High-Order Current-Mode Universal Filter Using CCIIs and Grounded Passive Components

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 8, August 2013)

608

High-Order Current-Mode Universal Filter Using CCIIs and

Grounded Passive Components

Chen-Nong Lee1

1

Department of Computer and Communication Engineering, Taipei Chengshih University of Science and Technology, Taipei, Taiwan, R. O. C.

Abstract—This paper presents a new high-order universal filter structure with multiple-inputs and single-output. The structure only employs n second-generation current conveyors (CCIIs), n grounded capacitors, and n grounded resistors, which can realize nth-order universal filtering responses (lowpass, highpass, bandpass, band-reject, and allpass) from the same topology. Moreover, the proposed high-order filter still achieves many advantages like the employment of all grounded passive components, and the minimum number of active and passive components, in addition to having no need of inverting-type input signals or double-type input signals for the use of special input signals, no need of component matching conditions, high output impedance and low sensitivity performance. H-Spice simulation results confirm the theory.

Keywords—Active filters, second-generation current conveyors, current-mode, high-order filter, universal filter.

I. INTRODUCTION

The applications and advantages in the designing current-conveyor-based active filters have received considerable attentions. Several current-conveyor-based high-order voltage-mode or current-mode filters have been presented in the literature [1-7]. Such structures have often been developed with different design criteria in mind, including the realization of all five universal filtering responses, reduced number of active and passive elements, and employment of grounded passive elements. Using signal-flow graph approach, several high-order transfer function syntheses using CCIIs have been present [1-3].

For example, In [1], a nth-order allpass voltage-mode filter

was proposed. The allpass filter employs n+1

current-conveyors, n-1 floating and one grounded capacitors, and 2n+1 floating and two grounded resistors. In [2], a n th-order lowpass voltage-mode filter was proposed. The lowpass filter contains n current-conveyors, n capacitors (only one capacitor grounded), and n floating resistors. In [3], a general synthesis method for the realization of n th-order voltage transfer function was proposed. The filter

structure employs n+2 current-conveyors, n capacitors

(only one capacitor grounded), and 2n+3 resistors (only one

resistor grounded).

However, all these filter structures [1-3] use many floating passive elements. Since the circuits using only grounded passive elements have many advantages in integrated circuit (IC) realization, some high-order voltage-mode or current-voltage-mode current-conveyor-based filters using only grounded passive elements have been presented in [4-6].

The recently reported two high-order

current-conveyor-based current-mode filters [4, 5] employs only n grounded

capacitors [4, 5], and n grounded resistors [4], (i.e. the minimum number of passive components). However, the

two high-order filter structures need to use either n+1

current-conveyors [4] or n+1 current-controlled conveyors

(CCCIIs) [5]. Moreover, they can not realize high-order allpass response. In 2009, a good high-order current-mode and transimpedance-mode (i.e. input as current and output as voltage) universal filter was proposed in [7]. The filter can realize lowpass, bandpass, highpass, band-reject, and allpass responses from one current-output terminal and one voltage-output terminal but it needs to use n+1 MOCCIIs

and one floating resistor, in addition to n grounded

capacitors and n grounded resistors. In 2011, two digitally

programmable high-order current-mode universal filter structures were presented [8]. However, they need to use 2n+3 or 3n+2 active elements, 2n or 2n-1 floating resistors, and n grounded capacitors. Only one [6] can realize high-order current-conveyor-based voltage-mode allpass transfer function with the minimum number of active and grounded

passive components (i.e. only n current conveyors, n

grounded capacitors, and n grounded resistors). In [6],

Chang and Swamy use the very effective analytical synthesis method (ASM) [6, 9-15] to synthesize a new current-conveyor-based high-order allpass filter structure which can achieve all of the main advantages. Up until now, no current-conveyor-based high-order universal filter (lowpass, bandpass, highpass, band-reject, and allpass) using the minimum number of active and grounded passive

components (i.e. only n CCIIs, n grounded capacitors, and

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Current-mode filters using current-conveyors have received considerable attention, because they have higher signal bandwidths, greater linearity, lower power consumption, and larger dynamic range than the voltage-mode counterparts [16, 17]. Since the OTA has high input and output impedances, it is more suitable for transadmittance-mode (i.e. input as voltage and output as current) circuit applications Also, the OTA will pose a stability problem at high frequencies [4]. Since the CCII has unity voltage and current gains, it has not such a problem [4]. Hence, this leads to prospective research work: investigating and developing a high-order CCII-based filter which can realize nth-order universal filtering responses (lowpass, highpass, bandpass, band-reject, and allpass) from the same topology using the minimum number of active and grounded passive components (i.e.

only n CCII, n grounded capacitors, and n grounded

resistors) without requiring matching conditions and inverting or double-types amplifiers for special input signals.

