Universal Pseudo-Differential Filter Using DDCC and DVCCs

In the paper, a universal preudo-differential second-order filter operating in voltage mode, where both intup and output are differential, is presented. The circuit is formed by one differential difference current conveyor (DDCC), two differential voltage current conveyors (DVCCs), and five passive elements. The filter is characterized by high input impedance, minimum number of passive elements that are all grounded, and high common-mode rejection ratio (CMRR). The proposed filter structure is able to realize all five standard frequency filter responses. Non-ideal analysis has been performed by considering the real parasitic parameters of the active elements. The optimization of passive element values has been done in terms of minimal shift of the pole-frequency and to obtain the maximum stop-band attenuation of the high-pass filter response. Functionality is verified by simulations and experimental measurements using readily available integrated circuit UCC-N1B 0520. DOI: http://dx.doi.org/10.5755/j01.eie.23.6.19694


I. INTRODUCTION
Frequency filters are widely used in the vast majority of electrical equipments such as in video signal processing, communication systems, telephone circuitry, broadcasting systems, control and instrumentation systems, etc.Therefore, a significant number of filters are available in the open literature using various types of function blocks.For designing frequency filters (fully differential, single-ended, or pseudo-differential) operational transconductance amplifiers (OTAs) [1]- [4] current follower transconductance amplifiers (CFTAs) [5], [6], current differencing transconductance amplifiers (CDTAs) [7], [8] were commonly used during the last two decades.Frequency filters can also be utilized using basic types of current conveyors (CC) [9]- [11], fully differential current conveyors (FDCC) [12], [13], differential voltage current conveyors (DVCC) [14], [15], or differential difference current conveyor (DDCC) [16], [17].Currently, the design of function blocks is emphasized on low supply voltage and low-power consumption solutions [18]- [21].However, by decreasing the supply voltage of function blocks it has the consequence in reduced dynamic range of the signals being processed due to reduced signal-to-noise ratio (SNR).Therefore, an increased interest in designing fullydifferential frequency filters using various types of new active elements can be observed [22]- [28].In comparison to their single-ended frequency filter counterparts, differential filters are generally capable to maintain sufficient SNR, are characterized by lower total harmonic distortion (THD), feature high common-mode signal rejection (CMRR), and furthermore with reduced input noise [29].To design a fullydifferential frequency filter, mostly a single-ended prototype is mirrored around the ground plane, which requires the usage of fully-differential active elements and also symmetry in passive elements can be observed [30].This design technique results in quite complex structures and therefore the pseudo-differential filters were presented in which both input and output are assumed in differential form, but the internal structure of the filter is single-ended [16], [17], [31]- [32].
In this paper, a new second-order voltage-mode universal pseudo-differential filter using three active elements (one DDCC and two DVCCs) is presented.Together with the active elements only five passive elements (two capacitors and three resistors), each of them grounded, are used.Theoretically, the input-impedance of the proposed filter is infinitely high and hence it is suitable for easy cascading.Even if it is pseudo-differential, such filter still exhibits with high CMRR and low signal distortion.The proposed universal pseudo-differential filter realizes all five standard types of frequency filters, i.e. (low-pass, high-pass, bandpass, band-reject, and all-pass).The behavior of the filter was verified by simulations and furthermore by experimental measurements that show the functionality of the proposed solution.

