Research Article  Open Access
Operational Simulation of LC Ladder Filter Using VDTA
Abstract
In this paper, a systematic approach for implementing operational simulation of LC ladder filter using voltage differencing transconductance amplifier is presented. The proposed filter structure uses only grounded capacitor and possesses electronic tunability. PSPICE simulation using 180 nm CMOS technology parameter is carried out to verify the functionality of the presented approach. Experimental verification is also performed through commercially available IC LM13700/NS. Simulations and experimental results are found to be in close agreement with theoretical predictions.
1. Introduction
Current mode approach has received a considerable attention in the last few years for analog signal processing applications due to their low power consumption, large dynamic range, higher frequency ranges of operation, better accuracy, higher slew rate, and less complexity. As a result, a large number of current mode active elements such as operational transconductance amplifier (OTA), current conveyor (CC), current controlled conveyor (CCC), current feedback amplifier (CFOA), operational transresistance amplifier (OTRA), differential voltage current conveyor (DVCC), current differencing buffered amplifier (CDBA), current differencing transconductance amplifier (CDTA), and voltage differencing transconductance amplifier (VDTA) are published. A literature review of such analog active block is presented in [1, 2]. The VDTA is a recently proposed analog building block composed of two transconductance amplifiers and may be used to implement different analog processing application such as floating and grounded inductor simulation [3, 4], analog filter [5–10], and oscillators [11–13].
For the active simulation of higherorder LC ladder filter, mainly three methods exist, which are wave active method, topological simulation, and operational simulation. In wave active approach, a wave equivalent is developed for inductor in series branch and then it is configured for other passive components by making suitable connection [14–21]. Large numbers of active blocks are used in this approach. In the second method, topological simulation or element replacement method, the inductor of LC ladder structure is replaced by appropriate configured active elements [22, 23]. The drawback of this configuration is that a floating capacitor is generally required and this degrades the performance of the derived filter topology in high frequency application. In the third approach, operational simulation or leapfrog method [23–30], simulation is carried out for the operation of ladder rather than its component.
Literature survey reveals the operational simulation of ladder filter using operational amplifier (OA) and current controlled conveyor (CCCII) [24], OTA [25, 26], CC [27], multiple output second generation current controlled conveyor (MOCCCII) [28], current feedback amplifier (CFA) [29], and CFOA [30]. This paper presents a systematic approach for operational simulation of LC ladder filter using voltage differencing transconductance amplifier (VDTA). The proposed operational simulation of LC ladder using VDTA has the following advantage over existing circuits:(i)Lesser numbers of active blocks are used as compared to [24, 26, 28–30].(ii)There is no use of resistors in realization, while [25, 29, 30] use both floating and grounded resistors and [27] uses only grounded resistors.(iii)Only grounded capacitors are used in proposed implementation, while [25, 29] use floating capacitors too.(iv)Proposed operational simulation of LC ladder also possesses electronic tunability of cutoff frequency, while [27, 29, 30] do not.
As an example, a fourthorder Butterworth low pass filter is simulated by outlined approach and the workability of the filter is confirmed through PSPICE simulation using 180 nm CMOS technology parameter. The functionality of the ladder filter is also tested experimentally through IC LM13700/NS.
2. VDTA
The voltage differencing transconductance amplifier is consisting of two transconductance amplifiers [5]. Figures 1 and 2 represent the symbolic representation and CMOS implementation of VDTA.
The port relationship of VDTA in matrix form is characterized by the following equation:where and are the input and output transconductance gain of VDTA. The input transconductance amplifier converts the input voltage difference () into current at terminal and the voltage developed at terminal is converted into current at and terminal by output transconductance amplifier. In this paper, VDTA is used as an active analog building block because of(i)the simple CMOS implementation of VDTA,(ii)presence of two transconductance amplifiers giving resistorless realization,(iii)the transconductance gain of VDTA which can vary via bias current, therefore providing the electronic tunability to designed filter.
3. Operational Simulation Using VDTA
The operational simulation method takes a different approach from topological simulation or wave active method, as it simulates the operation of ladder rather than its component [23]. The circuit equations and voltagecurrent relationship of each element are written using KVL and KCL. Then these equations are represented by block diagrams or signal flow graph. Each block represents some analog operation such as summation, integration, and subtraction. The final circuit is obtained by properly combining these blocks.
