Design of a voltage-mode universal second-order CFA filter

1 Introduction

Voltage operational amplifiers are basic active devices in analog circuit design. The operating frequency of a circuit composed of ordinary voltage operational amplifiers is relatively low. Current feedback amplifiers (CFA) are a new type of operational amplifier. They not only provide a bandwidth close to a constant value, but also have a high conversion rate. The circuit composed of them has better performance than the circuit composed of OTA in terms of frequency characteristics and dynamic range [1-30]. In recent years, current feedback amplifiers have been applied in second-order filter circuits [6-10], and literature on voltage-mode or current-mode biquadratic filters composed of current feedback amplifiers (CFA) has been continuously reported. There are two main forms: one is a single-input multi-output filter; the other is a three-input single-output filter. However, according to the literature, most circuits use a large number of CFA devices. This paper proposes a three-input single-output voltage-mode universal second-order filter circuit. The circuit is composed of only two current feedback amplifiers (CFAs), two capacitors, and three resistors. The circuit structure is simple and can realize second-order low-pass, band-pass, high-pass, notch, and full-pass filter functions. The circuit was simulated using PSpice. The simulation results showed that the circuit design was correct and the theoretical analysis was consistent with the simulation results.

2 CFA circuit structure and principle

The current feedback amplifier (CFA) is a four-port device as shown in Figure 1. Its circuit transfer characteristics are:

That is, Iy=0, Vx=Vy, Ix=±Iz, Vo=Vz. In formula (1), "+" corresponds to CFA+, and "-" corresponds to CFA-. It can be seen that the voltage at the x-terminal follows the voltage at the y-terminal, and the current at the z-terminal follows the current at the x-terminal. The y-terminal is a high-impedance input, Iy=0, and the voltage at the z-terminal follows the voltage at the o-terminal [6-9].

3 Second-order filter principle

This article uses the filter circuit shown in Figure 2, which is composed of 2 CFAs, 2 capacitors and 3 resistors. Circuit analysis of the circuit in Figure 2 yields:

From the above equation, the circuit current transfer function can be obtained:

From formula (6), we can know that by changing the input signals V1, V2, and V3, low-pass, band-pass, high-pass, notch, and all-pass filter functions can be realized respectively. The corresponding relationship between the realization conditions and the filter types is shown in Table 1.

The circuit pole parameters are:

From equations (7) and (9), it can be seen that the pole angular frequency and the pole quality factor can be adjusted independently.

According to the definition of sensitivity, the change sensitivity of the characteristic frequency ωP,QP relative to the resistance element and the capacitance element, ωp,QP, the passive sensitivity is:

From equations (10) and (11), we can see that the passive sensitivity of ωp,QP is relatively small.

Considering the non-ideal characteristics of CFA, its port characteristics are:

Among them: a=1-ε1, ︱ε1︱＜＜《1, ε1 represents the current tracking error of the current feedback amplifier, β=1-ε2, ︱ε2︱＜＜1, ε2 represents the input voltage tracking error of the current feedback amplifier, γ1=1-ε3, ︱ε3 ︱＜＜1, ε3 represents the output voltage tracking error of the current feedback amplifier. Through analysis, the output voltage can be obtained as:

From equations (18) and (19), it can be seen that the active sensitivity of ωP and QP is also small.

4 Circuit Simulation

In order to verify the correctness of the designed filter circuit, the author used PSpice to simulate the circuit. When R1=R2=R3=1 kΩ, C1=C2=0.1 μF, from equation (8), we get: fp=1.59 kHz. Under PSpice9.1, the circuit shown in Figure 2 was simulated, and the amplitude-frequency characteristics (as shown in Figure 3) were consistent with the required technical parameters.

5 Conclusion

This paper proposes a voltage mode universal second-order filter circuit consisting of only two current feedback amplifiers (CFAs), two capacitors and three resistors, which can realize second-order low-pass, band-pass, high-pass, band-stop and all-pass filter functions. The circuit analysis was carried out to obtain the voltage transfer function and circuit parameters. The filter circuit was simulated using PSpice. The simulation results show that the filter circuit design is correct and the theoretical analysis is consistent with the simulation results. The circuit has the following characteristics:

(1) Able to realize voltage mode second-order low-pass, band-pass, high-pass, notch, and all-pass filtering functions;

(2) The circuit structure is simple;

(3) It has fewer components;

(4) Passive and active sensitivity is low;

(5)ωP, QP are adjustable

(6) The circuit is easy to implement.