CHAPTER 5 Low frequency tuned amplifier and oscillator using simulated inductor* * Partial contents of this Chapter has been published in. D.Susan, S.Jayalalitha, Low frequency amplifier and oscillator using simulated inductor, IEEE International Conference on Communication Technology and System Design, Procedia Engineering 3(), pp. (73-736). (SCI- INDEXED). D.Susan, S.Jayalalitha, Low frequency active tuned oscillator using simulated inductor, Research Journal of Applied Sciences, Engineering and Technology. 3 (Accepted & to be published) 55
5. Low frequency tuned amplifier and oscillator using simulated inductor 5. Introduction The tuned amplifiers are of great use when compared with other amplifiers. The reasons are (i) the tuned amplifier consists of a tank circuit comprising an inductor and a capacitor which can be tuned to the desired resonant frequency. It offers low or almost zero impedance to that resonant frequency and provides amplification. At the same time, it offers high impedance to other frequencies and amplify signals of other frequencies to a little extent (ii) The value of the resistance in the tuned circuit is very less which results in low voltage drop and hence low collector power supply is needed (iii) Since the tuned circuit offers very low resistance and employs only reactive components, the power loss is minimum.hence these amplifiers are more efficient than other amplifiers But the use of tuned circuit has certain disadvantages at low frequencies. They are (i) the tuned circuit is highly selective that it cannot be used to amplify signals of low frequency because single low frequency is seldom used. (ii) Tuned amplifiers cannot be used at low frequencies because of the requirement of very large value of L in the tuned circuit. This requirement of high value of L at low frequency is impossible because the size and weight of inductors become exceedingly large and Q becomes very low. Also the passive inductor requires considerable silicon area on IC chip. Hence, inductors are seldom used at such low frequencies. Their characteristics are not perfect. As mentioned in previous chapters, such inductors are not possible to manufacture in monolithic form and it is not compatible with any of the up-to-date techniques for assembling in electronic systems. So, it is necessary 56
Simulated L to replace such a high value of inductor by another one whose behavior is same as that of the basic inductor. 5. Single tuned amplifier The basic block diagram of the single tuned amplifier is given in the Figure 5. Vcc R C C Vo Vsin R R E C E Figure 5.. Circuit diagram of single tuned amplifier with simulated L The circuit consists of a common emitter amplifier with the tank circuit. To design the tuned amplifier for a frequency of Hz and assuming C=. µf, the requirement of L is.54h. Such a large value of inductor is impossible to realize. Hence the inductor value of L=.54 H is replaced by the simulated inductor. The design values of the common emitter amplifier and 57
the simulated inductor are given below. The complete PSPICE simulation circuit diagram using simulated L is given in Appendix A. 5.. Design of Single tuned amplifier and Simulated L Amplifier Design : Given : V V, I ma, 5, S CC C Designed values : Voltage Dividers : R 5.9647, R. k Stabilizat ion resistor and Capacitor : RE k, CE 5nF Tank circuit Design : f Hz, C F L. 536H Simulated L design : L CR C F R. 59k The frequency response of the single tuned amplifier tuned to a cut off frequency of Hz is shown in the Figure 5.. A m p l i t u d e V 8V 4V Resonant frequency = Hz V.Hz Hz Hz.KHz V(R5:) Frequency Figure 5. Frequency response of single tuned amplifier with simulated L 5.3 Hartley oscillator and Colpitts oscillator The essential features of LC oscillators are (i) the tank circuit determines the frequency of oscillation (ii) the amplifier amplifies the oscillations produced by the tank (iii) the network 58
in the feedback path provides positive feed back. A Hartley oscillator is essentially any configuration that uses two series-connected coils and a single capacitor in the feedback network. There is no need to have mutual coupling between the two coil segments. It consists of two inductors in series, which need not be mutual and one tuning capacitor. Diverse sinusoidal oscillator arrangements are illustrated in the technical literature [74-8]. The frequency of oscillation for Hartley oscillator is given by f ---------------------------------------------------------- (5.) ( L L ) C If L L L then f ------------------------------------------------------ (5.) LC The frequency of oscillation for Colpitts oscillator is given by f CC ( C C ) L ---------------------------------------------------- (5.3) If C C C then f -------------------------------------------------- (5.4) LC The basic block diagrams of the Hartley oscillator and the Colpitts oscillator are shown in Figure 5.3 and Figure 5.4 respectively. AMPLIFIER Output TANK CIRCUIT Simulated L Simulated L C Figure 5.3 Block diagram of Hartley oscillator with simulated L 59