II. DESCRIPTION OF DVCC AND DDCC
For the design of universal pseudo-differential filter the DVCC and DDCC active elements have been used, which schematic symbols are shown in Fig. 1.First, the DVCC is a five terminal building block with two high-impedance voltage inputs Y1 and Y2, one low-impedance current input X, and two high-impedance current outputs Z1+ and Z1-.Relation between the terminal currents and voltages is described by: The DDCC is a six-terminal building block with three high-impedance voltage inputs Y1+, Y2-and Y3+, a lowimpedance current input X, and two high-impedance current outputs Z1+ and Z1-.The relation between terminal currents and voltages is given as: III. PSEUDO-DIFFERENTIAL FILTERS Generally, when analyzing the differential circuits operating in voltage mode, the following relations are assumed [29]: where v1d, v2d and v1c denote differential input voltage, the differential output voltage, and the common-mode input voltage, respectively.Signal v1d is the difference between the two input signals v1+ and v1-, while v1c is expressing common-mode input signal as the average of the two input signals v1+ and v1-.Taking into consideration (3), then the differential output voltage v2d is defined as follows where Adm and Acm are differential and common-mode signal gains, respectively.The rejection of common-mode signal is expressed using CMRR as [29] dm cm 20 log , which determines the ability of an active element or a differential structure to suppress unwanted common-mode input signal that is common to both inputs, to the desired differential input signal.In ideal case Acm = 0 and hence CMRR is infinite.
As mentioned in the Section I., the fully-differential filters are designed using e.g. the mirroring technique, [30].However, it is obvious from the mathematical description point of view (3)-( 5) that for sake of analysis of such function blocks only the input and output signals are considered.Therefore, it is possible to describe and propose so-called pseudo-differential structures, which have differential input and output voltage terminals, however, the inner circuit topology is non-differential.These types of filters still provide high CMRR similarly as fully-differential structures and furthermore, are less complex because of the internal non-differential structure.In practice, in combination with fully-differential circuits the pseudodifferential function blocks can be used as the last section(s) of front-end analog signal processing path, where very high CMRR is no more required [31].

IV. PROPOSED UNIVERSAL PSEUDO-DIFFERENTIAL FILTER
For the design of a pseudo-differential filter, similarly to the design of fully-differential filters, a single ended prototype is also used.However, as described in [31], in case of pseudo-differential filters only the non-differential input and output are to be transformed into differential one.

A. Single-Ended Prototype
The single-ended structure shown in Fig. 2 was described in [34] and it is a pattern for the proposed universal pseudodifferential filter.The prototype is realized using three active elements, i.e. two DVCCs, one second generation current conveyor (CCII-3) and four passive elements such as two grounded capacitors and two grounded resistors.This filter uses known connection Y-Z of the conveyors, which advantage is applying the input signal to high-impedance terminal Y of the active element and it ensures its simple connection in cascade.
Circuit given in Fig. 2 allows realizing four basic singleended second-order frequency filter responses (LP, BP, HP, and BR), which are described by the following equations: A detailed analysis of this filter and its performance verification can be found in [34].

B. Proposed Universal Pseudo-Differential Filter
Using the techniques described in [31], the proposed second-order pseudo-differential frequency filter is shown in Fig. 3.The proposed filter is composed from one DDCC and two DVCCs.The structure also includes four passive elements, namely three resistors and two capacitors.To obtain a differential input, the DVCC1 in Fig. 2 was substituted by DDCC1 as it can be observed in Fig. 3. Hence, the differential input signal is applied to the input terminals Y1+ and Y2-of the active element.In order to obtain a bandreject response, the DVCC2 in Fig. 2 has been extended via Z2-output terminal, whereas the resistor R3 has been added with the same value as resistor R1.To obtain differential band-pass response, the CCII-3 in Fig. 2 was substituted by DVCC3, where the inner voltage inverter is used.The remaining passive elements R1, R2, C1, and C2 are unchanged.The advantageous features of the pseudo-differential filter are the same as they are in case of the single-ended prototype.Furthermore, it features with high CMRR, it is characterized by lower THD, and its structure is generally less complex in comparison with a fully-differential solution designed by the mirroring technique.

