Voltage Mode Astable Multivibrator Using Single CDBA

This paper aims at presenting three voltagemode square wave generator circuits using single current differencing buffered amplifier (CDBA), a recently proposed mixed mode building block. The first proposed circuit produces a variable frequency output having fixed duty cycle, whereas the rest of the circuits have variable duty cycle. One of the circuits uses passive element adjustment to control the duty cycle, whereas electronic control is used in the other circuit. The workability of the proposed circuits is confirmed through SPICE simulations and experimental work.


Introduction
It is well known that inherent wide bandwidth which is virtually independent of closed loop gain, greater linearity and large dynamic range [1] are the key performance features of current mode technique.The CDBA is one such active element which exploits these advantages.In addition, it is free from parasitic capacitances [2] and, hence, is appropriate for high frequency operation.It provides further flexibility to the designers, enabling a variety of circuit designs, as it can operate in both current and voltage modes [3].
The square wave generator finds extensive applications in communication systems, control systems, instrumentation, and signal processing.The literature review reveals that several triangular/square wave generators using various analog building blocks have already been presented [4][5][6][7][8][9][10][11].All these designs use a current source to alternately charge and discharge a capacitor followed by a Schmitt trigger to generate triangular/square wave.Conventional voltage-mode square wave generators [4] employ an op-amp working in the nonlinear region to produce a square wave signal.These voltage-mode generators, however, have a limitation on their maximum frequency due to lower slew rate and constant gain-bandwidth product of the op-amps.
The aim of this paper is to present three square wave generator circuits using single CDBA and three to five passive elements.In Section 2, the function of a CDBA is introduced followed by the description of proposed circuits with analytical formulation for the frequency of oscillation.Section 3 explores the effect of nonidealities of CDBA on the proposed circuits.PSPICE simulation results and experimental results are presented in Section 4 which are in confirmation with the theoretical propositions.Section 5 concludes the paper.

Circuit Descriptions
The circuit symbol of CDBA is shown in Figure 1.The port characteristics are given as follows 2.1.Circuit I.The circuit for the astable multivibrator is shown in Figure 2. It uses a single CDBA block, two resistors and a capacitor.The resistor   and capacitor  form a positive feedback loop.The load resistance   connected to the  terminal is large enough to drive the device output  0 into one of the two saturation levels  + sat or  − sat .This results in charging of the capacitor present in the feedback loop.When the voltage across the capacitor reaches a value at which the current through   is not large enough to maintain the output voltage at  + sat the output switches to  − sat and the capacitor starts charging in the opposite direction as shown in Figure 3.
Routine analysis suggests that the output will switch between its maximum ( + sat ) and minimum ( − sat ) value when the capacitor voltage reaches the following two threshold voltages: The time required to charge ( on ) the capacitor from a value of  TL to  TH is given by Similarly, time taken for discharging ( off ) from  TH to  TL is From ( 4) and ( 5), it is clear that   >   .Thus, the output of the multivibrator is a symmetric square wave having amplitudes of  + sat and  − sat , at a frequency (  ) given by Though the circuit is simple and output frequency can be controlled through passive components, however, the on and off duty cycles of the output are fixed at 50%. based on the scheme discussed in [11] and has been adapted for implementation with CDBA.

Circuit II. The circuit of
Neglecting the drop across the diodes, the parameters  TH ,  TL ,  on and  off may be obtained as From ( 9) and ( 10), the frequency (  ) of modified square wave generator can be written as , where It can be seen clearly that  on and  off can be controlled by changing  2 and  1 .

Circuit III.
The circuit shown in Figure 5 is another astable multivibrator.In this circuit, the duty cycle can be electronically controlled by the application of an external DC source  dc .Routine analysis for this circuit gives the  TH and  TL as  These values of  TH and  TL result in  on and  off as follows: These results show that the on and off duty cycles of the output can be controlled with the help of externally applied voltage  dc .

