Reconnection-Less Electronically Reconfigurable Filter with Adjustable Gain Using Voltage Differencing Current Conveyor

This paper presents a novel reconnection-less and electronically reconfigurable analogue filter. It employs two active elements, Voltage-Differencing Current Conveyor (VDCC) and Dual-Output Current Amplifier (DO-CA) with two independently tunable gains. Filter has the single input and single output topology (SISO). The current-mode transfer function of the filter can be tuned electronically from the low-pass (LP) response to the high-pass (HP) response, via the band-stop (BS) response, without reconnection of the input or output terminal. It is designed in order to provide tuning of both the stop-band gain and also pass-band gain of all the transfer functions, because also transfer functions with additional and intended zero in transfer function are available. The theoretical presumptions are confirmed by both simulations and lab measurements with available devices. DOI: http://dx.doi.org/10.5755/j01.eie.22.6.17221


A. Reconfigurability of the Transfer Function
Possibility of modification or fine adjusting of the transfer function of an analogue circuit is always a very important requirement in the signal processing domain [1].Reconfigurability is a very useful feature of the analogue filters since it represents the possibility of very fast change of the type of the frequency response.However, manual galvanic reconnection is usually necessary in order to change the type of the transfer response in standard multifunctional solutions.Unfortunately, manual reconnection is not possible or easily accessible in many cases (e.g. in case of on-chip implementation).Many recent scientific works [2]- [7] solve the problem by the filters referred to as multifunction.These filters have several transfer functions available, but between different nodes of the network.These circuits are referred to as a single input -multiple output (SIMO) [8] or a multiple input -single output (MISO) [9].Required change of the filtering function can be realized also by switches -this concept is similar to the SIMO and MISO circuits.However, switching of inputs or outputs is not very favourable and causes additional problems (power consumption, overshoots, interferences of clock signal to analogue path, and area consumption on chip).Additionally, some effects caused by discontinuous regime of switching are undesired.Therefore, a very interesting concept is to use two-port structure without changing internal topology or a position of input or output port, used also in microwave technique, for instance [10].These circuits are referred to as single input -single output (SISO).Our paper focuses on the filtering solution that allows reconnection-less and switch-less control of the type of the transfer function electronically by the parameter(s) of advanced active element and also tuning of the stop-band and/or pass-band attenuation.
Many papers present the filters referred to as reconfigurable [11], [12] but in point-of-view of adjustability of bandwidth or quality factor (in the case of band-pass response).From our point of view, reconfigurable filter [13], [14] represents the type of transfer function where reconfigurability is available without any reconnection in the structure.

B. Active Elements
Many advanced active elements have been reported in recent works.A detailed summarization is available in [15].However only active elements with the electronically adjustable parameter(s) are interesting for purposes of reconfigurable filters.We focus our attention on adjustable current amplifiers [15]- [17], operational transconductance amplifiers (OTAs) [15], [18] and current conveyors (CC) [15], [19] because of their useful features, wide availability and easy mutual interconnection.
Several other active elements were derived from these fundamental active elements, usually by complementing two active elements into one structure with particular features.
The typical examples are numerous modifications of the current differencing transconductance amplifier (CDTA) [15], [20]- [22].Several more complex active elements, based on OTA section and CC of the second generation (CCII) have been also proposed.For example, current conveyor transconductance amplifier (CCTA) [15]- [23] utilizes independent Rx and gm control in some of its variants [24].Modification of CCTA in [10] employs current gain control.Controllable current gain in frame of CCII seems to be a valuable advantage [25], [26].This active element is usually referred to as ECCII (Current Conveyor of the second generation with electronically adjustable gain between X and Z terminal).Another interesting active element is Voltage Differencing Current Conveyor (VDCC) [15], [27]- [29].Also simple current followers (CF) and voltage buffers (VB) or their variations are useful.

C. Comparison with other SISO Solutions in Literature
Several solutions of reconnection-less and reconfigurable filters of SISO type have been published in open literature [30]- [38]. 1 st -order filters are summarized in Table I, 2ndorder filters in Table II.Note that the solution presented in this paper is of the 2 nd order and therefore it is included in Table II in order to provide a comparison.Our solution consists of only two active elements (it is not so common), operates in the current mode (none of already published 2nd-order filters) and it provides LP, HP, LPZ, HPZ and BS functions.Its features were verified also by lab measurement.Note that its pass-band gain is tunable independently of the stop-band gain.None of the previously reported filters provides this combination of the features.

II. DEFINITION OF ACTIVE ELEMENTS
The Dual Output Current Amplifier (DO-CA) with two independent gains is the first active element with schematic symbol depicted in Fig. 1, together with a description of internal topology.Behaviour of DO-CA is as follows Direction of all voltages and currents and meaning of variables from (1) is obvious from Fig. 1.The Voltage Differencing Current Conveyor (VDCC) is the second type of active element that is present in the designed filter.It is well-known active element consisting of OTA and CCII as is obvious from Fig. 2.
All voltages, currents and variables from Fig. 2 are again included in the matrix