In this paper, the proposed structure is a new high-order

current-mode universal filter using only n CCIIs, n

grounded capacitors, and n grounded resistors. In Table I, the main features of the proposed new high-order circuit are compared with those of previous high-order works as following advantages: (i) the minimum number of active

components, (ii) the realization of nth-order universal

filtering responses (lowpass, highpass, bandpass, band-reject, and allpass) from the same topology, (iii) the employment of all grounded passive components, (iv) no need to impose components choice conditions to realize

specific nth-order filtering functions, (v) no need of

inverting-type or double-type amplifiers for the use of special input signals, (vi) low active and passive sensitivities.

II. HIGH-ORDER CURRENT-MODE UNIVERSAL FILTER

Figure 1 shows the proposed nth-order filter structure where In, In-1, In-2 ,…, I2, I1, I0 are the filter input currents whose setting determine the filter functions as shown later, Iout is the filter current output. The choice of the subscript +/- of the output terminal Zn+/- in the CCII(n) depends on an

even/odd order n of the high-order filter, respectively.

Using standard notation, the port relations of a CCII can be characterized by IY = 0, VX = VY and IZ± = ±IX. The

multiple current outputs of CCII(n) can be simply

reconstructed using current mirrors. Moreover, all current outputs have very high output impedance.

TABLEI

PERFORMANCE PARAMETERS OF RECENTLY REPORTED HIGH-ORDER CURRENT-CONVEYOR BASED FILTERS

Circuits Advantages

[i] [ii] [iii] [iv] [v] [vi]

Ref. [8] No Yes No Yes Yes Yes

Ref. [4] No No Yes Yes Yes Yes

Ref. [7] No Yes No Yes Yes Yes

Ref. [5] No No Yes Yes Yes Yes

Ref. [6] Yes No Yes Yes Yes Yes

Ref. [3] No Yes No No Yes No

Ref. [1] No No No No Yes No

Ref. [2] Yes No No No Yes No

The new circuit Yes Yes Yes Yes Yes Yes

Routine circuit analysis for Figure 1 yields the following transfer functions:

0 1 2 2 2 2 1 1

0 0 1 1 2 2 2 2 2 2 1 1 1

... ...

a s a s a s

a s a s a

I a s I a s I a s

I a s I a s I a I

n n n n n n

n n n n n n n n n out

    



 

 



 _

  

    

 

(1) Where

 



n

i i

n C

a

1

,

    

  

      

 

  

n

k

j j

k

i i

k C G

a

1 1

for k1,2,3,...,n1

 



n

j j

G a

1 0

The choice of the +/- of (a0I0) term is based upon an

even/odd order n of the high-order filter, respectively.

From equation (1), the high-order universal filter transfer functions are obtained according to input current conditions as follows.

(i) Highpass: In = Iin , and all the other input currents are zero.

(ii) Lowpass: I0 = Iin , and all the other input currents are zero.

[image:2.612.326.561.168.360.2]

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International Journal of Emerging Technology and Advanced Engineering

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(iv)Band-reject: In = I0 = Iin , and all the other input currents are zero.

[image:3.612.56.281.160.506.2]

(v) All-pass: In = In-1 = In-2 =…= I2 = I1 = I0 = Iin.

Figure 1. Proposed current-mode nth-order universal filter structure.

Note that there are no critical component-matching conditions or cancellation constraints in the design. Moreover, the structure does not need inverting-type input current signals or double-type amplifier for realizing any filter transfer functions. Note that by adding an extra Z- terminal to the CCII(n) (i.e. multiple current outputs CCII) and then adding an extra grounded resistor to this Z- terminal, the proposed circuit can also realize current-mode

and transimpedance-mode nth-order universal filtering

responses (lowpass, highpass, bandpass, band-reject, and allpass) from one current-output terminal (Iout , shown in Figure 1) and one voltage-output terminal (i.e. the extra Z-terminal ) without using additional active elements and floating passive elements.

