# Voltage Mode Astable Multivibrator Using Single CDBA

Authors: Rajeshwari Pandey; Neeta Pandey; Sajal K. Paul; Kashish Anand; Kranti Ghosh Gautam
Journal: ISRN Electronics
 (2013)

---

## Abstract

This paper aims at presenting three voltage mode 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.


---

## Body

## 1. 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 [4–11]. 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.Triangular/square wave generators presented in [5–11] use current mode building-blocks-based circuits. The study of these circuits reveals that (i)
references [5, 6, 10] employ more than one active element;(ii)
references [6–10] use four or more passive elements;(iii)
references [6–11] lack electronic controllability of duty cycle of output.The aim of this paper is to present three square wave generator circuits using single CDBA and three to five passive elements. In Section2, 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.


## 2. Circuit Descriptions

The circuit symbol of CDBA is shown in Figure1. The port characteristics are given as follows
(1)[IzVwVpVn]=[001-1100000000000][VzIwIpIn].Figure 1
Block diagrammatic representation of CDBA.


### 2.1. Circuit I

The circuit for the astable multivibrator is shown in Figure2. It uses a single CDBA block, two resistors and a capacitor. The resistor RF and capacitor C form a positive feedback loop. The load resistance RL connected to the z terminal is large enough to drive the device output V0 into one of the two saturation levels Vsat+ or Vsat-. 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 RL is not large enough to maintain the output voltage at Vsat+ the output switches to Vsat- and the capacitor starts charging in the opposite direction as shown in Figure 3.Figure 2
Astable multivibrator with fixed 50% duty cycle.Figure 3
Output of the astable multivibrator of Figure2.Routine analysis suggests that the output will switch between its maximum(Vsat+) and minimum (Vsat-) value when the capacitor voltage reaches the following two threshold voltages:
(2)VTL=(RL-RF)RLVsat-,(3)VTH=(RL-RF)RLVsat+.
The time required to charge (Ton) the capacitor from a value of VTL to VTH is given by
(4)Ton=RFCln[2RLRF-1].
Similarly, time taken for discharging (Toff) from VTH to VTL is
(5)Toff=RFCln[2RLRF-1].
From (4) and (5), it is clear that RL>RF.Thus, the output of the multivibrator is a symmetric square wave having amplitudes ofVsat+ and Vsat-, at a frequency (fo) given by
(6)fo=1Ton+Toff=12RFCln[2RL/RF-1].
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%.


### 2.2. Circuit II

The circuit of Figure2 can be modified for variable duty cycle output by replacing the resistor RF with two diodes and two resistors and is depicted in Figure 4. It is based on the scheme discussed in [11] and has been adapted for implementation with CDBA.Figure 4
Astable multivibrator having resistor-controlled duty cycle.Neglecting the drop across the diodes, the parametersVTH, VTL, Ton and Toff may be obtained as
(7)VTL=(RL-R1)RLVsat-,(8)VTH=(RL-R2)RLVsat+,(9)Ton=R2Cln(2RL-R1R2),(10)Toff=R1Cln(2RL-R2R1).
From (9) and (10), the frequency (fo) of modified square wave generator can be written as
(11)fo=1R2Cln[(2RL-R1)/R2]+R1Cln[(2RL-R2)/R1],whereRL>R1,R2.
It can be seen clearly that Ton and Toff can be controlled by changing R2 and R1.


### 2.3. Circuit III

The circuit shown in Figure5 is another astable multivibrator. In this circuit, the duty cycle can be electronically controlled by the application of an external DC source Vdc.Figure 5
Astable multivibrator having electronically controlled duty cycle.Routine analysis for this circuit gives theVTH and VTL as
(12)VTH=Vsat+(1-RFRL)+VdcRFRS,(13)VTL=Vsat-(1-RFRL)+VdcRFRS.
These values of VTH and VTL result in Ton and Toff as follows:
(14)Ton=RCln[2RL/RF-1]-RLVdc/Vsat+RS[1-VdcRL/Vsat+RS],Toff=RCln[2RL/RF-1]-VdcRL/Vsat-RS[1-VdcRL/Vsat-RS].
These results show that the on and off duty cycles of the output can be controlled with the help of externally applied voltage Vdc.


