Oscillator circuit

Thread Starter

xxxyyyba

Joined Aug 7, 2012
289
Hello. Here is my task:

burdalic.png

Oscillator circuit is shown.
a) Calculate frequency of oscillations,
b) Calculate minimum value R1 for which circuit still oscillates,
c) Calculate amplitude of voltage VB, for which voltage VA start cuting off

Vz=6.3V, R1=100K, R2=120K, R3=470, R4=2R6=10K, C1=C2=100nF, Vd=0.7V, R4=R5.

I completed task a) and task b)
I got f_oscillations=232.7Hz and R1_min=250k.
I don't know how to solve task c)
Any idea?
Thanks in advance.
 

Jony130

Joined Feb 17, 2009
5,186
Well, find Vb/Va = gain for Fo and do you know the "cutting off" voltage for this simple diode limiter?
VA start cutting off = "cutting_off voltage" * gain.
 

Thread Starter

xxxyyyba

Joined Aug 7, 2012
289
burdalic.png

\(
-I_1-I_2+I_3+I_4=0,
-\frac{V_B}{R_1}-\frac{V_A-V_X}{R_2}+\frac{V_X-V_B}{\frac{1}{sC_2}}+\frac{V_X}{R_3}=0,
\frac{V_B}{R_1}=-\frac{V_X}{\frac{1}{sC_1}}=-sC_1V_X\Rightarrow V_x=-\frac{V_B}{R_1C_1s},
V_X(\frac{1}{R_2}+sC_2+\frac{1}{R_3})-V_B(\frac{1}{R_1}+sC_2)=\frac{V_A}{R_2},
-\frac{V_B}{R_1C_1s}(\frac{1}{R_2}+sC_2+\frac{1}{R_3})-V_B(\frac{1}{R_1}+sC_2)=\frac{V_A}{R_2},
\frac{V_B}{R_1C_1s}(\frac{1}{R_2}+sC_2+\frac{1}{R_3})+V_B(\frac{1}{R_1}+sC_2)=-\frac{V_A}{R_2}\)
And we can find now VB/VA. Is it ok?
 
Last edited:

Jony130

Joined Feb 17, 2009
5,186
But the gain is depend on s. My formula is a valid only at Fo. And if you solve for Vb(s)/Va(s) you already have a voltage gain expression.
All you need is to find gain at Fo frequency.
burdalic.png
 

Thread Starter

xxxyyyba

Joined Aug 7, 2012
289
Jony30,
I got same result as you in post #5 using analysis in post #4.
I got w0=sqrt((R2+R3)/(R1*R2*R3*C1*C2))=924.3361 rad/s
 

Jony130

Joined Feb 17, 2009
5,186
Good for you.
And the transfer function (if i do not make any error) in standard form is :
\(\frac{V_b}{V_a} =-\frac{ \frac{1}{C2 R2}s } { s^2+\frac{(C1+C2)}{C1C2R1}s\frac{R2+R3}{C1C2R1R2R3}[\tex]\)

T(s) = (a1*s)/(s^2 + ωo/Q + ωo^2)

And the gain at Fo is

Av =(a1*Q)/ωo = (C1 R1)/((C1 + C2) R2)
 
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