AMPLIFIER Output TANK CIRCUIT C C Simulated L Figure 5.4 Block diagram of Colpitts oscillator with simulated L 5.3. Design of Hartley and Colpitts oscillator with simulated L To design the oscillator for Hz and assuming C=.μF, the value of L is.68h for Hartley, using equation (5.) and.536 H for Colpitts using the equation (5.4). Since such a large value is physically not realizable, the passive component L is replaced by the simulated L. The design of oscillators which includes the amplifier and the tank circuit consisting of simulated inductor are given below Amplifier Design : Given : VCC V, IC ma, 5, S Designed values : Voltage Dividers: R 33k, R 3. 99k Stabilizat ion resistor and Capacitor : R k, C.67 F Tank circuit (Hartely oscillator) Design : f Hz, C F L L. 68H Simulated L design : L CR C F E R. 6k Tank circuit (Colpitts oscillator) Design : f Hz, C C F L. 536H Simulated L design : L CR C F R. 59k E The mutual inductance is neglected in the design. The output of the Hartley and colpitts oscillator is given in the Figure 5.5 and Figure 5.6 respectively designed for Hz. 6
A m p l i t u d e 5.V V -5.V s us us 3us V(R44:) Time Figure 5.5. Output wave form of Hartley oscillator for Hz A m p l i t u d e 5.V V -5.V s us us 3us V(R44:) Time Figure 5.6. Output wave form of Colpitts oscillator for Hz 6
5.4 Active tuned oscillator using band pass filter Oscillators like RC phase shift and Wein Bridge can be used for audio frequency ranges. But when tuned oscillators are designed at such low frequencies of audio level, the value of inductors becomes large. So there is need for the use of simulated inductor for the design of tuned oscillators. There are number of applications of oscillators at very low frequencies like bioelectronics, geophysical and control system test in instrumentation [8]. 5.4. Basic Active tuned oscillator The block diagram given in the Figure 5.7 shows the basic active tuned oscillator. It consists of a high Q band pass filter with a hard limiter connected in positive feed back. The output of the band pass filter is a sine wave whose frequency is the centre frequency, f o of the band pass filter. This output is fed back through a limiter which produces a square wave and whose levels are determined by the limiting levels of the limiter.the corresponding frequency is f o. The square wave is then fed to the band pass filter which filters out the harmonics and provides the spectral purity sinusoidal wave as the output at the fundamental frequency f o. The purity of the sine wave will be the direct function of the selectivity of the band pass filter. The frequency stability of the oscillator will be directly determined by the frequency stability of the band pass filter. Band pass filter V o Limiter Figure 5.7 Basic active tuned oscillator 6
5.4. Design of band pass filter using simulated L To design a tuned oscillator for a frequency Hz using the band pass filter, assuming C= 6nF, gives the value of L as 58.5H. Such a high value of inductor can be implemented using the simulated inductor. The band pass filter is obtained from the basic circuit of the LCR resonator given in the Figure.3. of Chapter.By properly connecting the input, output and ground nodes of the parallel LCR circuit ie., in proper mode, it will act as a band pass filter. The transfer function of such filter is given by T s s CR ---------------------------------------------------------------- (5.5) s s CR LC The frequency response of the band pass filter for the centre frequency f o =Hz is shown in the Figure 5.8. A m p l i t u d e V 5V Cut off frequency = Hz V.Hz Hz Hz.KHz KHz KHz V(U3:OUT) Frequency Figure 5.8 Frequency response of band pass filter 63
5.4.3 Design of active tuned oscillator Design values: Single tuned Oscillator f Hz, C C 6nF, L 58.47H, R 99.53k, R R pot (5 5) k 6 k, 5.4.4 Active tuned oscillator using Simulated L The oscillator uses a variation in the band pass filter based on Antoniou inductor simulation circuit as shown in Figure 5.9. The resistor R and C 4 are interchanged. The complete oscillator circuit is shown in Figure 5.. The resistor R 6 and the two diodes are used as level limiters. The circuit is simulated using PSPICE. The sine wave obtained at the point V is shown in Figure 5.. A _ + R R R R 3 C4 Vi C + _ A R 5 Figure 5.9 Band pass filter using simulated L obtained from parallel LCR circuit 64
