Third Order Universal Filter Using Single Operational Transresistance Amplifier

Abstract

This paper proposes a multi-input single-output (MISO) third order voltage mode (VM) universal filter using only one operational transresistance amplifier (OTRA). The proposed circuit realizes low-pass, high-pass, all-pass, band-pass, and notch responses from the same topology. The PSPICE Simulation results using 0.5 μm CMOS technology agree well with the theoretical design.

1. Introduction

Operational transresistance amplifier (OTRA) has emerged as an alternate current mode analog building block [1, 2] since it inherits all the advantages offered by other current mode building blocks such as current conveyor (CC) [3–6], operational transconductance amplifier (OTA) [7], current differencing buffered amplifier (CDBA) [8], differential voltage current conveyor (DVCC) [9]. The input terminals of OTRA are internally grounded, thereby eliminating parasitic capacitances at the input. OTRA has the advantages of a high slew rate and wide bandwidth. It is a high-gain current input voltage output device. Some analog filters using OTRA have been reported in [10–16] and references cited there in. It is well known that higher order analog filters using different kinds of active elements are of considerable interest, as they may be used for some special applications where sharp cut off is desirable and at the same time also useful to implement digital filters. Higher order filters can be obtained by various methods such as cascading lower order filter or state variable method or signal flow graph. Although OTRA based third order filters are reported in the literature [17–19], they all involve more that one OTRA.

In this work an attempt is made to propose a third order voltage mode (VM) universal filter employing single OTRA as an active element. All of the five filters, namely lowpass (LPF), highpass (HPF), allpass (APF), bandpass (BPF), notch (NF), can be obtained from the same topology.

2. Circuit Description

The circuit symbol of an OTRA is illustrated in Figure 1. The characteristic equations of this element can be described as 𝑉_𝑝𝑉_𝑛𝑉₀=𝑅000000_𝑚−𝑅_𝑚0𝐼_𝑝𝐼_𝑛𝐼₀. (1) A CMOS-based OTRA using 0.5 μm CMOS technology is given in Figure 2 [2].

Figure 1 

Block diagram of OTRA.

Figure 2 

Internal circuit of OTRA [2].

A generalized 𝑛th order filter topology using single OTRA is shown in Figure 3 [20]. The routine analysis gives a voltage transfer function as 𝑉_out(𝑠)𝑉_in(𝑠)=𝑌_𝑎−𝑌_𝑏𝑌_𝑐−𝑌_𝑑. (2) The proposed third order universal filter is obtained from Figure 3, if one considers 1/𝑌_𝑎=𝑍_𝑎=𝑅_a1‖1/𝑠𝐶_a1‖(𝑅_a2+1/𝑠𝑐_a2), 1/𝑌_𝑏=𝑍_𝑏=1/𝑠𝐶_b1‖(𝑅_𝑏+1/𝑠𝑐_b2), 1/𝑌_𝑐=𝑍_𝑐=𝑅_𝑐‖1/𝑠𝐶_𝑐, 1/𝑌_𝑑=𝑍_𝑑=𝑅_𝑑‖1/𝑠𝐶_𝑑 and splits the 𝑌_𝑎 terminal into three parts and 𝑌_𝑏 terminal into two parts as shown in Figure 4.

Figure 3 

Generalized nth order filter.

Figure 4 

Proposed third order universal filter.

The routine analysis gives output voltage as 𝑉_out=𝑁(𝑠)𝐷(𝑠), (3) where 𝑁(𝑠)=𝑅_𝑐1+𝑠𝐶_𝑑𝑅_𝑑×1+𝑠𝐶_b2𝑅_𝑏1+𝑠𝐶_a2𝑅_a2𝑉₁−𝑠𝐶_a1𝑅_a11+𝑠𝐶_b2𝑅_𝑏1+𝑠𝐶_a2𝑅_a2𝑉₂−𝑠𝐶_a2𝑅_a21+𝑠𝐶_b2𝑅_𝑏𝑉₃−𝑠𝐶_b1𝑅_a11+𝑠𝐶_b2𝑅_𝑏1+𝑠𝐶_a2𝑅_a2𝑉₄−𝑠𝐶_b2𝑅_a11+𝑠𝐶_a2𝑅_𝑐𝑉₅,𝐷(𝑠)=𝑅_a11+𝑠𝐶_b2𝑅_𝑏1+𝑠𝐶_a2𝑅_a2×1+𝑠𝐶_𝑐𝑅_𝑐1+𝑠𝐶_𝑑𝑅_𝑑−𝑠𝐶_𝑑𝑅_𝑐. (4)

