þ kÞ þ C1C2R1xpðC2 þ C1ð1þ kð3þ kÞÞ þ C1C2R1xpkð1þ kÞÞÞ1þ C2R1xpð1þ kÞ > 0 ð11bÞ

ðxpððC1 � C2Þ2ð2þ kÞ þ R1xpððC1 � C2ÞðC1C2k þ C22ð2þ kÞ þ C2

1ð2þ k þ k2ÞÞþC1C2R1xpð�2C2

2 � C1C2kð2þ k þ k2Þ þ C21ð2þ kð4þ kð2þ kÞÞÞþ

C1C2R1xpkðC1 þ 2C1k þ C2 þ C2kð1þ kÞ þ C1C2R1xpkð1þ kÞÞÞÞÞÞðC1 � C2 þ R1xpðC2

2 þ C21ð1þ kÞ þ C1C2R1xpðC2 þ C1ð1þ kð3þ kÞÞ þ C1C2R1xpkð1þ kÞÞÞÞ > 0 ð11cÞ

Analog Integr Circ Sig Process (2007) 51:181–189 185

123

the notch and for the all-pass cases, respectively. The fre-

quency response at high frequencies is close to ideal response

due to the feed-forward capacitor C1. Also, in Fig. 6,

time-domain simulation result of the circuit as an all-pass

filter for peak-to-peak 3 V sinusoidal output voltage at

100 kHz, is depicted for the passive element values given

above. The THD of the filter is found to be –33 dB.

6.2 Electronic tunability

To show electronic tunability of the presented circuit, the

circuit in Fig. 4(c) as a notch filter is tested with the capacitor

values of C1 = 400 pF, C2 = 200 pF. The resistor values are

changed between R1 = R2 = 13 kW (IC1 = IC2 = 1 lA) and

R1 = R2 = 1.3 kW (IC1 = IC2 = 10 lA) as shown in Fig. 7.

Simulations show that the center frequency is electronically

tunable between 57.5 kHz and 575 kHz. Also, ideal and

simulated time domain analysis results are given in Fig. 8

for resistor values of R1 = R2 = 0.13 kW (IC1 = IC2 = 100

lA). There is a 0.5 V DC voltage level shift at the output and

the THD is less than –40 dB.

6.3 Comparison with other notch filter circuits

in the literature

In order to emphasize advantage of the proposed circuit, we

compared it with other notch/all-pass filter circuits shown in

Fig. 9 [2]–[3]. For a fair comparison we obtain the CCII-

used in [2]–[3] from the current conveyor in Fig. 1. The

center frequency of the filter is chosen as f0� 281 kHz. The

Soliman’s circuit [3] in Fig. 9(a) is designed with the passive

element values Ra = Rb = 2 kW, C1 = C2 = 400 pF,

Table 2 SPICE parameters of the transistors used in simulations

.MODEL PR100N PNP (IS = 73.5E–018 BF = 110 VAF = 51.8 IKF = 2.359E–3 ISE = 25.1E–16 NE = 1.650 BR = 0.4745 VAR = 9.96

IKR = 6.478E–3 RE = 3 RB = 327 RBM = 24.55 RC = 50 CJE = 0.180E–12 VJE = 0.5 MJE = 0.28 CJC = 0.164E–12 VJC = 0.8

MJC = 0.4 XCJC = 0.037 CJS = 1.03E–12 VJS = 0.55 MJS = 0.35 FC = 0.5 TF = 0.610E–9 TR = 0.610E–8 EG = 1.206 XTB = 1.866

XTI = 1.7)

.MODEL NR100N NPN (IS = 121E–018 BF = 137.5 VAF = 159.4 IKF = 6.974E–3 ISE = 36E–16 NE = 1.713 BR = 0.7258 VAR = 10.73

IKR = 2.198E–3 RE = 1 RB = 524.6 RBM = 25 RC = 50 CJE = 0.214E–12 VJE = 0.5 MJE = 0.28 CJC = 0.983E–13 VJC = 0.5

MJC = 0.3 XCJC = 0.034 CJS = 0.913E–12 VJS = 0.64 MJS = 0.4 FC = 0.5 TF = 0.425E–9 TR = 0.425E–8 EG = 1.206 XTB = 1.538

XTI = 2)

Frequency1.00KHz 10.0KHz 100.0KHz 1.00MHz 8.68MHz

_ _ _ _ Simulated ____Ideal

-20.0

-10.0

0

-28.1

Gain[dB]

100Hz 10KHz 1.0MHz 100MH10Hz 1.0GHz

_ _ _ _ _ Simulated ______ Ideal

-400d

-300d

-200d

-100d

-0d

-5

0

5

Frequency

Gain [dB]

Phase [Degree]

(a)

(b)

Fig. 5 Ideal and simulated frequency responses (a) Notch filter for

IC = 3.25 lA (f0 � 199 kHz and Q = 1) (b) All-pass filter for

IC = 6.5 lA (for f0 � 281 kHz and Q ¼ffiffiffi

2p

).

