PRACTICAL DESIGN OF PHASE-SHIFT OSCILLATOR USING BJT

EDITOR: B. SOMANATHAN NAIR

1. INTRODUCTION

RC phase-shift oscillators (PSOs) are a very popular type of sinusoidal oscillators in the audio-frequency range. In this article, we give practical designs of three different types of PSOs, which are shown, respectively, in Figs. 1, 2, and 3. In Types 1 and 2, we use phase-leading networks and in Type 3, we use phase-lagging network as the B (feedback) network.

2. DESIGN OF RC PSO USING PHASE-LEAD NETWORK: TYPE 1

SPECIFICATIONS

·        Output voltage swing                      :           4.5 V

·        Current swing                                  :           1 mA

·        Frequency of oscillation                 :           1 kHz

DESIGN PROCEDURE

Steps 1 to 6: Standard-Amplifier Design

We first complete the design of the Standard Amplifier following the steps given in our blog on RC-coupled amplifier. Since the voltage gain required for the PSO is -29, we need use only one stage of a CE amplifier employing partial feedback. Figure 1 shows the RC PSO with a partial feedback network incorporated in it. This network consists of the emitter potentiometer R_E and the emitter bypass capacitor C_E connected between the variable arm of the pot and the earth. The pot is adjusted to produce the required gain of 29 exactly.

Step 7: Design of the Feedback Network

Frequency of oscillation of the PSO of Type 1 is given by                               

                                                            f_o  = 1/2πRC√[6+4(R_C/R)]  (1)

In the given problem, f_o = 1 kHz. To find R and C, we first fix C because capacitors with only specified values are available in the open market. Here, we choose

                                                                 C = 0.01 mF

Then substituting given values in Eq. (1) and solving the resultant quadratic yields the value of R as                            

                                                R = 4.5 kW; choose 4.7-kW resistors

Step 8: Design of Resistor R¢

In the third RC section, the resistor R is replaced by a resistor R¢ whose value is given by

                                                            R¢ = R ‒ h_ie (2)

                                                                                                                                     

where h_ie is the input impedance of the BJT amplifier in the hybrid model. The reason for this modification in the value of R stems from the fact that the third-section resistor comes in series with h_ie and therefore h_ie has to be taken into account of in calculating the value of R. Assuming that typical value of h_ie = 1.5 kW, we find

                                                R¢ = R ‒ h_ie = 4.7 k‒1.5 k = 3.3 k

The completely designed RC phase-shift oscillator Type 1 is shown in Fig. 1.

Note: An important question that can arise in the case of the RC PSOs is: Will the three RC sections produce equal amount of phase-shift or are they different?  

To answer this question, let us inspect the feedback network consisting of the three RC sections shown in Fig. 1. In this network, we notice that the rightmost (third) RC section is not loaded by any subsequent stages and hence its phase-shift can be greater than 60º (and of course, less than 90º).             The middle (second) RC section is loaded by the third RC section; hence it will produce a phase-shift less than that produced by the third RC section. Therefore, to a good guess, we can assume that it produces a phase-shift of 60º.             The leftmost (first) RC section is loaded by the third and second RC sections; hence it will produce a phase-shift less than that produced by the second RC section. This suggests that this section will produce a phase-shift of less than 60º.             Thus we may therefore conclude that the first RC section will produce a phase-shift of less than 60º, while the middle RC section will produce a phase-shift of 60º and the last RC section will produce a phase-shift of greater than 60º. For example, we may assume the phase-shifts to be 59º, 60º and 61º, respectively.

2. DESIGN OF RC PSO USING PHASE-LEAD NETWORK: TYPE 2

Figure 2 shows a PSO in which collector resistor R_C is also a part of the feedback network. Hence, the expressions for oscillations become

                                                         f_o  = 1/2πRC√6  (3)                                         

            In this design, since R_C is also the collector resistor, there exists an upper limit on the value of R_C. This limit is dependent on the maximum value of the output impedance of the CE amplifier, which is typically about 80 kW. Therefore, value of R_C should be much less than this upper limit. R_C may be hence be chosen to be between 4.7 kW and 10 kW. We employ partial feedback in this case also for adjusting the gain. The design follows the design steps given above. The completely designed circuit for a frequency of oscillation of 1 kHz is shown in Fig. 2.

 

  

3. DESIGN OF RC PSO USING PHASE-LAG NETWORK: TYPE 3

Figure 3 shows a PSO which makes use of a phase-lag network as the feedback network. From analysis, we get the expressions for oscillations as

                                                         f_o  = √6/2πRC (4)

DESIGN PROCEDURE

Design steps are exactly similar to those of Type 1. However, we use two coupling capacitors of 10 microfarads each in this case to provide DC isolation for the feedback network.

  

 Note: To generate pure sinusoids, the following steps must be taken.

·                   Feedback network must be isolated from the amplifier part by using coupling capacitors. If DC is permitted to flow through the B network, then oscillations will never take place.

·                   For maximum output swing, the operating point must be kept exactly in the middle of the active region of operation of the BJT.

·          Figure 4 shows a distorted waveform. We notice that the amplitude is unsymmetrical about the x axis. This is due to the shift in the Q-point from the middle of active region, i.e., if the Q-point is not exactly in the middle of the active region, then the waveform becomes unsymmetrical.

·                        Figure 5 shows a clipped sinusoid. This results in when the gain of the amplifier is much greater than 29. This can be corrected, by slowly adjusting the 1-kΩ potentiometer until a pure sinusoid appears on the screen of an oscilloscope.