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3 years ago

6

Consider a sinusoidal oscillator consisting of an amplifier having a frequency-independent gain A (where A is positive) and a se

cond-order bandpass filter with a pole frequency ω0, a pole Q denoted Q, and a positive center-frequency gain K.
a) Find the frequency of oscillation, and the condition that A and K must satisfy for sustained oscillation.

1 answer:

mafiozo [28]3 years ago

4 0

Sinusoidal oscillator frequency of oscillation is given below.

Explanation:

The criterion for a stable oscillator is given in the equation

l A(jw)β(jw) l ≥ 1

In this task A represents the gain of the amplifier , and

β represents gain/attenuation of the second-order bandpass filter.

This sinusoidal oscillation is a special edge case where the product is equal to one.

So the condition is A-K=1

to obtain the sustained oscillations at the desired frequency of oscillations, the product of the voltage gain A and the feedback gain β must be one or greater than one. In this case, the amplifier gain A must be 3. Hence, to satisfy the product condition, feedback gain β must be 1/3.

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Consider a single crystal of some hypothetical metal that has the BCC crystal structure and is oriented such that a tensile stress is applied along a [121] direction. If slip occurs on a (101) plane and in a [111] direction, compute the stress at which the crystal yields if its critical resolved shear stress is 2.9 MPa.

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Explanation:

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The critical yield resolved shear stress is $\sigma = 2.9Mpa$

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$\lambda = cos^{-1} [\frac{(u_1 u_2 + v_1 v_2 + w_1 w_2}{\sqrt{u_1^2 + v_1 ^2+ w_1^2})\sqrt{( u_2^2 + v_2^2 + w_2 ^2)} } ]$

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$\O = cos^{-1} [\frac{(u_1 u_3 + v_1 v_3 + w_1 w_3}{\sqrt{u_1^2 + v_1 ^2+ w_1^2})\sqrt{( u_3^2 + v_3^2 + w_3 ^2)} } ]$

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$\O = cos^{-1} [\frac{1* 1 + 2*0 + 1*1 }{\sqrt{1^2 + 2^2 + 1^2 } \sqrt{(1^2 + 0^2 + 1^2 )} } ]$

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$\sigma = \frac{\tau_c}{cos \O cos \lambda }$

$= \frac{2.9}{cos 54.74^o cos 61.87^o}$

$= \frac{2.9}{0.2722}$

$\sigma = 10. 655 MPa$

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