模拟电路教程_ADC

dθ(ω) ∆ω dω
1 ][ ω (1 - ∆ω ω )]
(
dθ(ω) dω
-
θ(ω) ω
) ∆ω ω
© © 2005 H.K. Page 12
EECS 247 Lecture 2: Filters
Wgnitude and Phase Impairment
vOUT(t) = A1 G(jω) sin
{ω[ t+
θ(ω) ω
]} +
θ(ω+∆ω) ω+∆ω
+ A2 G[ j(ω+∆ω)] sin Since ∆ω then ∆ω 2 à0 ω <<1 ω
{ (ω+∆ω) [ t +
]}
[ ]
θ(ω+∆ω) ω+∆ω
≅ ≅
[ θ(ω)+
θ(ω) + ω
• • • • • Butterworth Chebyshev I Chebyshev II Elliptic Bessel
– Group delay comparison example
EECS 247 Lecture 2: Filters © © 2005 H.K. Page 1
Filters
H ( jω )
•
τPD ≡ -θ(ω)/ω is called the “phase delay” and has units of time
EECS 247 Lecture 2: Filters
© © 2005 H.K. Page 13
What is Group Delay? Signal Magnitude and Phase Impairment • Phase distortion is avoided only if: dθ(ω) dω • • •
•
EECS 247 Lecture 2: Filters
© © 2005 H.K. Page 15
Summary Group Delay
• Phase delay is defined as: τPD ≡ -θ(ω)/ω [ time] • Group delay is defined as :
τGR ≡ -dθ(ω)/dω [time]
• Inductor Q :
YL =
•
1 Rs + jω L
QL = ω L Rs
Rs
L
Capacitor Q :
ZC =
1 1 + jωC Rp
QC = ω CRp
Rp C
EECS 247 Lecture 2: Filters
© © 2005 H.K. Page 8
Pole Quality Factor
EE247 - Lecture 2 Filters
• Material covered today: – Nomenclature – Filter specifications
• Quality factor • Frequency characteristics • Group delay
– Filter types
© © 2005 H.K. Page 3
EECS 247 Lecture 2: Filters
Filter Specifications
• Frequency characteristics (lowpass filter): – Passband ripple (Rpass) – Cutoff frequency or -3dB frequency – Stopband rejection – Passband gain Phase characteristics: – Group delay SNR (Dynamic range) SNDR (Signal to Noise+Distortion ratio) Linearity measures: IM3 (intermodulation distortion), HD3 (harmonic distortion), IIP3 or OIP3 (Input-referred or outputreferred third order intercept point) Power/pole & Area/pole
jω
s-Plane
ωx
σx
ωP
σ
QP o l e =
ωx 2σ x
© © 2005 H.K. Page 9
EECS 247 Lecture 2: Filters
Bandpass Filter Quality Factor (Q)
H ( jf )
0
Q= fcenter /∆f
0 Magnitude (dB) -3dB
Lowpass Highpass
H ( jω )
Bandpass
H ( jω )
Band-reject (Notch)
H ( jω )
All-pass
H ( jω )
H ( jω )
ω
ω
ω
ω
ω
Provide frequency selectivity
Phase shaping or equalization
3dB
H ( jω )
Transition Band
Stopband Rejection
0
H ( jω )
fc
Frequency (Hz)
f stop
Passband
Stopband Frequency
x 10
f
EECS 247 Lecture 2: Filters
© © 2005 H.K. Page 5
they’re not free of phase distortion
EECS 247 Lecture 2: Filters © © 2005 H.K. Page 14
What is Group Delay? Signal Magnitude and Phase Impairment • If τGR= τPD à No phase distortion vOUT(t) = A1 G(jω) sin ω t - τGR
• The filter output is:
vOUT(t) = A1 G(jω) sin[ωt+θ(ω)] + A2 G[ j(ω+∆ω)] sin[(ω+∆ω)t+ θ(ω+∆ω)]
EECS 247 Lecture 2: Filters © © 2005 H.K. Page 11
What is Group Delay?
Quality factor is defined as:
Q=
X (ω ) Energy Stored → A v e r a g e P o w e r Dissipation R (ω )
EECS 247 Lecture 2: Filters
© © 2005 H.K. Page 7
Inductor & Capacitor Quality Factor
-
θ(ω) ω =0
•
Clearly, if θ(ω)=k ω, k a constant, à no phase distortion This type of filter phase response is called “linear phase” àPhase shift varies linearly with frequency τGR ≡ -dθ( ω)/d ω is called the “group delay” and also has units of time. For a linear phase filter τGR ≡ τPD =k à τGR= τPD implies linear phase Note: Filters with θ( ω)=k ω+c are also called linear phase filters, but
vOUT(t) = A1 G(jω) sin
{ ω [t +
θ(ω) ω
]} +
dθ(ω)
+ A2 G[ j(ω+∆ω)]sin
•
{ (ω+∆ω) [ t + θ(ωω) +( dω
- ω
θ(ω) ∆ω ω
) ]}
•
If the second term in the phase of the 2nd sin wave is non-zero, then the filter’s output at frequency ω+∆ω is time-shifted differently than the filter’s output at frequency ω à “Phase distortion” If the second term is zero, then the filter’s output at frequency ω+∆ω and the output at frequency ω are each delayed in time by -θ(ω)/ω
• If θ(ω)=kω, k a constant, à no phase distortion • For a linear phase filter τGR ≡ τPD =k
EECS 247 Lecture 2: Filters © © 2005 H.K. Page 16
Filter Types Lowpass Butterworth Filter
G(jω) ≡ G(jω)e