An MOS-C Multifunction Filter Employing DXCCTA for High-Frequency Operation

Abstract

This article introduces a biquad multifunction filter using an advanced current-mode building block termed as “Dual X Current Conveyor Transconductance Amplifier (DXCCTA)’’ which is a combination of dual X second generation Current Conveyor (DXCCII) followed by Operational Transconductance Amplifier (OTA). Single Input Multiple Output (SIMO) characteristics of the multifunction filter produce the filter responses and come with a single DXCCTA block with few grounded capacitors along with MOS-based resistors. All high-frequency responses of biquad multifunction filters are verified using CMOS model of DXCCTA as well as experimental verification using off the shelf ICs AD844 as “Current Feedback Operational Amplifier” and CA3080 as “Operational Transconductance Amplifier”.

1 Introduction

An advance active block dominance in the current scenario is now considered as an important active device in microelectronics engineering which gives a suitable platform for the generation of signal processing circuits viz. active filters [1,2,3,4,5,6,7,8,9,10,11,12,13], oscillators [14,15,16], Schmitt trigger [17, 18], chaotic circuits [19, 20], active inductor design [21] and many more. Initially, voltage-mode op-amp has the major contribution for almost every electronic circuits but after the emergence of current-mode circuits [22] became a new trend for the design of active mode circuitry with low power dissipation, greater linearity, inbuilt tunability, wide bandwidth, higher frequency of operation and few others [23]. Some very popular advance active blocks are CCII [1, 4], CCCII [10], OTRA [24], FTFN [7, 13], CDTA [8], VDCC [9], DVCC [3, 12], CCTA [5], DDCCTA [25], DVCCTA [26], DXCCTA [27], FTFNTA [28] and few other. A wide array of second-order filters is available and can be treated as the fundamental filter circuitry in the analog domain. Moreover, literature is also enriched with different input–output combination filter as with SIMO [1,2,3], MISO [4,5,6,7,8,9] and MIMO [10,11,12]. In the case of multifunction filter, SIMO operation plays a significant role due to single input source which causes attractive design procedure without the selection of various input sources as in the case of MIMO and MISO. An intensive study of literature [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] have the following characteristics:

• 1. Excess number of active block elements [1, 2, 5, 6, 11]

• 2. More input signal to realize output filter [7,8,9]

• 3. Absence of electronic tenability [1, 24]

• 4. Low cut off frequency response [1, 4, 8, 24]

• 5. Component mismatch and circuit topology to get different responses [1, 5,6,7,8,9]

• 6. Necessary to use external passive components for measurement of different filter responses in current-mode topology [27].

This research paper brings a SIMO filter topology for the multifunction filter responses viz. Low pass (LP), Band Pass (BP) and High Pass (HP) filter by utilizing active MOS resistors and grounded capacitors with single active block DXCCTA. The proposed design is suitable for a very high-frequency operation up to 200 MHz. The examination of the frequency test of the multifunction filter is well executed through PSPICE simulation. An experimental test of the filter is also examined by using the ICAD844 and CA3080 to construct the DXCCTA for filter operation.

2 Circuit Description

A DXCCTA active block comprises a combination of DXCCII and an OTA. The schematic of DXCCTA and its internal MOS-based design is shown in Fig. 1, where the port characteristics can be mathematically defined as:

Fig. 1

DXCCTA a Schematic symbol, b internal CMOS circuit

$$I_{Y} = 0,I_{X \pm } = I_{Z \pm } ,V_{X \pm } = \pm V_{Y} ,I_{O \pm } = \pm g_{m} V_{{{\text{Z}}^{ - } }}$$

(1)

where g_m corresponds transconductance of DXCCTA and expressed as:

$$g_{m} = \sqrt {\mu_{n} C_{OX} \frac{W}{L}I_{\text{B}} }$$

(2)

The term µ_n, C_OX and W/L are the conventional parameters of a MOSFET and I_B be the input bias current.

A simple filter of the proposed SIMO filter is shown in Fig. 2. Where Z₁, Z₂ and Z₃ represent the impedance term. Z₁ and Z₃ be the parallel combination of the active MOS resistor and capacitor and Z₂ be an active MOS resistor.