[image:3.612.327.557.232.550.2]

With respect to the high-order current-mode and transimpedance-mode filters in [7], the new proposed structure uses one fewer CCII and no floating passive elements. To illustrate the proposed current-mode high-order filter structure, Figure 2 shows a sixth-high-order highpass filter with low input and high output impedance suitable for direct cascading and easy to be connected to next stage without any buffer.

Figure 2. Proposed sixth-order high-pass current-mode filter.

III. NONIDEAL ANALYSIS

Taking the tracking errors of the CCII into account, the relationship of the terminal voltages and currents can be written as: IY = 0, VX = β(s)VY, IZ± = ±α(s)IX, where α(s) and β(s) represent the frequency transfer functions of the internal current and voltage followers of the CCII. They can be approximated by the first order lowpass functions

[18, 19], whose corner frequencies 300MHz by using

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International Journal of Emerging Technology and Advanced Engineering

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For frequencies much less than the corner frequencies of the CCII, all α(s) and β(s) are real quantities of magnitudes slightly less than one [18, 19]. Assuming the circuit works

at frequencies much less than the corner frequencies of α(s)

and β(s), namely, α(s) = α = 1－εi and εi (εi << 1) denotes the current tracking error and β(s) = β = 1－εv and εv (εv << 1) denotes the voltage tracking error of the CCII.

Taking into account the non-idealities [18, 19] of the

CCII(n), CCII(n-1),……, CCII(2), CCII(1), we obtain the

non-idealities as below:

0  Y

I ,V_X _nV_Y,I_Z__n₀I_X,I_Z₁__n₁I_X,

X n

Z I

I ₂_ ₂ ,I_Z₃_ a_n₃I_X,…..,I_Zn__nnI_X for CCII(n) (2)

0  Y

I ,V_X _n_₁V_Y, I_Z_₍_n_₁₎₀I_X

for CCII(n-1) (3) 0

 Y

I ,V_X _n_₂V_Y, I_Z_₍_n_₂₎₀I_X

for CCII(n-2) (4)



0  Y

I ,V_X ₂V_Y, I_Z_₂₀I_X

for CCII(2) (5)

0  Y

I ,V_X ₁V_Y, I_Z_₁₀I_X

for CCII(1) (6)

The non-ideal denominator of the nth-order universal

filter transfer function shown in equation (1) becomes

0 1 2 2 1

1

'

)

(

s

a

s

a

s

a

s

a

s

a

D



_n n



_n_ n







(7) Let 0 0 1 1 2 2 2 2 1 1 ' ' , ' ' , ' ' ,..., ' ' , ' ' A a a A a a A a a A a a A a a n n n n n n n n

n _ _ _ _ _

   

(8) We can obtain that:

n n nn n n n n n n C C C C C G G G G G A 1 3 2 1 0 ) 1 ( 0 ) 2 ( 30 20 10 1 3 2 1 1 3 2 1 0 .... .... .... ....               (9) n n n n n n n n n n C C C C C G G G G G A 1 4 3 2 ) 1 ( 0 ) 1 ( 0 ) 2 ( 40 30 20 1 4 3 2 1 4 3 2 1 .... .... .... ....                 (10) n n n n n n n n n n C C C C C G G G G G A 1 5 4 3 ) 2 ( 0 ) 1 ( 0 ) 2 ( 50 40 30 1 5 4 3 1 5 4 3 2 .... .... .... ....                 (11)



n n n n n n n n n n n n n C C C G G G A 1 2 3 0 ) 1 ( 0 ) 2 ( 1 2 1 2 3                (12) n n n n n n n n n C C G G A 1 2 0 ) 1 ( 1 1 2           (13) n n n n n C G

A _₁   1 (14)

The relative sensitivities are the values of filter characteristic parameters (An-1, An-2 ,…, A2, A1, A0) with respect to circuit elements. By using equations (9)–(14), the sensitivities of filter characteristic parameters (An-1, An-2 ,…,

A2, A1, A0) can easily be calculated and equal to 0 or 1. All of which are small.

