CDBA-Based Universal Biquad Filter and Quadrature Oscillator

The voltage-mode universal biquadratic filter and sinusoidal quadrature oscillator based on the use of current differencing buffered amplifiers (CDBAs) as active components have been proposed in this paper. All the proposed configurations employ only two CDBAs and six passive components. The first proposed CDBA-based biquad configuration can realize all the standard types of the biquadratic functions, that is, lowpass, bandpass, highpass, bandstop, and allpass, from the same topology, and can also provide orthogonal tuning of the natural angular frequency (ωo) and the bandwidth (BW) through separate virtually grounded passive components. By slight modification of the first proposed configuration, the new CDBA-based sinusoidal quadrature oscillator is easily obtained. The oscillation condition and the oscillation frequency are independently adjustable by different virtually grounded resistors. The sensitivity analysis of all proposed circuit configurations is shown to be low. PSPICE simulations and experimental results based upon commercially available AD844-type CFAs are included, which confirm the workability of the proposed circuits.


INTRODUCTION
Current-mode universal active components have two distinct advantages: they provide wide bandwidths and high slew rate. On the other hand, many of today's analog signal processing applications require voltage-mode operation. Therefore, it is advantageous to implement current-mode active elements in voltage-mode circuits [1].
Recently, a current differencing buffered amplifier (CDBA) that is one of the current-mode components has been introduced [2]. It can offer advantageously features such as high slew rate, free from parasitic capacitance, wide bandwidth, and simple implementation [3]. Since the CDBA consists of a unity-gain current differential amplifier and a unity-gain voltage amplifier, this element would be suitable for the implementation of voltage and current-mode signal processing applications. As far as the applications of the CDBA are concerned, various voltage-mode filters [2,[4][5][6][7][8] and oscillators [1,9,10] have been reported in literature. Only few can perform both biquadratic filter and oscillator in the same circuit configuration [1]. However, it is restricted for only bandpass filter function design and cannot be realized by another type of the standard biquadratic function characteristics. Moreover, it generates a single-phase output voltage when it performs as a sinusoidal oscillator. There is no CDBA-based circuit configuration, which can realize the universal biquad filter and quadrature oscillator both in the same circuit configuration.
Thus, the voltage-mode universal biquadratic filter and sinusoidal quadrature oscillator using two CDBAs, four virtually grounded resistors, and two capacitors are described in this paper. The first proposed CDBA-based biquad filter can realize lowpass (LP), bandpass (BP), highpass (HP), bandstop (BS), and allpass (AP) biquadratic functions without changing the circuit topology. The filter also provides an orthogonal control of the natural angular frequency (ω o ) and the bandwidth (BW). Moreover, a CDBA-based sinusoidal quadrature oscillator circuit can be realized by slightly modifying the first proposed CDBAs-based circuit configuration. All passive components used in the circuit realization are really and virtually grounded, which is insensitive to the effects of the stray capacitance. The oscillation condition and the frequency of oscillation can be controlled independently through different virtually grounded resistors. In addition, the sensitivity analysis shows that all of the proposed circuits have low-sensitivity performance. PSPICE simulation 2 Active and Passive Electronic Components  and experimental results using commercially available active component AD844 are also included to verify the theoretical analysis.

CURRENT DIFFERENCING BUFFERED AMPLIFIER (CDBA)
The circuit symbol of the CDBA is shown in Figure 1, where p and n are the positive and negative current input terminals, respectively, z is the current output terminal, and w is the voltage output terminal. Its current and voltage characteristics can be described by the following matrix equations [1,2]: According to the above set of describing equations, the terminal z behaves as a current source that takes the difference of currents at the inputs, and the terminal w behaves as a voltage source that copies the output voltage at the z terminal. Thus, the CDBA can be considered as a collection of a noninverting and an inverting current-mode, and noninverting voltage-mode unity-gain cells, which can be realized by a cascade connection of a current substractor and a voltage follower. Although the CDBA can be realized by using several well-known circuit techniques, one possible practical implementation is given in Figure 2 [4,11]. Figure 3 shows the proposed voltage-mode universal biquadratic filter, which consists of only two CDBAs, four virtual-grounded resistors, and two capacitors. By straight- Figure 3: Proposed CDBA-based universal biquad filter.

PROPOSED CDBA-BASED UNIVERSAL BIQUAD
forward analysis, the single output voltage function realized by this configuration is found to be From (2), by choosing the component values of R 1 = R 3 and R 2 = R 4 , we can see that Clearly, the proposed filter can be used as a voltage-mode three-input single-input universal filter that can realize all the standard types of the biquad filter functions.
Also from (2), the natural angular frequency (ω o ), the bandwidth (BW), and the quality factor (Q) in all cases are given by where R A = R 1 = R 3 and R B = R 2 = R 4 . Note that the filter parameters ω o and BW are adjustable properly by the virtualgrounded resistor R A or the capacitor C 1 , and by the virtualgrounded resistor R B or the capacitor C 2 , in that order.
Taking the nonidealities of the CDBA into account, the relationship of the terminal currents and voltages given in (1) can be rewritten as where α p = 1 − ε p and ε p (|ε p | 1) is the currenttracking error from p terminal to z terminal, α n = 1 − ε n Worapong Tangsrirat et al. Figure 4: Proposed CDBA-based sinusoidal quadrature oscillator. and ε n (|ε n | 1) is the current-tracking error from n terminal to z terminal, and β = 1 − ε v and ε v (|ε v | 1) is the voltage-tracking error from z terminal to w terminal of the CDBA. Therefore, including these nonidealities into the voltage transfer function, the modified filter parameters are derived as where α pi ,α ni , and β i are the parameters α p , α n , and β of the ith CDBA (i = 1, 2). The active and passive sensitivities of this universal filter are shown as follows: It is clearly observed from (6) that all of the sensitivities are low.