1) Ideal Pseudo-Differential Filter Analysis
Assuming ideal active elements differential-output voltage for individual filters, i.e. high-pass, low-pass, all-pass, bandpass, band-reject transfer functions can be determined as described below.For an instance, using the notation (3)-( 5), the positive and negative output voltage of the differential high-pass filter can be given as: whereas for differential-output voltage vHPd it applies: Comparing ( 9) with (4) we get differential gain whereas the common-mode signal gain is zero.Remaining four frequency filter responses can be obtained using the corresponding positive and negative output as defined in Fig. 3. Hence, low-pass differential gain is the following all-pass differential gain can be expressed as band-pass differential gain can be calculated as and for R1 = R3 band-reject differential gain can be found as Due to the fact that the common-mode gain Acm for all frequency filters equals to 0, the CMRR equals to infinite, if ideal active elements are considered.For universal pseudodifferential filter the characteristic pole-frequency ω0 and quality factor Q are defined as:

2) Non-Ideal Analysis of Pseudo-Differential Filter
Taking into consideration the non-idealities of the active elements [31], [34] the terminal relations of DVCC can be expressed as: Similarly, the non-ideal behavior of the DDCC can be defined as follows: where m To investigate the influence of the non-ideal voltage and current gains ( 17) and ( 18) of the active elements, the highpass response was chosen for further analysis.The differential and common-mode signal can be determined as: and according to (5), the CMRR equals to From (15) it is obvious that high rejection of the commonmode signal is ensured in case when 1 2    .
Due to non-ideal voltage and current gains of active elements, the characteristic pole-frequency and quality factor modify to: As voltage and current tracking errors of active elements are minimal [35], effect of non-ideal voltage and current gains on filter properties is not significant.
The performance of the filter is more affected by the parasitic impedances of the active elements.In Fig. 4, the most significant [31], [34] parasitics are represented by Rv, Rw, Cv, Cw, that describe the finite impedance of the Y and Z terminals of the active elements.
Re-analysis of the filter yields the following differential gain of the high-pass filter where Ry, Rx, Rz and Cy, Cy are parasitic resistors and capacitors, respectively, wheras for sake of simplicity, the voltage and current gains of the active elements were assumed to be unity.For proper function of frequency filter it has to apply R1; R2 « Rv; Rw, and the following pole-frequency and quality factor can be given: To suppress the parasitic behavior of the active elements as much as possible, the values of passive elements should be kept as: C1 » Cv, C2 » Cw and R1; R2 » Rx

V. SIMULATION AND EXPERIMENTAL MEASUREMENTS
The performance of the proposed pseudo-differential filter has been evaluated by simulations PSpice and later also by experimental measurements.To realize the active elements, the universal current conveyor UCC-N1B 0520 [35] was used.The parameters of non-ideal properties of active elements are taken from the datasheet [35].Simulations assume parasitic impedances of these active elements, trying to acquire the most optimal values of passive elements.

A. Optimization of Universal Pseudo-Differential Filter
The optimization of pseudo-differential filter has been done in two phases, whereas the high-pass response was assumed.The aim of this optimization process is to obtain the most optimal values of passive elements.During the optimization, theoretical pole-frequency f0 = 100 kHz and quality factor Q = 0.707 were assumed.
The first optimization phase was to minimize the shift of the pole-frequency f0sim determined by (23) from theoretical frequency f0teo defined by (15).The shift between these frequencies is evaluated as their ratio, whereas the optimal value of such ratio is unity.In Fig. 5 the ratio between theoretical and simulated pole-frequency is shown.The second optimization phase focused on obtaining the highest attenuation in the stop-band of the high-pass frequency response, i.e. to minimize the ratio of the s 0 terms in the numerator and denominator of ( 22) Varying the values of capacitors C1 and C2, the ratio AdmHP_SB is shown in Fig. 6, whereas the values of resistors R1 and R2 were determined using ( 15) and ( 16) for theoretical pole-frequency f0 = 100 kHz and quality factor Q = 0.707.Fig. 6.Variant for attainment of maximal attenuation for Q = 0.707.