If a second-order filter (n = 2) is given as an example, the equations (7)–(14) are obtained as below:

2 1 2 1 22 10 2 1 2 2 21 2 2 ) ( C C G G C G s s s

D         (15)

The ω0 and Q of the non-ideal current-mode universal biquad are: 2 1 2 1 22 10 2 1 0 C C G

G    

  (16)

1 2 2 2 1 1 10 22 21 1 C G C G Q     

 (17)

The active and passive sensitivities of ω0 and Q are:

2 1 0 2 1 22 10 0 2 1 0 2

1,  ,  , , , 

S_C _C S_G _G S_ _ _ _

2 1 2 1 10 22 2 1 1

2, , , ,

   



 Q Q Q

G C Q

G

C S S S

S _ _ _ _

1

21





Q

S

_ 0 0 23 21 20

11, , ,      a S

0

23 20 11, ,



Q

a

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In summary, the proposed current-mode universal filter has low active and passive sensitivities.

IV. H-SPICE SIMULATIONS

A CMOS implementation of the CCII± is shown in

Figure 3 [20] with the NMOS transistor aspect ratios (W/L=5μm/1μm) and PMOS transistor aspect ratios (W/L=10μm/1μm). Note that the multiple current outputs of CCII applying the realization of current replicas are very simple. To verify the theoretical analysis of the high-order universal filters, the H-SPICE simulations, using the TSMC 0.25μm process with the parameters of level 49 for the proposed circuits of Figure 1, were performed with the component values: R1 = R2 = … = R5 = R6 = 10kΩ, and C1 = C2 = … = C5 = C6 = 5pF for the sixth-order high-pass, low-pass, band-pass, and band-reject filters of the Figure 1,

leading to a center frequency of f0 = 3.183MHz, and (ii) C1

= C2 = C3 = 5pF, R1 = 20kΩ, R2 = 10kΩ, and R3 = 5kΩ for the third-order all-pass filter of the Figure 1, leading to a center frequency of f0 = 3.183MHz. Their supply voltages

are VDD =－Vss = 1.25V, Vb1 = －0.3V, and Vb2 = －0.6V.

[image:5.612.332.542.146.310.2]

Figure 4 presents the simulated sixth-order highpass, lowpass, bandpass, and band-reject amplitude-frequency responses. Figure 5 presents the simulated third-order all-pass phase and amplitude-frequency responses. As can be seen, there is a close agreement between theory and simulation.

Figure 3. CMOS implementation of the CCII±.

105 106 107 -200

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

frequency(Hz)

m

a

g

n

it

u

d

e

(d

b

)

Figure 4. Amplitude-frequency responses of the proposed current-mode sixth-order high-pass, low-pass, band-pass, and band-reject

signals (＊, simulated high-pass response; Δ, simulated low-pass response; ○, simulated band-pass response; ×, simulated band-reject

response; and ____,theoretical curve ).

104 105 106 107 -400

-300 -200 -100 0 100 200

frequency(Hz)

p

h

a

s

e

(d

e

g

re

e

)

m

a

g

n

it

u

d

e

(d

b

)

20

10

0

-10

-20

-30

-40

Figure 5. Phase-frequency and amplitude-frequency responses of the proposed current-mode third-order all-pass signals (○, simulated

phase; Δ, simulated amplitude; and ____,theoretical curve).

V. CONCLUSIONS

Using n CCIIs, n grounded capacitors, and n grounded resistors, a current-mode universal high-order filter is

presented which can realize nth-order low-pass, high-pass,

[image:5.612.341.549.381.534.2] [image:5.612.55.285.464.613.2]

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Moreover, the proposed high-order circuit offers the following advantages: the minimum components, using grounded capacitors attractive for integration, using grounded resistors suitable for the variation of filter parameters, high output impedance good for cascadability, no need to change the filter topology, no component-value constraints, no need of inverting or double-type amplifiers for special input signals, and low active and passive sensitivities. H-Spice simulations with TSMC 0.25μm process and ±1.25V supply voltages are included and confirm the theoretical predictions.

Acknowledgements

The author would like to thank the National Science Council of Taiwan, R. O. C. The National Science Council, Republic of China supported this work under grant number NSC 101-2221-E-149-008-.

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