PROPOSED CDBA-BASED QUADRATURE OSCILLATOR
From the first configuration of Figure 3, by setting V 1 = V 2 = V 3 = 0 V (grounded) and connecting the resistor R 1 between the terminals p and wof the CDBA2, the second  proposed CDBA-based sinusoidal quadrature oscillator can be obtained as shown in Figure 4. In this case, the characteristic equation of the second proposed configuration can be given by The oscillation condition and the oscillation frequency (ω o ) of this configuration can be obtained, respectively, as Note from (8) that the oscillation condition of the proposed oscillator of Figure 4 can be adjusted by R 1 or/and R 4 without affecting the oscillation frequency ω o . The ω o can be adjusted by R 2 or/and R 3 . Therefore, the oscillation condition and the oscillation frequency of the proposed oscillator circuit can be controlled independently. From the configuration of Figure 4, the relationship between two quadrature output voltages V o1 and V o2 can be expressed as where the phase shift is φ = 90 • . This guarantees that the proposed oscillator circuit provides the quadrature outputs V o1 and V o2 . Taking into account the nonideal CDBAs in Figure 4, the characteristic equation becomes The modified oscillation condition and the oscillation frequency (ω o ) in this case are obtained as It should be noted from (11) and (12) that the oscillation condition and ω o of the proposed quadrature oscillator are altered slightly by the effects of the CDBA current-and voltage-tracking errors. However, they can still be controlled independently. Sensitivities calculated from (12) using relative sensitivity formula are obtained as The circuit has optimum sensitivity performance in the sense that all values are equal to 0.5 in magnitude.

SIMULATION AND EXPERIMENTAL RESULTS
In order to confirm the theoretical analysis, all the proposed circuits given in Figures 3 and 4 have been simulated using the PSPICE program. In simulations, the CDBA circuit was constructed with two AD844 ICs of analog devices, as shown in Figure 2. The model parameters of AD844 were taken from the built-in library (AD844/AD), and the supply voltages were taken as ±12 V. Theoretical analysis and simulation results were also verified by experimental testing.
For the experiments, the proposed circuits were constructed in laboratory using commercially available current feedback amplifier (CFA) AD844 ICs with the same components used in simulation.
Worapong Tangsrirat et al.  Figure 5 shows the simulated frequency characteristics for the LP, BP, and HP filter functions of the proposed CDBAbased multifunction biquad circuit in Figure 3 with the theory frequency responses. The passive component values were chosen as R 1 = R 2 = R 3 = R 4 = 10 kΩ and C 1 = C 2 = 1 nF, which is designed to obtain a universal filter with a natural angular frequency of f o = ω o /2π ∼ = 15.91 kHz and the quality factor of Q = 1. With the same setting, the simulation and experimental results for the gain and phase responses of the BS and AP filters verifying theory values are, respectively, depicted in Figures 6 and 7. It appears from all figures that the simulation and experimental results are in excellent agreement with the theoretical values.
As an example to demonstrate the workability of the proposed CDBA-based quadrature oscillator circuit in Figure 4, the following passive component values were chosen as R 1 = R 2 = R 3 = 10 kΩ and C 1 = C 2 = 1 nF. The simulated quadrature output waveforms V o1 and V o2 of the oscillator are illustrated in Figure 8, where the value of R 4 ∼ = 10.5 kΩ was chosen to be slightly larger than R 1 to ensure that the oscillations will start. The simulated frequency was measured as 15.37 kHz, which is lower than the theoretical value of 15.91 kHz, owing to the parasitic elements R x , z, and C z of the AD844 [12,13]. Figure 9 shows the simulated frequency spectrums of the quadrature outputs, giving the total harmonic distortion (THD) less than 2.95%. The results of the THD analysis obtained from the simulations are summarized in Table 1. Figure 10 shows the experimental output waveforms V o1 and V o2 of Figure 4, and the oscillation frequency f o was measured as 15.52 kHz. The controllability of f o through R 2 without influencing the oscillation condition is shown in Figure 11.

CONCLUSION
In this paper, a voltage-mode universal biquad filter using two CDBAs, four virtually grounded resistors, and two capacitors has been presented. By appropriately connecting input voltage terminals, the proposed CDBA-based biquadratic filter can realize all the standard types of the biquadratic filter functions. The filter permits orthogonal adjustment of the parameters ω o and BW. Furthermore, a CDBA-based quadrature oscillator can be obtained easily by  slightly modifying the proposed CDBA-based biquad filter. Its oscillation condition and oscillation frequency can be controlled separately via different virtually grounded resistors. In addition, the sensitivities of all proposed circuits are shown to be low. It is shown that the simulation and experimental results conform very well to the theoretical conclusions.