Fig. 2

Proposed MOS-C current-mode multifunction filter

$$\left. \begin{aligned} Z_{1} & = R_{{{\text{MOS}}1}} \left\| {\frac{1}{{sC_{1} }}} \right. = \frac{{R_{{{\text{MOS}}1}} }}{{1 + sC_{1} R_{{{\text{MOS}}1}} }} \\ Z_{2} & = R_{{{\text{MOS}}2}} \\ Z_{3} & = R_{{{\text{MOS}}3}} \left\| {\frac{1}{{sC_{3} }}} \right. = \frac{{R_{{{\text{MOS}}3}} }}{{1 + sC_{3} R_{{{\text{MOS}}3}} }} \\ \end{aligned} \right\}$$

(3)

The MOS resistor exhibits a numerical resistance value in the saturation region as:

$$R_{\text{MOS}} = \frac{1}{{2\mu_{n} C_{OX} \left( {\frac{W}{L}} \right)(V_{\text{GS}} - V_{\text{Th}} )}}$$

(4)

A simple routine analysis gives the transfer functions for LP, BP and HP as:

$$T_{\text{LP}} \left( s \right) = \frac{{I_{\text{LP}} }}{{I_{\text{IN}} }} = \frac{{\frac{{g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}}{{s^{2} + \frac{{g_{m} }}{{R_{{{\text{MOS}}2}} C_{3} }}s + \frac{{g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}}$$

(5)

$$T_{\text{BP}} \left( s \right) = \frac{{I_{\text{BP}} }}{{I_{\text{IN}} }} = \frac{{\frac{{g_{m} }}{{R_{{{\text{MOS}}2}} C_{3} }}s}}{{s^{2} + \frac{{g_{m} }}{{R_{{{\text{MOS}}2}} C_{3} }}s + \frac{{g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}}$$

(6)

$$T_{\text{HP}} \left( s \right) = \frac{{I_{\text{HP}} }}{{I_{\text{IN}} }} = \frac{{s^{2} }}{{s^{2} + \frac{{g_{m} }}{{R_{{{\text{MOS}}2}} C_{3} }}s + \frac{{g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}}$$

(7)

The above equations of the filter function give the pole frequency ($\omega_{0}$) and quality factor (Q₀) as:

$$\omega_{0} = \sqrt {\frac{{g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}$$

(8)

$$Q_{0} = \sqrt {\frac{{R_{{{\text{MOS}}2}} C_{3} }}{{g_{m} R_{{{\text{MOS}}1}} R_{{{\text{MOS}}3}} C_{1} }}}$$

(9)

Here, the performance of ($\omega_{0}$) and (Q₀) can be electronically tunable with a bias current that tune g_m and bias voltage for MOS resistors.

3 Non-Ideal Study

To study the non-ideal analysis, we have examined the transfer function using non-ideal characteristic of DXCCTA. In non-ideal characteristic condition, DXCCTA port relation is express as [27]

$$I_{Y} = 0,I_{X \pm } = \alpha I_{Z \pm } ,V_{X} = \pm \beta V_{Y} ,I_{O \pm } = \pm \gamma g_{m} V_{{Z^{ - } }} ;$$

(10)

where (α, β and $\gamma$) be the current transfer gain, non-ideal voltage-transfer gains and transconductance inaccuracies present in the DXCCTA, respectively. By using non-ideal parameters (α, β and $\gamma$), the current-mode LP, BP and HP transfer function of the multifunction filters are observed as:

$$\left. {T_{\text{LP}} \left( s \right)} \right|_{\alpha ,\beta ,\gamma } = \left. {\frac{{I_{\text{LP}} }}{{I_{\text{IN}} }}} \right|_{\alpha ,\beta ,\gamma } = \frac{{\frac{{\alpha \beta \gamma g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}}{{s^{2} + \frac{{\gamma g_{m} }}{{R_{{{\text{MOS}}2}} C_{3} }}s + \frac{{\alpha \beta \gamma g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}}$$

(11)

$$\left. {T_{\text{BP}} \left( s \right)} \right|_{\alpha ,\beta ,\gamma } = \left. {\frac{{I_{\text{BP}} }}{{I_{\text{IN}} }}} \right|_{\alpha ,\beta ,\gamma } = \frac{{\frac{{\alpha \gamma g_{m} }}{{R_{{{\text{MOS}}2}} C_{3} }}s}}{{s^{2} + \frac{{\gamma g_{m} }}{{R_{{{\text{MOS}}2}} C_{3} }}s + \frac{{\alpha \beta \gamma g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}}$$

(12)

$$\left. {T_{\text{HP}} \left( s \right)} \right|_{\alpha ,\beta ,\gamma } = \left. {\frac{{I_{\text{HP}} }}{{I_{\text{IN}} }}} \right|_{\alpha ,\beta ,\gamma } = \frac{{\alpha s^{2} }}{{s^{2} + \frac{{\gamma g_{m} }}{{R_{{{\text{MOS}}2}} C_{3} }}s + \frac{{\alpha \beta \gamma g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}}$$

