A New CFA Based Current-Mode Universal Biquad Filter

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The proposed current-mode second order universal filter is shown in Figure 2. The routine analysis of the circuit using port relations of CFA yields the following current-mode transfer functions.

(2)

(3)

(4)

Selecting the admittances as Y₁=sC₁, Y₂=G₂, Y₃=G₃, Y₄=G₄, and Y₅=sC₅, then the current transfer functions become

(5)

(6)

(7)

Figure 2. Proposed generalized circuit of CM universal filter

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The circuit realizes highpass filter at I_HP, a bandpass filter at I_BP, and a lowpass filter at I_LP simultaneously. The natural frequency ω_O and quality factor Q are given by

(8)

(9)

From eqn. (8) and eqn. (9) it is evident that the natural angular frequency ω_O and quality factor Q of the current-mode filter are dependent on each other, that is whenever ω_O is changed, the value of quality factor Q gets disturbed. But if ratio of either C₁ and C₅ or G₂ and G₃ is kept constant, then ω_O can be varied without disturbing the quality factor. The direct addition of I_HP and I_LP yields current-mode notch filter where as allpass filter can be obtained directly from the three available responses i.e. I_HP, I_LP and I_BP without any additional hardware.

3. Non-ideal Equivalent Circuit of CFA

Figure 3 shows the non-ideal equivalent circuit model of the CFA. R_x is the input resistance of the x-terminal, R_y// (1/sC_y) represents the y-terminal parasitic input impedance and R_p// (1/sC_p) gives the parasitic impedance value at z-terminal ^[7]. The values of the various parasitics for the bipolar CFAs (AD844) are R_x=50Ω, C_p=5.5pF, R_p= 3MΩ, R_y=2MΩ and C_y=2pF. The effect of these parasitic impedences is prominent at sufficiently high frequencies.

Figure 3. Non-ideal equivalent circuit of the CFA includes the parasitic impedances

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4. Sensitivity Analysis

Taking into account the tracking errors of current feedback amplifier, the terminal equation (1) get modified as

(10)

where denotes the current tracking error, is the input voltage tracking error and is the output voltage tracking error of the current feedback amplifier. The natural angular frequency ω_O, quality factor Q and bandwidth of filter of Figure 2 becomes

(11)

(12)

(13)

The active and passive sensitivities of the proposed filter have been found to be fairly small and are computed below.

From above results it is obvious that the active and passive sensitivities of the proposed filter are low and not larger than unity.

5. Simulation Results

The proposed current-mode second order universal biquadratic filter has been simulated with TINA Pro simulation program. The universal filter has been designed for f_O = 10.5KHz and Q=1. The CFA has been realized with commercially available AD844s. The values of passive components used are C₁=C₅=10nF, R₂=R₃= R₄=1kΩ, The supply voltages are ±12V.The simulated magnitude responses of lowpass, bandpass, highpass and notch filters are shown in Figure 4. The phase response of second order allpass filter is shown in Figure 5. The simulation results agree well with theoretical analysis of the filter.

Figure 4. Simulation results of the proposed universal filter

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Figure 5. Phase response of second order allpass circuit

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