1. Connection with Transfer Function:
Given: a transfer function G(s),2. Frequency Response Plots of Elementary Transfer Functions
Amplitude Ratio, AR = B/A = |G(iw)| , magnitude of G(iw) and
Phase Shift, f(w) = arg( G(iw) ) , argument of G(iw)
a) Gain3. Transfer Functions in Series.
Transfer Function : K LM vs w : horizontal line at 20 log |K| dB Phase vs w : if K>0, horizontal line at 0o
if K<0, horizontal line at -180ob) First Order Lag
Transfer Function : 1/(ts+1) LM vs w : -low frequency approx a horizontal line at 0 dB
-high frequency approximated by a line sloping at
-20dB/ decade
-at w=1/t, LM = -3dBPhase vs w : -low frequency approx a horizontal line at 0o
-high frequency approx a horizontal line at -90o
-at w=1/t, phase = -45o with a slope= -66o/decadec) First Order Lead
Transfer Function : ts+1 LM vs w : -low frequency approx a horizontal line at 0 dB
-high frequency approximated by a line sloping at
+20dB/ decade
-at w=1/t, LM = +3dBPhase vs w : -low frequency approx a horizontal line at 0o
-high frequency approx a horizontal line at +90o
-at w=1/t, phase = +45o with a slope= +66o/decaded) Second Order Underdamped Lag (z<1)
Transfer Function : 1/ ( t2s2 + 2zts +1) LM vs w : -low frequency approx a horizontal line at 0 dB
-high frequency approximated by a line sloping at
-40dB/ decade
-at w=(1/t)(1-2z2)1/2 LM attains maximum
where the peak increases as z goes towards zeroPhase vs w : -low frequency approx a horizontal line at 0o
-high frequency approx a horizontal line at -180o
-at w=1/t, phase = -90o with a slope= (-132/z)o/decadee) Delay
Transfer Function : exp(-td s) LM vs w : horizontal line at 0 dB Phase vs w : starts at 0o and drops exponentially.
( the larger td is, the earlier the drop occurs )f) Integrator
Transfer Function : 1/(ts) LM vs w : -one line sloping at -20 dB/decade
-0 dB at w=1/tPhase vs w : horizontal line at -90o g) Differentiator
Transfer Function : t s LM vs w : -one line sloping at +20 dB/decade
-0 dB at w=1/tPhase vs w : horizontal line at +90o
Let G(s) = G1(s) G2(s)then
|G(iw)| = |G1(iw)| |G2(iw)|and
or
LM(G) = LM(G1) + LM(G2)arg( G(iw) ) = arg( G1(iw) ) + arg( G2(iw) )
or
f( G ) = f( G1 ) + f( G2 )