AMPLITUDE

Time

284.00us 288.00us 292.00us 296.00us 300.00us280.26us 303.80us

_ _ _ Simulated _ _ _ _ _ _ Ideal

-2.0V

-1.0V

0V

1.0V

2.0VFig. 6 Time domain response

for peak-to-peak 3 V sinusoidal

output voltage at 100 kHz

186 Analog Integr Circ Sig Process (2007) 51:181–189

123

R1 = 1 kW, R2 = 2 kW. The Higashimura’s circuit [2] in

Fig. 9(b) is designed with the passive element values

R1 = 2.857 kW, R2 = 3.265 kW, C1 = 490 pF, C2 = 70 pF,

Ra = 2 kW, Rb = 2 kW (the passband gain cannot be made

equal to unity). In the proposed circuit of Fig. 4(c) the pas-

sive elements are selected as C1 = 100 pF, C2 = 400 pF, and

the bias currents are IC1 = IC2 = 3.25 lA result in R1 =

R2 = 4 kW.

Frequency responses of the circuits are shown in

Fig. 10. Due to active component non-idealities, some

deviations from the theoretical value of the center

frequency occur, which is around 6%. Thanks to the

tunability of the circuit in Fig. 4(c), we correct the

deviation at the center frequency by applying IC1 =

IC2 = 3.35 lA. The circuit proposed in [2] has a low

voltage gain for the selected element values as in the

original work of Higashimura and Fukui. In the circuit

proposed by Soliman [3], the gain decreases at 3 MHz

and 30 MHz around 1.5 dB and 3 dB, respectively. At

frequencies beyond 200 MHz gains of the circuits in [2]–

[3] start to decrease rapidly. We can say that the pre-

sented circuit is better than other circuits in [2]–[3] from

frequency response point of view.

In order to compare time domain performances of the

circuits, we show total THD values using SPICE simula-

tions in Fig. 11. Since the gain of the circuit in [2] is lower

than unity as in the original work of Higashimura and

Fukui in for the selected component values a fair THD

comparison may not be possible. Instead we compared

THD performances of the presented circuit with the Soli-

man’s notch filter since in this case both circuits have

approximately equal magnitude outputs. We applied 1 kHz

sinusoidal input signal with various amplitudes to the input

of the circuit. We tested both of the circuits of Fig. 4(b) and

Frequency

100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHz11Hz 100MHz

Gain [dB] -20.0

0

-39.7

Ic=1µA

Ic=3.5µA

Ic=10µA

Fig. 7 Illustrating electronic

tunability of the proposed

circuit. The center frequency of

the filter is tuned between

57.5 kHz and 575 kHz through

various control currents (Q = 1)

Time440.00us 445.00us 450.00us 454.23us

_ _ _ Simulated _____ Ideal

-1.00V

0V

1.00V

2.00V

-1.62V

Amplitude

Fig. 8 Time domain response

for peak-to-peak 3 V sinusoidal

output voltage at 300 kHz for

IC = 100 lA. The THD is less

than –40 dB

Fig. 9 Notch/all-pass filter examples from the literature. (a) Soli-

man’s notch/all-pass filter circuit (b) Higashimura’s notch/all-pass

filter circuit

Analog Integr Circ Sig Process (2007) 51:181–189 187

123

(c) in terms of the THD analysis. Although the presented

circuit has a slightly larger gain (0 dB), its THD values are

lower than the circuit in Fig. 9(a).

7 Conclusions

In this work, a new approach is presented for the analog

filter design with high dynamic range. Trade-offs between

cascadability, high input impedance property, and dynamic

range are discussed. As an example, a VM second order

notch/all-pass filter is presented using minimum number of

passive elements and a first generation current conveyor.

The presented circuit has several advantages such as being

suitable for low power applications due to low component

count, and high frequency operation due to its inherent

feed-forward capacitor between its input and output.

Moreover it can be easily made electronically tunable. A

current controlled CCI is given to test the functionality of

the proposed circuit.

Acknowledgments This work is/was supported by Bogazici Uni-

versity Research Fund, with the project code 05A201D.

References

1. Pal, K., & Singh, R. (1982). Inductorless current conveyor all-pass

filter using grounded capacitors. Electronics Letters, 18(1), 47.

2. Higashimura, M., & Fukui, Y. (1988). Realization of all-pass and

notch filters using a single current conveyor. International Journalof Electronics, 65(4), 823–828.

3. Soliman, A. M. (1999). New all-pass and notch filters using current

conveyors. Frequenz, 53(3–4), 84–86.