B. Simulations and Experimental Measurements of Transfer Functions
According to the above given optimization graph Fig. 5, in order to obtain the minimal shift in pole-frequency the optimal values of capacitors should be within the range of C1 = C2 = < 1, 10 > nF.From Fig. 6, to achieve at least 40 dB or higher attenuation in the stop-band of the high-pass filter, the values of capacitors should be selected C1 = C2 = 1 nF or higher.Therefore, for simulations and experimental measurements, the values of capacitors C1 = C2 = 1 nF were selected and the values of resistors were determined as R1 = R3 = 1125 Ω and R2 = 2251 Ω to obtain the polefrequency 100 kHz and quality factor Q = 0.707.During the simulations and experimental measurements, the resistor values were selected from the E24 series, i.e.R1 = R3 = 1100 Ω and R2 = 2200 Ω.These passive element values were used for all types of measurements.As the filter uses one DDCC and two DVCCs, for simulations and the experimental measurements three universal current conveyors UCC-N1B 0520 had to be used, [35].
The performance of the filter has firstly been verified by simulations and furthermore by experimental measurements, whereas the obtained frequency responses of the universal pseudo-differential second-order filter working in voltage mode is shown in Fig. 7. From both the simulations and experimental measurements shown in Fig. 7 we can claim that they are in very good agreement with the theory and performance analysis described in Section IV.B-2.Lower attenuation of the high-pass response in the stop-band than expected during the optimization phases is caused by the parasitic characteristics of the active elements, especially lower impedance of the output terminals Z. Increase of the magnitude of the low-pass filter at the frequency of approximately 450 kHz is caused by the non-ideal behavior of the active elements.Assuming parasitic properties, a detailed analysis of the transfer function shows non-zero term with the Laplace operator s 2 , causing increase of the magnitude and could be already observed during the simulations.The other frequency responses agree to theory and the performed optimization phases.
In Fig. 8, the measured common-mode rejection ratios of all types of the corresponding transfer functions are shown.The reached value of CMRR is approximately 36 dB and is constant up to 1 MHz.The drop of CMRR above this frequency is caused by the real behavior of the UCC-N1B 0520 realizing the DDCC1 from Fig. 3 and different polefrequency of the voltage-gains 1  and 2  [35].Next to CMRR the THD of the low-pass filter response has been measured.Evaluating THD, the first major harmonic components were considered, whereas the 1 kHz input signal has been applied to Vin.From Fig. 9 it can be observed that the total harmonic distortion is below 1 % for the amplitude of the input signal up to 1 V. Increase of THD for higher amplitudes of the input signal is caused by the saturation of the active elements, i.e.UCC-N1B 0520, being supplied with the  1.65 V supply voltages.
To measure the performance of the pseudo-differential filter in practice the network analyser 4395A has been used.Therefore, additional single-to-differential (S/D) and differential-to-single (D/S) voltage converters, as shown in Fig. 10, have been used.The S/D convertor uses the readily available AD 8476 [36], whereas the D/S converter is composed of AD 8429 [37].To enable the evaluation of the CMRR via Vcom, the S/D convertor uses also AD 8271 [38], which can be found in more detail in [31].

VI. CONCLUSIONS
In this paper we presented a new current conveyor-based universal pseudo-differential filter working in voltage mode.The proposed filter employs one differential difference current conveyor and two differential voltage current conveyors as active elements, and five passive elements (two capacitors and three resistors), whereas all are grounded.The proposed structure is able to realize all five standard frequency filter responses.The circuit has a high-impedance input and is sufficiently suppressing the common-mode signal.Assuming the parasitic parameters of the active elements, the values of the passive elements have been optimized in terms of minimal shift of the pole-frequency and to obtain the maximum stop-band attenuation of the high-pass filter response.The functionality and performance of the filter has been verified by both simulations and experimental measurements.The total harmonic distortion is less than 1 % for the amplitude of the input signal below 1 V.The value of CMRR reached by measurements is 36 dB and can be generally increased by proper selection of the active elements.Based on these measurements we can say that the filter offers sufficient rejection of common-mode signal in respect to its complexity.

Fig. 2 .
Fig. 2. Single-ended filter as prototype for the pseudo-differential filter design.
and n = {1, 2}) are the voltage and current gains of the DDCC, and | vm  | « 1 and | in  | « 1 denote the voltage and current tracking errors.

Fig. 5 .
Fig. 5. Variant of theoretical pole-frequency in proportion of simulated frequency for Q = 0.707.