Realizing a CDBA and Nonideality Analysis
In the analysis so far, ideal characteristics of the CDBA were considered.However, in this section, the effect of the parameters of a practical model of the CDBA is investigated.For the proposed circuits, the CDBA was realized using current feedback operational amplifier (CFOA) ICAD844 as shown in Figure 6 [12].The equivalent circuit of Figure 6, which uses practical model of AD844 [13], is shown in Figure 7. Herein, the CFOAs have been replaced with current conveyors having finite input resistances (  ) and finite resistance at its  terminal (  ).Ideally, the input resistance at the  terminal is zero and is infinite at the  terminal.circuit is used for exploring the nonideal behavior of all the three proposed circuits.From Figure 7, various currents can be calculated as follows: Ideally,   should be equal to  1 , which can be approximated only if   ≫   , which is true for AD844.Also, the approximation that the input terminals are virtually grounded will be true only if the external resistance at the input terminal of the CDBA is much larger than   .If these two conditions are satisfied, the CDBA constructed with AD844 closely approximates an ideal CDBA.
Taking into account the afore mentioned approximations, from (15),   , the current from  terminal, can be calculated as And the output voltage   is given as If the equivalent circuit of CDBA constructed with AD844 is used in Figure 2 (circuit I), then the threshold limits of the output get modified to Since   ≪   and   ≫   , (18) and (19) reduce to (2) and (3), respectively.The threshold limits of the output of Figure 4 (circuit II), on using the equivalent CDBA model, get modified to where  1 and  2 are forward resistances of the diodes  1 and  2 , respectively, and are of very small order as compared to  1 and  2 .Also, since   ≪   and   ≫   , ( 20) and ( 21) can be approximated to ( 7) and ( 8), respectively.Similarly, for the astable circuit shown in Figure 5 (circuit III), the modified threshold limits of the output can be expressed as The external resistance at the input of the CDBA should be much larger than   so that the feedback current can be absorbed into the input terminals.Since   ,   ,   , and   ≫   , ( 22) and ( 23) reduce to ( 12) and ( 13), respectively.

Simulation and Experimental Results
To validate the theoretical predictions, the proposed astable multivibrator circuits have been simulated using PSPICE macromodel of current feedback operational amplifier (CFOA) AD 844 and experimented using commercially available AD 844AN.The CDBA realization using CFOA AD 844 is shown in Figure 6.Simulations were carried out to investigate the maximum and minimum frequencies that proposed circuit configuration of Figure 2 (circuit I) can offer before the output signal gets distorted.Supply voltage of ±10 V was used for simulations.Figure 8 shows the output of the proposed circuit for minimum and maximum frequencies which can be achieved, with frequency deviation not more than 5%.The simulated square wave output obtained with component values as   = 20 KΩ,   = 50 KΩ and  = 10 F is shown in Figure 8(a).This is the minimum frequency that can be obtained from the circuit and its value is observed to be 2 Hz as against the theoretically computed value of 1.9 Hz.Similarly output for maximum achievable frequency is shown in Figure 8(b).Component values used are   = 1 KΩ,   = 40 KΩ and  = 100 pF.The simulated frequency is noted to be 1.2 MHz showing a minor deviation from the theoretically calculated value of 1.14 MHz.
To test the tunability of this circuit, the variation in frequency, against the passive components ,   , and   , was observed.The variation of frequency against the capacitor  is presented in Figure 9(a), whereas Figures 9(b) and 9(c) plot the variations against the resistors   and   , respectively.Figure 11 shows the output of circuit III for three different values of  dc , that is, 2 V, 5 V, and −2 V, while rest of the The functionality of the proposed square wave generator circuits is verified experimentally as well.The commercial  AD844AN is used to implement a CDBA.Supply voltages used are ±10 V.
Figure 13 shows typical experimental results for circuit I for three different frequencies.Figure 13

Conclusion
Three astable multivibrator circuits using single CDBA are proposed.The first circuit (circuit I) produces a variable frequency output with fixed duty cycle.The other two proposed circuits (circuit II and circuit III) provide output with variable duty cycle; for circuit II, duty cycle control is accomplished through passive component adjustment, and for circuit III, electronic control is used.Nonideality analysis is presented to explore the effect of the parameters of a practical model of the CDBA.The workability of the proposed circuits is demonstrated through SPICE simulations and experimental work.AD-844-based CDBA is used for simulation and

Figure 10 :
Figure 10: (a) Output of circuit II.(b) Variation of calculated and simulated values of frequency with .

Figure 11 :
Figure 11: (a) Output of circuit III with  dc = 2 V. (b) Output of circuit III with  dc = 5 V. (c) Output of circuit III with  dc = −2 V.

Figure 12 :Figure 13 :
Figure 12: (a) Variation of calculated and simulated value of frequency with DC bias.(b) Variation of duty cycle with DC bias.
(a) is output for component values of   = 82 KΩ,   = 15 KΩ, and  = 10 nF.The measured frequency of 1.547 KHz closely matches the theoretical frequency of 1.46 KHz as obtained from (6).Output for component values of   = 3.9 KΩ,   = 1 KΩ, and  = 2 nF is shown in Figure 13(b), wherein the measured frequency of oscillation is 123.3KHz as against the computed value of 130 KHz.Another screen shot of oscilloscope is shown in Figure 13(c) for   = 40 KΩ,   = 1 KΩ, and  = 100 pF.Observed output is having a frequency of oscillation as 824 KHz and the corresponding calculated value is found to be 1.14 MHz.Experimental outputs for the circuit III are shown in Figure 14 for different values of  dc , which depicts the variation of duty cycle with  dc .