The current differencing transconductanceamplifier (CDTA)Jun Xu and Chunhua Wang - January 28, 2013

Editor’s note: Most modern designs have been using voltage mode elements like op-amps forimplementation of various electronic circuits. These elements are used widely due to their smallsizes and good performance. With the demand for portable battery powered equipment increasing,designers have begun to look into different architectures to fit these demanding designs. This issueis not easily solved with voltage mode elements since the voltage supply if reduced will causeproblems with realizing good, fully-functional circuits. Instead, current mode (CM) elements are nowbeing considered for the same circuits and these issues can then be addressed.

The Current Differencing Transconductance Amplifier (CDTA) is the active element operating incurrent-mode and can be applied to various circuits such as comparators, second order high pass,second order low pass, second order band pass filters.

This article outlines a design method for CDTA-based resistor-less current-mode full balanced nth-order leapfrog ladder filter is presented. Second, circuit device’s parameters confirmation for actualdesign are analyzed in detail. Further, PSpice simulation for an actual 6th-order butterworth filter isconducted, and the result verifies the validity of the proposed circuits.

A new method for design of resistorless current-mode full balanced nth-order leapfrog ladder filterusing CDTA as active component is proposed in the paper. The proposed circuit, which adopts only nactive components and n grounded capacitors, can realize n-order filter’s function and shares simpleconfiguration, low power consumption. It contains minimum component and doesn’t use any resistor.

The proposed filter can be applied in many fields: for instance, RF transmitter/receiver, phase-lockedloop FM demodulator, wireless communication and instrumentation. In order to demonstrate thevalidity of the proposed circuit, PSpice simulation for actual 6th-order butterworth filter isconducted, and the result has good agreement with the theoretical analysis.

Introduction

Introduction1.

Filters are employed in many applications such as in a radio-frequency (RF) filter for image rejectionor in an intermediate-frequency (IF) filter for channel selection of a RF or wireless receiver.Among，on-chip RF filter mainly applies switched capacitors (SC) or continuous-time (CT) structure,especially for continuous-time current-mode techniques.

During the past few years, comparing with voltage-mode techniques, current-mode techniques havebeen received a wide attention due to its high slew rate, wide bandwidth, low voltage and low power

consumption etc. A number of current-mode devices, such as CCII, CFA, OTA, have been widelyapplied in circuit design.

Recently, a new current-mode active element with two current inputs and two kinds of currentoutput, which is called a current differencing transconductance amplifier (CDTA), has beenintroduced [1].The CDTA is a current mode device of real sense and offers wider frequencybandwidth advantages as compared to its close relative, the current differencing buffered amplifier (CDBA) [2]. So some CDTA-based current-mode circuit has been widely proposed, such as inductancesimulator circuits [4-6], sinusoidal oscillator circuits[7-8]，and it especially is a promising choice forrealizing the current-mode filters[9-20].

Obviously, from the reported filter circuits, researches on high-order filter are not adequateapparently [1, 21-25], especially in CDTA-based nth-order filter [23-24]. Literatures [21-22] proposetwo kinds of nth-order current-mode filter using CDBA. On the basis of analyzing signal flow diagram,the proposed circuit, which uses CDBAs, capacitors resistances, can realize high order filter’sfunction. Literatures [23-24] propose two kinds of CDTA-based nth-order filter independently.

The circuit [23] can realize nth-order lowpass filter’s function and shares simple structure, groundedcapacitors. Literature [24] proposes a design method of nth-order filter circuit. This method hasrelatively strong versatility in high-order filter design. However, most of above these circuits [1, 21-25] don’t take full advantage of the active component’s port characteristics and limit the flexibility ofcomponent’s usage.

Then these circuits’ structure is too complicated and involves too many components, especially forpassive resistor. Such as circuits [1, 21-25] require some external passive resistors and more CDTAsare also used in circuit [24, 25]. Adopting excessive resistor can be a disadvantage of current-modecircuit, which is not beneficial to integrated circuit (IC) fabrication and circuit’s frequencybandwidth.