To explain the above statement, a fourthorder low pass Butterworth filter of Figure 3 has been taken as a prototype. The transfer function of this prototype filter can be expressed asTo develop operational simulation in a systematic manner, consider the general ladder of Figure 4, where the series branch elements are labelled by admittance and the shunt branch elements are labelled by impedance . The ladder of Figure 4 can be described by the voltage and current equation as in (3a), (3b), (3c), and (3d) as follows:whereBoth voltage and current terms are present in (3a), (3b), (3c), and (3d). This problem can be easily resolved by scaling these equations by a resistor . where ; .
The subscript with voltages represents the fact that this voltage is derived from a current in the circuit.
Realization of (5a) to (5d) gives the operational simulation of prototype ladder filter of Figure 3. Implementation of (5a) and (5d) requires lossy integrator, while implementation of (5b) and (5c) requires lossless integrator. The lossy and lossless integrator can be easily realized using VDTA as discussed in the following section.
3.1. Lossy Integration
The implementation of lossy integration using VDTA is shown in Figure 5. The expression for output voltage of lossy integrator can be written aswhere
3.2. Lossless Integrator
Lossless integrator can be implemented using VDTA as shown in Figure 6 and its output voltage expression isAgain
3.3. Complete Realization Using VDTA
With the help of lossy and lossless integrator of Figures 5 and 6, the complete realization of prototype 4thorder filter using operational simulation approach is shown in Figure 7.
The value of capacitor used in VDTA 1 and VDTA 4 can be calculated by comparing (6a) and (6b) with (5a) and (5d) as follows.
From (6a) and (6b) and (5a),And .
Take the value of scaling resistorThenAnd from (6a) and (6b) and (5d)Similarly, the value of capacitor used in VDTA 2 and VDTA 3 can be calculated by comparing (7a) and (7b) with (5b) and (5c) as follows.
From (7a) and (7b) and (5b),And from (7a) and (7b) and (5c),
4. Simulation
The normalized component values of the prototype filter of Figure 3 are , , , , , and . The aspect ratio of various transistor used in CMOS implementation of VDTA is given in Table 1. The values of supply voltage and bias current for VDTA are V and I_{B1} = I_{B2} = I_{B3} = I_{B4} = 150 μA ( μS), respectively.

For cutoff frequency of 5 MHz, the values of capacitor used in Figure 7 can be calculated by (10), (12), (13), and (14) as pF, pF, pF, and pF. Figure 8 shows the frequency response of the low pass fourthorder Butterworth filter. The simulated cutoff frequency is 4.99 MHz, which is very close to the theoretical cutoff frequency of 5 MHz. The electronic tunability of the filter through simulation is demonstrated in Figure 9 by varying bias current from 25 μA to 250 μA. Time domain analysis is studied by applying two signals of frequency 500 KHz and 20 MHz and of magnitude 50 mV at input. The transient response and its spectrum are shown in Figures 10 and 11, respectively. The proposed filter structure is also tested for total harmonic distortion at output and it is found that it is within acceptable limit of 3% up to 600 mV pp signal of frequency 1 MHz as shown in Figure 12.
(a)
(b)
Noise analysis is also carried out for the proposed circuit by determining noise at output of the filter through simulation. The output noise variation within pass band frequencies is depicted in Figure 13 which shows that noise is in acceptable limit of nanovolt range. To examine effect of temperature variation on proposed filter circuit, the circuit is simulated at five different temperatures, 10°C, 25°C, 27°C, 50°C, and 100°C, and the results are depicted in Figure 14. The values of cutoff frequency for these temperatures are listed in Table 2. It is observed that cutoff frequency shifts towards lower frequencies as temperature decreases. This is due to the fact that the transconductance decreases with increases in temperature due to decrease in mobility. This shifting in cutoff frequency can be compensated through bias current variation from 104 μA (for f_{0} = 4.17 MHz at 100°C) to 164 μA (for f_{0} = 5.2 MHz at 10°C).

All the key parameters of the proposed filter structure are summarized in Table 3. The total power dissipated and output noise in simulation of the prototype filter are 2.16 mW and 5.7 × 10^{−9} V/Hz^{1/2}, while simulated values of these parameters for the VDTA implementation of the sameorder filter using wave active method are 6.48 mW and 1.65 × 10^{−8} V/Hz^{1/2} [20].