## 2.1. Circuit I

The circuit for the astable multivibrator is shown in Figure2. It uses a single CDBA block, two resistors and a capacitor. The resistor RF and capacitor C form a positive feedback loop. The load resistance RL connected to the z terminal is large enough to drive the device output V0 into one of the two saturation levels Vsat+ or Vsat-. 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 RL is not large enough to maintain the output voltage at Vsat+ the output switches to Vsat- and the capacitor starts charging in the opposite direction as shown in Figure 3.Figure 2
Astable multivibrator with fixed 50% duty cycle.Figure 3
Output of the astable multivibrator of Figure2.Routine analysis suggests that the output will switch between its maximum(Vsat+) and minimum (Vsat-) value when the capacitor voltage reaches the following two threshold voltages:
(2)VTL=(RL-RF)RLVsat-,(3)VTH=(RL-RF)RLVsat+.
The time required to charge (Ton) the capacitor from a value of VTL to VTH is given by
(4)Ton=RFCln[2RLRF-1].
Similarly, time taken for discharging (Toff) from VTH to VTL is
(5)Toff=RFCln[2RLRF-1].
From (4) and (5), it is clear that RL>RF.Thus, the output of the multivibrator is a symmetric square wave having amplitudes ofVsat+ and Vsat-, at a frequency (fo) given by
(6)fo=1Ton+Toff=12RFCln[2RL/RF-1].
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%.


## 2.2. Circuit II

The circuit of Figure2 can be modified for variable duty cycle output by replacing the resistor RF with two diodes and two resistors and is depicted in Figure 4. It is based on the scheme discussed in [11] and has been adapted for implementation with CDBA.Figure 4
Astable multivibrator having resistor-controlled duty cycle.Neglecting the drop across the diodes, the parametersVTH, VTL, Ton and Toff may be obtained as
(7)VTL=(RL-R1)RLVsat-,(8)VTH=(RL-R2)RLVsat+,(9)Ton=R2Cln(2RL-R1R2),(10)Toff=R1Cln(2RL-R2R1).
From (9) and (10), the frequency (fo) of modified square wave generator can be written as
(11)fo=1R2Cln[(2RL-R1)/R2]+R1Cln[(2RL-R2)/R1],whereRL>R1,R2.
It can be seen clearly that Ton and Toff can be controlled by changing R2 and R1.


## 2.3. Circuit III

The circuit shown in Figure5 is another astable multivibrator. In this circuit, the duty cycle can be electronically controlled by the application of an external DC source Vdc.Figure 5
Astable multivibrator having electronically controlled duty cycle.Routine analysis for this circuit gives theVTH and VTL as
(12)VTH=Vsat+(1-RFRL)+VdcRFRS,(13)VTL=Vsat-(1-RFRL)+VdcRFRS.
These values of VTH and VTL result in Ton and Toff as follows:
(14)Ton=RCln[2RL/RF-1]-RLVdc/Vsat+RS[1-VdcRL/Vsat+RS],Toff=RCln[2RL/RF-1]-VdcRL/Vsat-RS[1-VdcRL/Vsat-RS].
These results show that the on and off duty cycles of the output can be controlled with the help of externally applied voltage Vdc.


## 3. 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 Figure6 [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 (Rx) and finite resistance at its z terminal (Rz). Ideally, the input resistance at the x terminal is zero and is infinite at the z terminal. For the AD844 CFOA, the input resistances Rx=50 Ω and Rz=3 MΩ [13]. This circuit is used for exploring the nonideal behavior of all the three proposed circuits.Figure 6
CDBA constructed with AD844.Figure 7
Equivalent circuit of CDBA constructed with AD844.From Figure7, various currents can be calculated as follows:
(15)Iz1=Ip,ID=Iz1(RzRx+Rz),Ix2=In-ID,Iz2=Ix2.Ideally,ID should be equal to Iz1, which can be approximated only if Rz≫Rx, 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 Rx. 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), Iz, the current from z terminal, can be calculated as
(16)Iz=(Ip-In).
And the output voltage Vw is given as
(17)Vw=Vz.
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
(18)VTL=(RL//Rz)-(RF+Rx)RL//RzVsat-,(19)VTH=(RL//Rz)-(RF+Rx)RL//RzVsat+.
Since RL≪Rz and RF≫Rx, (18) and (19) reduce to (2) and (3), respectively.The threshold limits of the output of Figure4 (circuit II), on using the equivalent CDBA model, get modified to
(20)VTL=(RL//Rz)-(R1+Rx+RD1)RL//RzVsat-,(21)VTH=(RL//Rz)-(R2+Rx+RD2)RL//RzVsat+,
where RD1 and RD2 are forward resistances of the diodes D1 and D2, respectively, and are of very small order as compared to R1 and R2. Also, since Rx≪RF and Rz≫RL, (20) and (21) can be approximated to (7) and (8), respectively.Similarly, for the astable circuit shown in Figure5 (circuit III), the modified threshold limits of the output can be expressed as
(22)VTH=Vsat+(1-RF+RxRL//Rz)+VdcRF+RxRS+Rx,(23)VTL=Vsat-(1-RF+RxRL//Rz)+VdcRF+RxRS+Rx.The external resistance at the input of the CDBA should be much larger thanRx so that the feedback current can be absorbed into the input terminals. Since RL, RF, RS, and Rz≫Rx, (22) and (23) reduce to (12) and (13), respectively.


