Given data,
Frequency = 1/Period.
Frequency = 1/100 x 10^-3 Hz
= 10 Hz

In MOSFET fabrication channel length is defined during Poly-Silicon gate patterning process

The open loop transfer function of a feedback control system is G(s).H(s)=1/(S+1)​ ³
Gain margin=?
→ Here, the formula is -3tan​ ^-1​ (W^{​ pc}​ ) = -180​ ⁰ tan​ ^-1​ (W​ ^pc​ ) = -180^{​ 0}​ /3
= -60​ ⁰
W​ ^pc​ =√3 rad/sec
G(s).H(s)=1/(S+1)​ ³
|G(s).H(s)|=X= 1/(1+W​ _pc​ ²​ )
=1⁄8
G(s).H(s)=1/X
= 8

The final value theorem is used to find the steady state value of the system output

Let x[n] be causal signal given by x[n] = a​ ⁿ​ u[n]
→ The Z-Transform of x[n] is given by

Region of Convergence(RoC)
Region of Convergence for a discrete time signal x[n] is dened as a continuous region in z plane where the Z-Transform converges. In order to determine RoC, it is convenient to represent the Z-Transform as a is rational X(z)=P(z)/Q(z)
1. The roots of the equation P(z) = 0 correspond to the ’zeros’ of X(z)
2. The roots of the equation Q(z) = 0 correspond to the ’poles’ of X(z)
3. The RoC of the Z-transform depends on the convergence of the polynomials P(z) and Q(z).

Given, the signal
V (t) = 3 0 sin 100t + 10 cos 300t + 6 sin (500t + π/4)
So, we have
ω ₁ = 100 rads
ω ₂ = 300 rads
ω ₃ = 500 rads
∴ The respective time periods are
T ₁ = 2π/ω₁ = 2π/100 sec
T ₂ = 2π/ω₂ = 2π/300 sec
T ₃ = 2π/ω₃ = 2π/500 sec
So, the fundamental time period of the signal is
LCM (T ₁ , T ₂ , T ₃ ) =LCM (2π,2π,2π)/HCF (100,300,500)
as T ₀ =2π/100
∴ The fundamental frequency, ω₀ =2π/T ₀ = 100 rad/s

(S/N _q)_dB
= (1.76 + 6 n) _dB
(SQNR) ₁ = 1 .76 + 6 n
(SQNR) ₂ = 1 .76 + 6 n(n + 1 ) = 1 .76 + 6 n + 6
(SQNR) ₂ − (SQNR) ₁ = 1 .76 + 6 n + 6 − 1 .76 − 6 n = 6 dB
So for every one bit increase in bits per sample will result is 6 dB improvement in signal to quantization ratio.

Power in sidebands may be calculated as modulation index.
→ Each sideband is 25%. Total modulation index=1.

Apply Ohms law, the resistance is equal to the voltage divided by the current. The resulting equivalent resistance is 5/6 Ω.
R=E/I
R=(2*(1/2)V)/3A
= ⅚
Note: This is the cube structure consisting of 12 resistors electrically connected between the 8 vertices. Each resistor is 1 Ω, but any value can be used so long as they are all the same.