Experimental verification is carried out for proposed circuit through commercially available IC LM13700/NS. The VDTA implementation using IC LM13700/NS is shown in Figure 15. The circuit of Figure 7 is breadboarded as shown in Figure 16 for experimental testing. Supply voltage of ±15 V is used. The bias current of 1.35 mA is set to obtain the transconductance of 24.89 mA/V. The capacitor values are selected as = C_{v4} = 10 nF and = C_{v3} = 25 nF for cutoff frequency of 303 kHz. The measured magnitude response along with simulated response is depicted in Figure 17. The experimental cutoff frequency is observed to be 292 kHz.
5. Conclusion
The paper presents a systematic methodology for active implementation of operational simulation of LC ladder filter. To explain the outlined approach, a 4thorder Butterworth filter is taken as prototype, and, for active implementation, VDTA is used as an analog building block. The proposed implementation is resistorless and uses only grounded capacitors, which is suitable for IC implementation. The proposed structure also possesses electronic tunability of cutoff frequency. Workability of the proposed implementation is verified through PSPICE simulation using 180 nm TSMC technology parameters. The functionality of proposed LC ladder is also verified experimentally through IC LM13700/NS.
Competing Interests
The authors declare that they have no competing interests.
References
 K. K. Abdalla, D. R. Bhaskar, and R. Senani, “A review of the evolution of currentmode circuits and techniques and various modern analog circuit building blocks,” Nature and Science, vol. 10, no. 10, 2012. View at: Google Scholar
 D. Biolek, R. Senani, V. Biolkova, and Z. Kolka, “Active elements for analog signal processing: classification, review, and new proposals,” Radioengineering, vol. 17, no. 4, pp. 15–32, 2008. View at: Google Scholar
 D. Prasad and D. R. Bhaskar, “Grounded and floating inductance simulation circuits using VDTAs,” Circuits and Systems, vol. 3, no. 4, pp. 342–347, 2012. View at: Publisher Site  Google Scholar
 W. Tangsrirat and S. Unhavanich, “Voltage differencing transconductance amplifierbased floating simulators with a single grounded capacitor,” Indian Journal of Pure and Applied Physics, vol. 52, no. 6, pp. 423–428, 2014. View at: Google Scholar
 A. Yeşil, F. Kaçar, and H. Kuntman, “New simple CMOS realization of voltage differencing transconductance amplifier and its RF filter application,” Radioengineering, vol. 20, no. 3, pp. 632–637, 2011. View at: Google Scholar
 A. Yeşil and F. Kaçar, “Electronically tunable resistorless mixed mode biquad filters,” Radioengineering, vol. 22, no. 4, pp. 1016–1025, 2013. View at: Google Scholar
 J. Satansup and W. Tangsrirat, “Compact VDTAbased currentmode electronically tunable universal filters using grounded capacitors,” Microelectronics Journal, vol. 45, no. 6, pp. 613–618, 2014. View at: Publisher Site  Google Scholar
 D. Prasadl, D. R. Bhaskar, and M. Srivastava, “Universal voltagemode biquad filter using voltage differencing transconductance amplifier,” Indian Journal of Pure and Applied Physics, vol. 51, no. 12, pp. 864–868, 2013. View at: Google Scholar
 J. Satansup, T. Pukkalanun, and W. Tangsrirat, “Electronically tunable currentmode universal filter using VDTAs and grounded capacitors,” in Proceedings of the International MultiConference of Engineers and Computer Scientists (IMECS '13), pp. 647–650, Hong Kong, China, March 2013. View at: Google Scholar
 A. Uygur and H. Kuntman, “DTMOSbased 0.4V ultra lowvoltage lowpower VDTA design and its application to EEG data processing,” Radioengineering, vol. 22, no. 2, pp. 458–466, 2013. View at: Google Scholar
 D. Prasad, M. Srivastava, and D. R. Bhaskar, “Electronically controllable fullyuncoupled explicit currentmode quadrature oscillator using VDTAs and grounded capacitors,” Circuits and Systems, vol. 4, no. 2, pp. 169–172, 2013. View at: Publisher Site  Google Scholar
 D. Prasad and D. R. Bhaskar, “Electronically Controllable Explicit Current Output Sinusoidal Oscillator Employing Single VDTA,” ISRN Electronics, vol. 2012, Article ID 382560, 5 pages, 2012. View at: Publisher Site  Google Scholar
