A square wave generator in the form of a relaxation oscillat

A square wave generator in the form of a relaxation oscillation circuit is shown in the following figure. For R_1 = R_2, show that the period of the square wave is 2.2RC. If R_1 = 10R_2, what is the oscillation frequency? In the practical circuit an extra pair of matched zener diodes are often included as shown in dotted lines in the figure. Explain qualitatively their functions in the circuit. Based on the circuit shown in the figure, sketch a modified relaxation oscillation circuit which will produce an asymmetrical square wave.

Solution

a)

Period of the Square wave T=2RCln((1+B)/(1-B))

where B=R1/R1+R2

if R1=R2, then B=R1/2R1=1/2

T=2RCln((1+0.5)/(1-0.5))

T=2RC ln(3)=2.2RC

b)

R1=10R2

B=10R2/11R2

B=10/11=0.91

T=2RC ln((1+0.91)/(1-0.91))

=2RC ln( 21.22)

T=6.11RC

c) Due to the zener diode the the amplitude of square wave is limited to the zener VoltageVz