If 𝐶_a2𝑅_a2=𝐶_𝑑𝑅_𝑑, then (4) modifies as 𝑁(𝑠)=𝑅_𝑐×1+𝑠𝐶_b2𝑅_𝑏1+𝑠𝐶_a2𝑅_a2𝑉₁−𝑠𝐶_a1𝑅_a11+𝑠𝐶_b2𝑅_𝑏1+𝑠𝐶_a2𝑅_a2𝑉₂−𝑠𝐶_a2𝑅_a21+𝑠𝐶_b2𝑅_𝑏𝑉₃−𝑠𝐶_b1𝑅_a11+𝑠𝐶_b2𝑅_𝑏1+𝑠𝐶_a2𝑅_a2𝑉₄−𝑠𝐶_b2𝑅_a11+𝑠𝐶_a2𝑅_𝑐𝑉₅,𝐷(𝑠)=𝑅_a11+𝑠𝐶_b2𝑅_𝑏×1+𝑠𝐶_𝑐𝑅_𝑐1+𝑠𝐶_𝑑𝑅_𝑑−𝑠𝐶_𝑑𝑅_𝑐=𝑅_a11+𝑠𝐶_b2𝑅_𝑏×𝑠²𝐶_𝑐𝑅_𝑐𝐶_𝑑𝑅_𝑑+𝑠𝐶_𝑑𝑅_𝑑+𝐶_𝑐𝑅_𝑐−𝐶_𝑑𝑅_𝑐+1=𝑅_a1𝑠³𝐶_b2𝑅_𝑏𝐶_𝑐𝑅_𝑐𝐶_𝑑𝑅_𝑑+𝑠²×𝐶_𝑐𝑅_𝑐𝐶_𝑑𝑅_𝑑+𝐶_b2𝑅_𝑏𝐶_𝑑𝑅_𝑑+𝐶_b2𝑅_𝑏𝐶_𝑐𝑅_𝑐−𝐶_b2𝑅_𝑏𝐶_𝑑𝑅_𝑐+𝑠𝐶_b2𝑅_𝑏+𝐶_𝑐𝑅_𝑐+𝐶_𝑑𝑅_𝑑−𝐶_𝑑𝑅_𝑐+1. (5) The specialization of (4), as shown in Tables 1 and 2, results the transfer function of low-pass filter (LPF), all-pass filter (APF), band-pass filter (BPF), and notch filter (NF) functions. Similarly high-pass (HPF) transfer function is obtained from (4) if 𝐶_b2𝑅_𝑏=𝐶_𝑑𝑅_𝑑.

Table 1 

The availability of each filer response and corresponding selection of 𝑉₁,𝑉₂,𝑉₃,𝑉₄, and 𝑉₅.

Table 2 

Condition of realization of each filter.

The natural frequency and quality factor of the proposed circuit for LPF, APF, BPF, NF can be obtained as 𝜔₀=₃1𝐶_𝑐𝐶_𝑑𝐶_b2𝑅_𝑐𝑅_𝑏𝑅_𝑑,𝑄=³𝐶_𝑑𝐶_𝑐𝐶_b2𝑅_𝑐𝑅_𝑏𝑅_𝑑𝐶_𝑐𝑅_𝑐+𝐶_𝑑𝑅_𝑑−𝐶_𝑑𝑅_𝑐+𝐶_b2𝑅_𝑏−³𝐶_𝑐𝐶_𝑑𝐶_b2𝑅_𝑐𝑅_𝑏𝑅_𝑑, (6) and for HPF as 𝜔₀=₃1𝐶_𝑐𝐶_𝑑𝐶_a2𝑅_𝑐𝑅_a2𝑅_𝑑,𝑄=³𝐶_𝑑𝐶_𝑐𝐶_a2𝑅_𝑐𝑅_a2𝑅_𝑑𝐶_𝑐𝑅_𝑐+𝐶_𝑑𝑅_𝑑−𝐶_𝑑𝑅_𝑐+𝐶_a2𝑅_a2−³𝐶_𝑐𝐶_𝑑𝐶_a2𝑅_𝑐𝑅_a2𝑅_𝑑. (7) The sensitivity of 𝜔₀ with respect to passive elements may be expressed as 𝑆^𝜔0_𝐶𝑐=𝑆^𝜔0_𝐶𝑑=𝑆^𝜔0_𝐶b2=𝑆^𝜔0_𝐶a2=𝑆^𝜔0_𝑅𝑐=𝑆^𝜔0_𝑅𝑏=𝑆^𝜔0_𝑅𝑑=𝑆^𝜔0_𝑅a21=−3. (8) It shows that the proposed circuit offers low sensitivity.