 R. Sotner, J. Jerabek, N. Herencsar, J. Petrzela, K. Vrba, and Z. Kincl, “Linearly tunable quadrature oscillator derived from LC Colpitts structure using voltage differencing transconductance amplifier and adjustable current amplifier,” Analog Integrated Circuits and Signal Processing, vol. 81, no. 1, pp. 121–136, 2014. View at: Publisher Site  Google Scholar
 I. Haritantis, A. Constantinides, and T. Deliyannis, “Wave active filter,” Proceedings of the Institution of Electrical Engineers, vol. 123, no. 7, pp. 676–682, 1976. View at: Publisher Site  Google Scholar
 K. Georgia and P. Costas, “Modular filter structures using CFOA,” Radio Engineering, vol. 19, no. 4, pp. 662–666, 2010. View at: Google Scholar
 N. Pandey and P. Kumar, “Realization of resistorless wave active filter using differential voltage current controlled conveyor transconductance amplifier,” Radioengineering, vol. 20, no. 4, pp. 911–916, 2011. View at: Google Scholar
 N. Pandey, P. Kumar, and J. Choudhary, “Current controlled differential difference current conveyor transconductance amplifier and its application as wave active filter,” ISRN Electronics, vol. 2013, Article ID 968749, 11 pages, 2013. View at: Publisher Site  Google Scholar
 M. Bothra, R. Pandey, N. Pandey, and S. K. Paul, “Operational transresistance amplifier based tunable wave active filter,” Radioengineering, vol. 22, no. 1, pp. 159–166, 2013. View at: Google Scholar
 H. Singh, K. Arora, and D. Prasad, “VDTAbased wave active filter,” Circuits and Systems, vol. 5, no. 5, pp. 124–131, 2014. View at: Publisher Site  Google Scholar
 N. Pandey, P. Kumar, and S. K. Paul, “Voltage differencing transconductance amplifier based resistorless and electronically tunable wave active filter,” Analog Integrated Circuits and Signal Processing, vol. 84, no. 1, pp. 107–117, 2015. View at: Publisher Site  Google Scholar
 H. Wupper and K. Meerkotter, “New active filter synthesis based on scattering parameters,” IEEE Transaction on Circuit and System, vol. 22, no. 7, pp. 594–602, 1975. View at: Publisher Site  Google Scholar
 A. A. M. Shkir, “10kHz, lpw power, 8th order eliptic band—pass filter employing CMOS VDTA,” International Journal of Enhanced Research in Science Technology & Engineering, vol. 4, no. 1, pp. 162–168, 2015. View at: Google Scholar
 M. E. Van Valkenburg and R. Shaumann, Design of Analog Filters, Oxford University Press, Oxford, UK, 2001.
 Y. Xi and H. Peng, “Realization of lowpass and bandpass leapfrog filters using OAs and CCCIIs,” in Proceedings of the International Conference on Management and Service Science (MASS '09), Wuhan, China, September 2009. View at: Publisher Site  Google Scholar
 M. V. Katageri, M. M. Mutsaddi, and R. S. Mathad, “Comparative study of LC ladder active filter using OTA and current conveyor,” International Journal of Advanced Computer and Mathematical Sciences, vol. 3, no. 3, pp. 321–325, 2012. View at: Google Scholar
 R. Schaumann, “Simulating lossless ladders with transconductanceC circuits,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 45, no. 3, pp. 407–410, 1998. View at: Publisher Site  Google Scholar
 V. Novotny and K. Vrba, “LC ladder filter emulation by structures with current conveyor,” in Proceedings of the 4th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision (ISCGAV '04), Tenerife, Spain, December 2004. View at: Google Scholar
 A. Câmpeanu and J. Gal, “LCladder filters emulated by circuits with current controlled conveyors and grounded capacitors,” in Proceedings of the International Symposium On Signals, Circuits and Systems (ISSCS '07), vol. 2, Iași, Romania, July 2007. View at: Publisher Site  Google Scholar
 T. S. Rathore and U. P. Khot, “CFAbased groundedcapacitor operational simulation of ladder filters,” International Journal of Circuit Theory and Applications, vol. 36, no. 56, pp. 697–716, 2008. View at: Publisher Site  Google Scholar
 P. K. Sinha, A. Saini, P. Kumar, and S. Mishra, “CFOA based low pass and high pass ladder filter—a new configuration,” Circuits and Systems, vol. 5, no. 12, pp. 293–300, 2014. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2017 Praveen Kumar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.