III. DESIGNED RECONNECTION-LESS RECONFIGURABLE FILTER
The designed reconnection-less reconfigurable filter of the SISO type is depicted in Fig. 3.It consists only of two active elements, two capacitors and one resistor. where From ( 3) and ( 4) it is obvious that pole frequency and quality factor are described by: The following transfer functions are obtained by controlling of adjustable current gains (B1, B2): Note that B2 < 0 and/or B1 < 0 can be obtained with help of current mode multiplier, but this concept was not used in this paper.Moreover, if gm = G is varied, pole frequency is controlled without disturbing quality factor value (Q).Note that if only one additional current amplifier (with gain equal to B3) is connected between Z1and node with C2 capacitor, Q can be also controlled independently with respect to the pole frequency as obvious from the following equation.Denominator (3) changes to  ( ) , where n11 represents non-ideal current transfer from X terminal to Z1-(theoretically equal to -1) and n12 represents non-ideal current transfer from X terminal to Z2+ (theoretically equal to 1).It is an easy task to calculate nonideal fp and Q from (8) (therefore it is omitted in this paper).If n11 and/or n12 are not unity (in absolute value), it has observable impact only on pass-band gain of transfer functions (LP, LPZ and BS).Note that this can be compensated by tuning of B1 gain in opposite direction, therefore it represents no problem in practice.
Another non-ideality that should be taken into account is that current and voltage gains in the terminal relationships of the active elements may not be valid at high frequencies due to the non-idealities of active components.In order to observe impact of these non-idealities, gm, B1, B2, n11 and n12 were considered as frequency dependent, i.e. gm(s), B1(s), B2(s), n11(s) and n12(s) where x should be replaced by gm, B1, B2, n11 and n12 and X(s) by gm(s), B1(s), B2(s), n11(s) and n12(s).Further, τx = 1/ω0, where ω0 stands for angular frequency forming the pole of the first-order function.A detailed analysis in Maple confirmed a well-known fact that in order to operate according to the theory up to frequency of, for instance, 10 MHz, f0 = ω0/2π should be at least 100 MHz (10 times higher).
Relative sensitivities of the important parameters of this filter (ωp and Q) on its parameters can be obtained by routine calculations from (6) and are low because none of them overcome ±0.5.

V. SIMULATION AND MEASUREMENT RESULTS
A filter from Fig. 3 was prepared to be measured.DO-CA active element was implemented by part of the UCC-N1B circuit [39] (forming DO-CF part from Fig. 1 Implementation of current amplifier by EL2082 circuit limits possible range of current gain (B1 or B2) adjusting.As obvious from [40], current gain of EL2082 is adjusted by external DC voltage (VG) and only 0 ≤ VG < 5 V is allowed.For range starting from 0 up to 2.5, current gain is approximately equal to control voltage in its numerical value (B ≈ VG).
In order to suppress the expected impact of parasitic capacitances in nodes of the circuit on printed-circuit board (PCB), the values of working capacitors were decreased to C1 = 470 pF, C2 = 235 pF.
The results for pure LP configuration (B1 = 1, B2 = 0) are depicted in Fig. 4 for three different pole frequencies.At frequencies above 10 MHz, the measured results are damaged by UCC-s features that have very limited operating bandwidth and are not designed to be operated at such high frequencies.However, the overall results are satisfactory in order to prove the concept.The results for pure HP configuration (B1 = 0, B2 = 1) and pure BS configuration (B1 = 1, B2 = 1) are depicted in Fig. 5 and Fig. 6 respectively.Real measured pole frequencies are only slightly different than was expected from simulation in all three cases, as summarized in Table III.Figure 7 and Fig. 8 provide the results for pass-band gain tuning in case of both LP and HP filters respectively.Passband gain is directly proportional to the B gain as expected from (3) and obtained gains are summarized in Table IV.It is obvious from the graphs that when B is tuned from 0 to 1 (B2 in case of LP and B1 in case of HP), stop-band attenuation decreases (gain grows) and when B1 = B2 = 1, both functions change into BS.If B = 0.001 (B2 in case of LP and B1 in case of HP), stop-band gain should be theoretically −60 dB (K = 20•log100.001= −60 dB), however it is not possible to achieve because real implementation of filter on PCB using the above mentioned active elements is limited by −50 dB.

VI. CONCLUSIONS
The designed reconnection-less reconfigurable filter providing LP, HP, LPZ, HPZ and BS transfer function without any change or switching in the topology was presented.Its measured features are influenced by real parameters of the active elements that were used.Also real PCB and its design has direct impact on the measured characteristics.In our case, the highest attenuation was limited to 50 dB and the results are in good agreement with theory up to frequency of 10 MHz, tuning range was from 115 kHz to 959 kHz (in case of BS response).Nevertheless, we consider these results as very good.Of course, the test with real devices (UCC and EL2082) could be substituted or supplemented by the simulations with CMOS transistor structures.Behavioural modelling (as it was used and presented in this paper) is a very useful way how to verify the design.If the filter prepared with help of universal active elements, employed as a part of the behavioural model, works well, possible non-universal transistor structure would have much better features.

Fig. 4 .Fig. 5 .Fig. 6 .
Fig. 4. Overall measurement results for LP response with unity pass-band gain while tuning pole frequency in comparison with simulations.

1 Fig. 7 . 1 Fig. 8 .
Fig. 7. Overall measurement results for LP response with fP_THEOR = 919 kHz and while tuning pass-band gain by B1 in comparison with simulations.

TABLE III .
COMPARISON OF OBTAINED VALUES IN THE CASE OF INDEPENDENT TUNING OF THE POLE FREQUENCY (FIG.4, FIG. 5, FIG. 6).