Question

frequency response, bode plot

Answer 1

@nubeer

Answer 2

yes

Answer 3

\( \LARGE G(s) = \frac{10}{s+10}\)

Answer 4

umm yes so we would take 20log 10?

Answer 5

its basically asking, how is if you go on by changing the value of "S"

Answer 6

\[\frac{ 10 }{ 10+j \omega } \]

Answer 7

yes.

Answer 8

but you might as well write that as \[\large \frac{ 10 }{ 10(1+\frac{ j \omega }{ 10 }) }\]

Answer 9

umm yes..

Answer 10

which is \[\frac{ 10 }{ 1+j \frac{ \omega }{ 10 } }\] and what would be the magnitude?

Answer 11

hmm wouldn't that 10 in numerator would be cancelled out by the denominator one?

Answer 12

one step at a time :)
magnitude is: \[|G| = \frac{ 1 }{ \sqrt{1+\frac{ \omega ^2 }{ 10^2 }} }\]

Answer 13

ok.. getting so far.

Answer 14

when \( \omega\) is very very small, you know that \( \omega <<10\)

Answer 15

and |G| will be tending to 1

Answer 16

yes.

Answer 17

and hence, 20log(|G|) = 0

Answer 18

approximately 0 db

Answer 19

yes makes sense.. so a straight horizontal line at 0 db?

Answer 20

now let's take a look at when \( \omega >> 10\)

Answer 21

calling \(\frac{\omega}{10}=x\) you can get \[\frac{ 1 }{ \sqrt{1+x^2} }\]

Answer 22

but the \(x^2\) will be dominating under there.

Answer 23

so you can approximate it to \(\huge|G| = \frac{1}{\frac{\omega}{10}}\)

Answer 24

which is same thing as \(\huge \frac{10}{\omega}\)

Answer 25

yes.

Answer 26

ok give me a minute for the next part im gonna try and cram it all lol. i was practicing my latex haha

Answer 27

hahha no worries.

Answer 28

when \(\omega\) is equal to 10 omega by 10 is equal to 1.
so log of 1 = zero.

if you increase the frequency, persay, by some fold, 10-fold at some other frequency, 2 \(10\times \omega_1\) = \(\omega_2\)
.
\(log_2(10 \omega)_1\) what value do u get? meaning, increasing the frequency 10 times from anywhere, you simply get \(log(10)+log(\omega_1\)

Answer 29

log(10) = 1 and so you are basically adding 1 per frecqueyc. but in this example, omega is in the denominator, so you're actually subtracting 1.

Answer 30

-log\((\omega)\)

Answer 31

degree?