Transfer function of an element is.. input signal is.. output signal is... Find w and A?

Question

Transfer function of an element is P(s)=A/(1+10*s). Its input signal is u(t)=sin(wt). its output signal in quasi-stationary state is
y(t)=0.2*sin(wt-45°). Determine the values of w and and A

Answer 1

1/(1 + 10s) describes a simple RC low-pass filter with a pole at s=-0.1 and in this simple case with a sinusoidal excitation, s = jw and w = -0.1

For a low-pass filter, at very low frequencies (w << 0.1) the phase angle is 0 degrees and for very high frequencies the phase angle is -90 degrees. Right at the cutoff frequency, the phase angle is -45 degrees -- and that is what is given as the output, therefore w is 0.1 rad/sec.

Since this is a simple RC network, the amplitude, A, is simply 0.2.

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Answer 2

The 7408 TTL device is a quad 2-input AND gate. It is a positive logic device where the AND gates may be used independently. On any one gate, when either input is low, the output is low. When both inputs are high the output is high. Propagation delay 15 nanoseconds average Current per package 16 milliamperes average The 74LS08 is the LS - Low Power Schottky version of the above gate. '... Typical data Family Description TTL LS Propagation delay (ns)10 Toggle speed (MHz) 33 Power per gate @1 MHz (mW) 2 Typical supply voltage V (range) 5 (4.75-5.25) Introduction year 1976 Remarks Low power Schotky high speed ...( 1 )' '... LS Fan out 5 regular TTL inputs or 10 low power Schottky inputs Regular TTL fan out drives 10 regular TTL inputs or 20 LS TTL inputs LS output provides 8 mA and the input requires 0.4 mA Regular TTL provides 16 mA output and requires 1.6 mA input. Current for regular simple TTL gates about 8 mA plus or minus 50 %. Maximum frequency for regular TTL 35 MHz or 45 MHz for LS TTL. Temperature range (both families) 0 to 70 degrees C de-spiking one 0.01 to 0.1 microfarad disc capacitor for every four gate packages. ... (2)'