Generally speaking, design method of high-order filter is mainly based on cascading second-orderfilter and signal flow diagram (negative feedback). Among leapfrog simulation of the current-modeladder network is to use combinations of active and passive components in order to simulate eitherthe inductances or the operation of a high-order LC ladder. The leapfrog structure is one of the mostpopular choices in active filter design due to its lower sensitivity than the cascade method ,1] .[25

Thus, a new method for design of resistorless current-mode full balanced nth-order leapfrog ladderfilter using CDTA as active component is proposed in the paper. The proposed circuit, which adoptsonly n active components and n capacitors, can realize n-order filter’s function and shares simpleconfiguration. It contains minimum active component and passive component. So the circuits sharelow power consumption.

The circuit adopts grounded capacitor and doesn’t use any resistor, which is convenient forintegrated circuit (IC) fabrication. It is also easy to confirm the parametric values of the elementsfrom the coefficients of the transfer function. The proposed filter can be applied in many fields: forinstance, RF transmitter/receiver, phase-locked loop FM demodulator, wireless communication andinstrumentation. It also can be used in practice for the design of active filter instead of surfaceacoustic wave (SAW) filter used in GSM systems. In order to demonstrate the validity of theproposed circuit, PSpice simulation for an actual 6th-order butterworth filter is conducted, and theresult has good agreement with the theoretical analysis. Current Differencing TransconductanceAmplifier (CDTA) and its realization

.2 Current Differencing Transconductance Amplifier (CDTA) and its realization

The circuit symbol of the CDTA is shown in Fig.1, where p and n are positive and negative currentinput terminals, z and x are current output terminals. Its current characteristics can be describedby the following matrix Eq. (1).

（1）

Fig.1. Symbol for the CDTA

Where Vx=Iz*Zz, gm is the transconductance gain, and Zz is an external impedance connected atthe terminal z. According to above expression, the current through the terminal z follows thedifference of the currents through the terminals p and n (Ip - In), and flows from the terminal z intoan impedance Zz. The voltage drop at the terminal z is transferred to a current at the terminal x (±Ix)by gm, which is electronically controllable by an external bias current (IB).

Usually, it can be constructed using various techniques, one possible CMOS-based CDTA circuitrealization [18] suitable for the monolithic IC fabrication is given in Fig.2. It is also easy to know thatthe transconductance stage can be copied in a circuit, so the number of x port of the CDTA can bechosen a reasonably as actual needed.

Fig.2. Realization circuit of CMOS-based CDTA

3. Design method of current-mode nth-order leapfrog ladder filter

3.1 Design of CDTA-based integral circuit

Integrator is the basic unit of the filter circuit’s composition. Generally speaking, first-orderintegrator can be divided into two categories: lossless integrator and lossy integrator. CDTA-basedlossless and lossy integral circuits are designed in Fig.3.

Fig.3 (a) Fig.3 (b)

Fig.3 (a). CDTA-based lossless integrator circuit

Fig.3 (b). CDTA-based lossy integrator circuit

From Fig.2, CDTA-based lossless and lossy integrator circuit transfer function can be written in Eqs(2), (3):

(2)

(3)

3.2 Analysis and derivation of the proposed circuit

In order to research current-mode leapfrog ladder filter’s circuit configuration, design methods andkeep circuit design’s generality, a current-mode nth-order all pole passive LC lowpass filter networkis chosen in Fig.4:

Fig.4. Current-mode nth-order passive LC ladder network

Its node equations are:

(4)

(5)

(6)

(7)

In order to use the current variable function to represent the above Eqs (4) to (7), the above voltagevariables are divided by the resistance Ro (conversion factor). So circuit’s current variable equationsare written in Eqs (8) to (11):

(8)

(9)

(10)

(11)

Assuming:

(12)

(13)

(14)

(15)

According to Eqs (8) to (15), circuit’s signal flow diagram can be shown in Fig.5.

From Fig.3 and Fig.5, the proposed CDTA-based current-mode nth-order leapfrog ladder filter canbe obtained as shown in Fig.6.

The proposed circuit of simple structure adopts n active components, n grounded capacitors anddoesn’t use any resistor, which is convenient for integrated circuit (IC) fabrication.

3.3 Calculation of circuit’s parameter

Assuming

(16)

Comparing Eqs (2), (3), (12) to (15), it is easy to get the components’ parameters relationship of thecircuits shown in Fig.4 and in Fig.6.