4. Cakir, C., Cam, U., & Cicekoglu, O. (2005). Novel all-pass filter

configuration employing single OTRA. IEEE Transactions onCircuits and Systems II, 52(3), 122–125.

5. Smith, K. C., & Sedra, A. S. (1968). The Current Conveyor: A

New Circuit Building Block. Proceedings of the IEEE, 56, 1368–

1369.

6. Aronhime, P., Nelson, D., & Adams, C. (1990). Applications of a

first generation current conveyor in current mode circuits. Elec-tronics Letters, 26(18), 1456–1457.

7. Fabre, A., Saaid, O., Wiest, F., & Boucheron, C. (1996). High

frequency applications based on a new current controlled con-

veyor. IEEE Transactions on Circuits and Systems I, 43(2), 82–91.

8. Frey, D. R. (1993). Log-domain filtering: an approach to current-

mode filtering. IEE Proceedings, Part G: Circuits, Devices andSystems, 140(6), 406–416.

10KHz 100KHz 1.0MHz 10MHz 100MHz 1.0GHz1.7KHz

-30

-20

-10

-0

Frequency

_____ Soliman_ _ _ _ Proposed ..... Higashamura

Gain [dB]

Fig. 10 The comparison of the

roll-off frequencies at high

frequency region of the

proposed filter with other notch/

all-pass filters in the literature

for f0 � 281 kHz.

Fig. 11 The comparison of THD values of the proposed filter with

another notch/all-pass filter in [3] for 1 kHz sinusoidal input signal

188 Analog Integr Circ Sig Process (2007) 51:181–189

123

Bilgin Metin received the

B.Sc. degree in Electronics and

Communication Engineering

from Istanbul Technical Uni-

versity, Istanbul, Turkey in

1996 and the M.Sc. and Ph.D.

degrees in Electrical and Elec-

tronics Engineering from Bo-

gazici University, Istanbul,

Turkey in 2001 and 2007

respectively. He served as re-

search assistant at the Electrical

and Electronics Engineering

Department of the Bogazici

University between 1999 and

2007. His research interests include continuous time filters, analog

signal processing applications, current-mode circuits, computer net-

works, and network security. He was given the best student paper

award of ELECO’2002 conference in Turkey. He has over 15 pub-

lications in scientific journals or conference proceedings.

Shahram Minaei received the

B.Sc. degree in Electrical and

Electronics Engineering from

Iran University of Science and

Technology, Tehran, Iran, in

1993 and the M.Sc. and Ph.D.

degrees in electronics and com-

munication engineering from

Istanbul Technical University,

Istanbul, Turkey, in 1997 and

2001, respectively. He is cur-

rently an Associate Professor in

the Department of Electronics

and Communication Engineer-

ing, Dogus University, Istanbul,

Turkey. He has over 60 publi-

cations in scientific journals or conference proceedings. His current

field of research concerns current-mode circuits and analog signal

processing. Dr. Minaei has served as a reviewer for a number of

international journals and conferences.

Oguzhan Cicekoglu received

the B.Sc. and M.Sc. degrees

from Bogazici University and

the PhD. degree from Istanbul

Technical University all in

Electrical and Electronics

Engineering in 1985, 1988 and

1996 respectively. He served as

lecturer at the School of Ad-

vanced Vocational Studies

Electronics Prog. of Bogazici

University where he held vari-

ous administrative positions be-

tween 1993 and 1999. He has

also given lectures at the Turk-

ish Air Force Academy. He was with the Biomedical Engineering

Institute of the Bogazici University between 1999 and 2001. He is

currently a professor at the Electrical and Electronics Engineering

Department of the same University.

Oguzhan Cicekoglu served in organizing and technical commit-

tees of many national and international conferences. He was the Guest

co-editor of a Special Issue of the Journal Analog Integrated Circuits

and Signal Processing Journal. One of the publications he co-authored

in IEEE Transactions on Circuits and Sytems II-Analog and Digital

Signal Processing is among the top cited papers listed in IEEE Cir-

cuits and Systems Society web page. He received the Research

Excellence Award of Bogazici University Foundation in 2004. Cur-

rently he serves as the co-chair of Amplifiers and Comparators track

in 50th IEEE Midwest-Newcas Joint Conference which will be held

in Montreal-Canada.

His current research interests include analog circuits, active fil-

ters, analog signal processing applications and current-mode circuits.

He is the author or co-author of about 150 papers published in sci-

entific journals or conference proceedings and conducts review in

numerous journals including Analog Integrated Circuits and Signal

Processing, IEEE CAS-I, IEEE CAS-II, International Journal of

Electronics, International Journal of Circuit Theory and Applications,

ETRI Journal, IEE Proceedings Pt.G, and others. Oguzhan Cicekoglu

is a member of the IEEE.

Analog Integr Circ Sig Process (2007) 51:181–189 189

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