R pot Simulated L C V R6 V D D Comparator V3 Integrator V4 D3 D4 Figure 5. Active tuned oscillator circuit using simulated L A m p l i t u d e.v V -.V 37ms V(R6:) 35ms 4ms 45ms 5ms Time Figure 5. Output waveform at point V 65
After getting the sinusoidal wave, the non sinusoidal waveforms can be obtained by using suitable additional circuits. A square wave is obtained at point V 3 by using a suitable comparator and a diode limiter consisting of back to back diodes. A triangular wave is obtained by using the integrator with suitable designed values. The square wave and triangle wave obtained at point V 3 and V 4 are shown in Figure 5. and 5.3 respectively. A m p l i t u d e 4.V V -4.V 3ms V(D5:A) 35ms 4ms 45ms 5ms Time Figure 5. Output waveform at point V 3 66
A m p l i t u d e.v V -.V 39ms V(C3:) 35ms 4ms 45ms 5ms Time Figure 5.3 Output waveform at point V 4 5.4.5 Effect of Quality factor The Quality factor of the filter is a very important parameter that affects the purity of the sine wave. The circuit is simulated for different values of R pot which decides the Q factor. The Table.5. shows the value of Q for different values of R and their corresponding settling time. Table 5. shows the value of Q for different values of R and their corresponding THD. The Figures 5.5(a-f) shows the amount of THD present in the sine wave for different values of R. The response of the circuit simulated for R pot = kω and designed for a frequency of Hz gives the Total Harmonic Distortion (THD) as 5% which is calculated using MATLAB.For this lowest THD and R pot = kω, the value of Q is found to be and it is calculated using the equation Q CR pot. The purity of wave increases with high value of Q thereby decreasing the value of THD. But this increases the settling time. Hence optimum value of Q and settling time is required. Figure 5.4 (a-b) shows the settling time for the generated waveform for different values of R 67
A m p l i t u d e.v V -.V s ms ms 3ms 4ms 5ms V(R6:) Time Figure 5.4 a Sine wave generated showing the settling time for R=5Kohm A m p l i t u d e.v V -.V s ms ms 3ms 4ms 5ms V(R6:) Time Figure 5.4 b Sine wave generated showing the settling time for R=Kohm 68
Mag Table 5. Sine wave generated with different values of R and its corresponding values of Q and settling time Value of R (KΩ) Value of Q Settling time 5.54 48.54ms 75.7536 75.877ms.48 97.87ms 5.56 9.737ms 5.57 43.86ms.96 7.55ms FFT window: of 5.5 cycles of selected signal - -.88.9.9.94.96.98 Time (s).5 For 5Kohm Fundamental (Hz) =.449, THD=.6%.5 3 4 5 6 7 8 9 Frequency (Hz) Figure 5.5 a. The sine wave and the frequency spectrum for 5 Kohm 69
Mag Mag FFT window: of 8. cycles of selected signal - -.46.48.5.5.54 Time (s).5 For 75Kohm Fundamental (94Hz) =.44, THD=.86%.5 94 88 8 376 47 564 658 75 846 94 Frequency (Hz) Figure 5.5 b. The sine wave and the frequency spectrum for 75 Kohm FFT window: of 3 cycles of selected signal - -.84.86.88.9.9 Time (s).5 For Kohm Fundamental (Hz) =.435, THD= 9.93%.5 3 4 5 6 7 8 9 Frequency (Hz) Figure 5.5 c. The sine wave and the frequency spectrum for Kohm 7
Mag Mag FFT window: of 3 cycles of selected signal - -...4.6.8 Time (s).5 For 5 Kohm Fundamental (Hz) =.435, THD= 7.3%.5 3 4 5 6 7 8 9 Frequency (Hz) Figure 5.5 d. The sine wave and the frequency spectrum for 5 Kohm FFT window: of 3 cycles of selected signal - -...4.6.8 Time (s).4..8.6.4. For 5 Kohm Fundamental (Hz) =.38, THD= 5.4% 3 4 5 6 7 8 9 Frequency (Hz) Figure 5.5 e. The sine wave and the frequency spectrum for 5 Kohm 7
Mag FFT window: of 3 cycles of selected signal - -.6.6.64.66.68 Time (s).5 for kohm Fundamental (Hz) =.44, THD= 4.8%.5 3 4 5 6 7 8 9 Frequency (Hz) Figure 5.5 f. The sine wave and the frequency spectrum for Kohm Table 5. Sine wave generated with different values of R and its corresponding values of Q and THD Value of R Value of Q Total Harmonic distortion(thd) 5 KΩ.54.7% 5 KΩ.7536 9.9 KΩ.48 6.94 5KΩ.56 6. 5 KΩ.57 6.6 KΩ.96 5.75 7
5.5 Conclusion This chapter dealt with the generation of the different types of waveforms at low frequency using the single tuned amplifier, Oscillators namely the Hartley and Colpitts oscillator and the active tuned oscillator. All these circuits make use of the simulated inductor and the results are presented. 73