Question

Determine the magnitude (in dB) and phase (in degrees) of H(ω) at ω=1 if H(ω) equals:

(a) 0.05 dB
(b) 125
(c) 2+jω/10jω
(d) 3/1+jω + 6/2+jω [2.5+2.5+2.5+2.5 Marks ]

Answer 1

To determine the magnitude and phase of H(ω) at ω=1 for each component, constant components have a 0-degree phase while the decibel magnitude can be determined directly or via a logarithmic conversion. For the complex components, magnitude and phase require separate calculations using polar form representation and summing terms where necessary.

Step-by-step explanation:

To determine the magnitude (in dB) and phase (in degrees) of H(ω) at ω=1 for each given H(ω):

1. For the constant value 0.05 dB, the magnitude is already given in decibels and since it is a constant, the phase is 0 degrees.
2. For the constant value 125, we must convert this to dB using 20*log10(125) which gives us 42 dB approximately, and again the phase is 0 degrees since it's a constant.
3. For 2+jω/10jω, we calculate the magnitude at ω=1, |H(1)| = |2+1/10j| which results in a magnitude of 20*log10(|2+j0.1|) dB, and a phase angle of arctan(0.1/2) degrees.
4. For 3/1+jω + 6/2+jω, we calculate |H(1)| individually for each term and sum the magnitudes considering the phase angles. First, we find |3/1+j| and |6/2+j| at ω=1, giving us 20*log10(|3/1+j|) + 20*log10(|6/2+j|) dB for the magnitude, and the phases will be the sum of arctan(1/1) plus arctan(1/2) degrees.

We then compute the decimal values to get the final results for magnitude and phase.