(13)

In this case, ($\omega_{0}$) and (Q₀) becomes

$$\left. {\omega_{0} } \right|_{\alpha ,\beta ,\gamma } = \sqrt {\frac{{\alpha \beta \gamma g_{m} }}{{R_{{{\text{MOS}}1}} R_{{{\text{MOS}}2}} R_{{{\text{MOS}}3}} C_{1} C_{3} }}}$$

(14)

$$\left. {Q_{0} } \right|_{\alpha ,\beta ,\gamma } = \sqrt {\frac{{\alpha \beta \gamma R_{{{\text{MOS}}2}} C_{3} }}{{\gamma g_{m} R_{{{\text{MOS}}1}} R_{{{\text{MOS}}3}} C_{1} }}}$$

(15)

The influence of non-ideal parameter is reflected in ($\omega_{0}$) and (Q₀). Moreover, the active and passive sensitivity of ($\omega_{0}$) and (Q₀) are observed as:

$$\left. \begin{aligned} S_{{\alpha ,\beta ,\gamma ,g_{m} }}^{{\omega_{0} }} & = \frac{1}{2},S_{{R_{{{\text{MOS}}1}} ,R_{{{\text{MOS}}2}} ,R_{{{\text{MOS}}3}} ,C_{1} ,C_{3} }}^{{\omega_{0} }} = - \frac{1}{2} \\ S_{{\alpha ,\beta ,R_{{{\text{MOS}}2}} ,C_{3} }}^{{Q_{0} }} & = \frac{1}{2},S_{{g_{m} ,R_{{{\text{MOS}}1}} ,R_{{{\text{MOS}}3}} ,C_{1} }}^{{Q_{0} }} = - \frac{1}{2},S_{\gamma }^{{Q_{0} }} = 0 \\ \end{aligned} \right\}$$

(16)

The sensitivity analysis (16) shows a low value that corresponds to good performances for filter design.

4 Simulation Results

To confirm the theoretical analysis, both simulation and experimental tests are performed for a multifunction filter. The first section of validation is done through PSPICE simulation in which DXCCTA is integrated with 0.18 µm CMOS TSMC parameters with supply voltage ±1.25 V and bias voltage 0.43 V.

Multifunction filter frequency response for LP, BP and HP is observed for a very high frequency in the range of 100 MHz. The active resistor have 1 KΩ reactance value and traditional capacitance with 1 pF exhibits $\omega_{0}$ of 177 MHz with a response in Fig. 3. The filter frequency response of BP filter is below 0 dB which can be improved by varying the bias current I_B values which gives freedom for independent gain control behaviour. The gain variation with different I_B values is well observed in Fig. 4 for the BP filter. Also, an experimental test for DXCCTA blocks is realized with CFOA (ICAD844) and OTA (CA3080) as shown in Fig. 5.

Fig. 3

Proposed CM-MF frequency response

Fig. 4

Gain variation in BP with different bias current I_O

Fig. 5

DXCCTA using ICAD844 and CA3080 for experimental test. a Circuit diagram, b physical experiment set up

A time-domain verification for filter is performed for $\omega_{0}$ 100 MHz by selecting the components values for the LP filter as $R_{{{\text{MOS}}1}} = R_{{{\text{MOS}}2}} = R_{{{\text{MOS}}3}}$ = 2 KΩ and $C_{1} = C_{2} = 1\,{\text{pF}}$. As we have designed for 100 MHz cut off frequency, the filter output can pass the input signal which is less than 100 MHz frequency in LP filter. Figure 6 shows the experimental result of a LP transient response for 50 MHz input supply. For LP filter the input and output waveform will be in phase as shown in Fig. 6.

Fig. 6

Experimental LP transient response for 50 MHz input

5 Conclusion

This article brings a high-frequency second-order filter using MOS resistors and capacitors. The behaviour of the proposed design is simulated with the PSPICE simulation by utilizing TSMC 0.18 µm technology and experimentally performed using off the shelf ICs. The influence of non-ideal behaviour is also observed. The results follow a close agreement with the theoretical prediction. Some useful characteristics of the proposed filter are as follows:

• 1. Use of single DXCCTA.

• 2. With less passive components.

• 3. High-frequency response in 100 MHz.

• 4. Provides electronic tunability by using bias current.

• 5. No need to disturb the input signal for different output responses.

• 6. Suitable for LP, BP and HP filters.