(17)

Then (18)

When i = 2, 4, K, n - 2,

(19)

Then (20)

When i = 3, 5, K, n - 1,

(21)

Fig.5. signal flow diagram of current-mode nth-order passive LC ladder network

Fig.6. Proposed CDTA-based resistorless current-mode full balanced nth-order leapfrogladder filter

Then (22)

(23)

Then (24)

So synthesizing Eqs (17) to (24),

When i = 1, 3, K, n - 1

(25)

When i = 2, 4, K, n

(26)

It is easy to confirm the parametric values of the elements from the known filter’s parameters. It isalso apparent that the cutoff angular frequency (ωo) of filter can be adjusted properly by IB.

Simulation and result4. Simulation and result

To verify the theoretical analysis, a current-mode 6th-order butterworth filter according to theproposed configuration is simulated in PSpice circuit simulation program using the CMOS-basedCDTA circuit given in Fig. 2. The filter circuit is shown in Fig.7. And it is simulated with theparameters of the 0.5µm MIETEC transistor model.

The 6th-order butterworth filter’s [26] cutoff frequency is 10MHz and the passive components’parameters are: C′1=0.824pF, L2=0.225mH, C′3=3.076 pF, L4=0.307mH, C′5=2.25pF,L6=0.082mH. Here, the CDTA circuit is supplied with symmetrical voltages of ±2.5V. The externalbias current are IB1 = IB2= 85µA, IB3= 200µA and the transconductance gain gmi is 457.83µS.

It is easy to get the value of Ci from above parameters, C1 =3.77pF, C2 =10.3pF, C3 =14.08pF, C4=14.08pF, C5 =10.3pF, C6 =3.77pF. Fig.8 shows the simulation results. It is noted that thetheoretical and simulation results are in good agreement. The circuit’s total power consumption islow, it is 0.02W.

Fig.7. Proposed CDTA-based resistorless current-mode full balanced 6th-order leapfrogladder filter

Fig.8. Frequency responses of the proposed filter and actual filter

Fig.9, 10 shows the transient response of the proposed filter. Input signal is a square waveformscurrent (±2µA/100kHz) and a sinusoidal current (±100µA/1MHz) in this simulation. The switchingdelay time of the filter is approximately 0.4µs. The filter circuit’s total harmonic distortion (THD)analysis is also investigated using PSPICE program (sinusoidal current at 1MHz). It is found inFig.11 that for an input current signal less than 300µA amplitude, circuit’s THD is no more than 2%.

Fig.9. Square waveforms transient response of proposed filter

Fig.10. The sinusoidal waveforms transient response of proposed filter

Fig.11. Common-mode rejection ratio (CMRR) of the filter

Fig.12. Total harmonic distortion of the filter

5. Conclusion

In this paper, a new method for design of resistorless current-mode full balanced nth-order leapfrogladder filter using CDTA is proposed in the paper. The proposed circuit, which adopts only n activecomponents and n capacitors, can realize nth-order filter’s function and shares simple configuration,low power consumption. It contains minimum active component and passive component.

The circuit adopts grounded capacitor and doesn’t use any resistor. It is also easy to confirm theparametric values of the elements from the coefficients of the transfer function. PSpice simulationfor an actual 6th-order butterworth filter is conducted, and the result has good agreement with thetheoretical analysis.

Acknowledgements

The authors would like to thank the National Natural Science Foundation of China for financiallysupporting this research under No. 61274020 and the Open Fund Project of Key Laboratory inHunan Universities under No. 12K011 and the Project supported by Hunan Provincial NaturalScience Foundation of China under No.11JJ6055.

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About authors

Author-Jun XU was born in Changsha, China, in 1986. He received the B.S. degree from ChangshaUniversity of Science & Technology , Changsha, China. He is currently studying in HunanUniversity for master degree. His research interests include RFIC design with focus on current-mode circuit. xujun5811487@163.com

Co-author-Chunhua WANG was born in Yongzhou, China, in 1963. He received the B.S. degree fromHengyang Normal University, Hengyang, China, the M.S. degree from Physics Department,Zhengzhou University, Zhengzhou, China, the Ph.D. degree from Beijing University of Technology,Beijing, China. He is currently a Professor and Doctoral supervisor of Hunan University, Changsha,China. His research includes current-mode circuit design, RFIC design and wireless communication.wch1227164@sina.com