## 4. 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 Figure6. 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 RF=20 KΩ, RL=50 KΩ and C=10 μF 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 RF=1 KΩ, RL=40 KΩ and C=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.Output of circuit I.
(a)
Minimum frequency output
(b)
Maximum frequency outputTo test the tunability of this circuit, the variation in frequency, against the passive componentsC, RL, and RF, was observed. The variation of frequency against the capacitor C is presented in Figure 9(a), whereas Figures 9(b) and 9(c) plot the variations against the resistors RL and RF, respectively.(a) Variation of calculated and simulated values of frequency withC for RF=15 KΩ and RL=40 KΩ. (b) Variation of calculated and simulated values of frequency with RL for C=100 pF and RF=5KΩ. (c) Variation of calculated and simulated values of frequency with RF for C=100 pF and RL=30KΩ.
(a)
(b)
(c)The circuit configuration of Figure4 (circuit II) was simulated to investigate the variation of duty cycle by changing the passive component values. A typical output of this circuit is given in Figure 10(a), wherein curve (1) is plotted for R1=25 KΩ and R2=2 KΩ and curve (2) for R1=4 KΩ and R2=15 KΩ. The values of RL and C are kept as 40 KΩ 1 nF, respectively, for both curves. It clearly shows that the on and off periods of the output are not fixed anymore. Figure 10(b) shows the plot of the calculated frequency and the simulated frequency of oscillation as a function of C while keeping RL=40 KΩ, R1=20 KΩ, and R2=4 KΩ. The deviation in frequency arises since the voltage drop across the diodes and their forward resistance is not taken into account in calculations.(a) Output of circuit II. (b) Variation of calculated and simulated values of frequency withC.
(a)
(b)Figure11 shows the output of circuit III for three different values of Vdc, that is, 2 V, 5 V, and −2 V, while rest of the component values are chosen as Rs=40 K, RL = 40 K, RF=15 K, and C=1 nF. It is evident that the output frequency and duty cycle can be controlled using Vdc.(a) Output of circuit III withVdc=2 V. (b) Output of circuit III with Vdc=5 V. (c) Output of circuit III with Vdc=-2V.
(a)
(b)
(c)Figure12(a) shows the comparison between the calculated frequency and the simulated frequency of oscillations as a function of Vdc, and Figure 12(b) shows variation of duty cycle with Vdc, for component values of RS=40 K, RL=40 K, RF=15 K, and C=1 nF. It is observed that all the simulated results are found in close agreement with the theoretically formulated values.(a) Variation of calculated and simulated value of frequency with DC bias. (b) Variation of duty cycle with DC bias.
(a)
(b)The functionality of the proposed square wave generator circuits is verified experimentally as well. The commercialIC AD844AN is used to implement a CDBA. Supply voltages used are ±10 V.Figure13 shows typical experimental results for circuit I for three different frequencies. Figure 13(a) is output for component values of RL=82 KΩ, RF=15 KΩ, and C=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 RL=3.9 KΩ, RF=1 KΩ, and C=2 nF is shown in Figure 13(b), wherein the measured frequency of oscillation is 123.3 KHz as against the computed value of 130 KHz. Another screen shot of oscilloscope is shown in Figure 13(c) for RL=40 KΩ, RF=1 KΩ, and C=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 Vdc, which depicts the variation of duty cycle with Vdc.Experimental output obtained from circuit I.
(a)
(b)
(c)Experimental outputs for circuit III for (a)Vdc=-5 V and (b) Vdc=2 V.
(a)
(b)


## 5. 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 hardware circuit tests. Results are found to be in conformity with the proposed theory.



---

*Source: 390160-2013-04-07.xml*