3. Effect of Nonidealities of OTRA

In this section the effect of finite transresistance gain (𝑅_𝑚)on the output of the filter circuit is considered and for high frequency applications a passive compensation is employed in the same line as of reference [10, 11]. Ideally the transresistance gain is assumed to approach infinity. However, practically 𝑅_𝑚 is a frequency dependent finite value. Considering the single pole model for the transresistance gain, 𝑅_𝑚 can be expressed as 𝑅_𝑚(𝑠)=𝑅₀1+𝑠/𝜔₀, (9) where 𝜔₀ is the pole frequency and 𝑅₀ is DC transresistance gain. In the case of high frequency application the transresistance gain 𝑅_𝑚(𝑠) reduces to 𝑅_𝑚(𝑠)=1𝑠𝐶_𝑃, (10) where 𝐶_𝑃=1𝑅₀𝜔₀. (11) Taking this effect into account the voltage transfer function (2) modifies to 𝑉_out(𝑠)𝑉_in(𝑠)=𝑌_𝑎−𝑌_𝑏𝑌_𝑐−𝑌_𝑑+𝑠𝐶_𝑝, (12) where 𝑠𝐶_𝑝 is the uncompensated error term. In the case of high frequency applications, passive compensation method may be employed to account for error introduced in (2) which is given in (11). Inspection of circuit of Figure 4 and denominator of (11) indicates that error term 𝑠𝐶_𝑝 may be realized by connecting a capacitor 𝐶_𝑃 in parallel to 𝑌_𝑐 or 𝐶_𝑐 for passive compensation. In other words the value of 𝐶_𝑐 may be decreased by 𝐶_𝑃 to absorb the nonideality effect and thus achieving self-compensation. There is another nonideality due to parasitic resistances and capacitances. Since the input nodes in an OTRA are inherently grounded, the effect of parasites are negligible.

4. Simulation Results

The performance of the proposed universal filter is evaluated with CMOS implementation of OTRA as shown in Figure 2 [2], with DC power supply voltages 𝑉_DD=−𝑉_SS=1.5V and bias voltage 𝑉_B=−0.5V. The simulations are performed using PSPICE based on 0.5 μm MOSIS (AGILENT) CMOS technology parameters. Aspect ratios used for different transistors are same as [2].

The designed values of resistances and capacitances to obtain multifunction filter output for a cutoff frequency of 𝑓₀=200KHz and quality factor of 𝑄=1 is shown in Table 3. The simulated frequency responses for gain of LPF, HPF, and BPF are shown in Figures 5, 6, and 7, respectively. It is observed that the simulated values closely agree with the theoretical results. Figures 8 and 9 show the frequency responses for both gain and phase for APF and NF, respectively. It is observed that there is deviation of simulated gain at higher frequency for notch filter (NF). To judge the quality of the output, total harmonic distortion is obtained for low-pass, high-pass, and band-pass filter as shown in Figure 10. It is evident that the output distortion is very low and within 0.2% up to 2 volts. Hence it may be claimed that the output is of very good quality and dynamic range is high.

Table 3 

Designed values of passive components used for VM third order filters.

Figure 5 

Frequency response of third order lowpass filter.

Figure 6 

Frequency response of third order highpass filter.

Figure 7 

Frequency response of third order unsymmetrical bandpass filter.

Figure 8 

Frequency response of third order allpass filter.

Figure 9 

Frequency response of third order unsymmetrical notch filter.

Figure 10 

Variation of %THD with respect to input voltage amplitude.

5. Conclusion

An OTRA based universal third order voltage mode filter is presented. Although a number of passive components matching is required, the proposed circuit offers the following advantageous features: (i) use of single OTRA, (ii) it has low output impedance, hence suitable for cascading, (iii) can implement all the five filter function such as lowpass, highpass, bandpass, allpass, and notch from same topology, (iv) moreover all the capacitors are grounded or virtually grounded, so suitable for monolithic IC implementation, and (v) effect of finite transresistance gain can be reduced by self-compensation method, hence no additional elements needed.