VOLTAGE-CONTROLLED OSCILLATOR USING BJTs

EDITOR: B. SOMANATHAN NAIR

1. INTRODUCTION

Voltage-controlled oscillator (VCO) is a circuit that produces an output frequency which is proportional to the input voltage of the circuit. We can construct a VCO by disconnecting the base resistors R_B1 and R_B2 of an astable multivibrator from V_CC and reconnect them to a new variable power supply V_BB as shown in Fig.1.

2. WORKING PRINCIPLES OF VCO

By disconnecting R_B1 and R_B2 from V_CC, and reconnecting them to a different supply +V_BB, we notice that capacitors charge from this value to +V_CC. The waveforms for this situation are shown in Figs. 2 and 3, respectively. 

            Now, consider the capacitor-charging equation

                                    v_C = V_F ‒ (V_F‒ V_I) exp(‒t/R_BC)  (1)

From Figs. 2 and 3, we find that v_C ≈ 0, V_F = V_CC, and V_I = −V_BB.  Substituting these in Eq. (1) yields

                                                                                            

                                                0 = V_CC ‒ (V_CC‒ V_BB) exp(‒t/R_BC)  (2)       

Rearranging and solving Eq. (2), we get the half-period of oscillation

                         T = R_BC ln [(V_CC‒ V_BB)/ V_CC] = R_BC ln [1+(V_BB/V_CC)]   (3)

           

From Eq. (3) we find that by varying V_BB, we can change the period and hence the frequency of oscillation. Now, full period of oscillation

                  2T = 2R_BC ln [1+(V_BB/V_CC)]   (4)

And hence frequency of oscillation

                                    f_o = 1/2T = 1/2R_BC ln [1+(V_BB/V_CC)]   (5)

3. WAVEFORMS OF VCO

As stated earlier, the waveforms associated with VCO are shown in Figs. 2 and 3, respectively. It can be seen that the waveforms of VCO are the same as those of the astable multivibrator shown in a previous blog with the exception that the capacitor charging voltage rises from ‒V_BB to +V_CC. Varying V_BB then varies the output frequency.

4. SPECIFICATIONS

                                    Variations required in frequency : 1 kHz to 10 kHz

  

5. DESIGN STEPS

The initial design for the astable multi follows the steps we have given in the earlier blog on Design of Astable Multi. We now have to find out the value of V_BB that will yield the vales of capacitors to produce the desired frequency range.

                                                                                                 

Now, for a frequency of 1 kHz, we find from Eq. (5)

                                               

                      1 kHz = 1/2T = 1/2R_BC ln [1+(V_BB1/V_CC)]   (6)

and for a frequency of 10 kHz, we find from Eq. (5)

10 kHz = 1/2T = 1/2R_BC ln [1+(V_BB1/V_CC)]   (7)                                                        

Substituting for V_CC = 10 V, R_B = 1 MΩ, and choosing C = 0.001 μF (or any other suitable value), in Eq. (6), we find

                              1/1 kHz =  2x10⁶ x 0.001x10^‒6 ln [1+(V_BB1/V_CC)]  

                                                ln [1+(V_BB1/10] = 0.5

Taking antilog and after some rearangements, we get

                     V_BB1  = 6.5 V

           

Similarly, for 10 kHz, we find from Eq. (7)

                                    1/10 kHz = 2x10⁶ x 0.001x10^‒6 ln [1+(V_BB2/V_CC)]  

                                                ln [1+(V_BB2/10] = 0.05

Taking antilog and after some rearangements, we get

                     V_BB2  = 0.51 V

            Thus we must have a supply voltage that can be from about 0.5 volt to 6.5 volts for producing a variation in frequency of 1 kHz to 10 kHz. The fully designed VCO is shown in Fig. 4.