Post on 14-Mar-2020
ESE319 Introduction to Microelectronics
12008 Kenneth R. Laker updated 07Dec09 KRL
Active Filters – an Introduction
Active Filters1. Continuous-time or Sampled-data2. Employ active elements (e.g. transistors, amplifiers, op-amps)
a. inductor-less (continuous-time)b. inductor-less & resistor-less (sample-data)c. gain ≥ 1in passband
Vin(s) V
out(s)
Filter circuitG(s)
+
--
+
ESE319 Introduction to Microelectronics
22008 Kenneth R. Laker updated 07Dec09 KRL
Active Filters – an Introduction
Vin(s) V
out(s)
Filter circuitG(s)
+
--
+
G s=aM s
MaM−1 sM−1....a1 sa0
sNbN−1 sN−1....b1 sb0
G s=aM sz1sz2........szM s p1s p2........s pN
M ≤ N Filter Order = N
ESE319 Introduction to Microelectronics
32008 Kenneth R. Laker updated 07Dec09 KRL
Ideal Filter Response Characteristics
∣G∣=∣G j∣=∣V out jV in j ∣
Stop-bandPassband Stop-band Passband
Passband
Lower Stop-band
Upper Stop-band
Stop-band
Lower Passband
Upper Passband
|G| |G|
|G| |G|
1 1
1 1
0 0
00
P P
PL PH SL SH
Low-pass (LP) High-pass (HP)
Bandpass (BP) Bandstop (BS)
ESE319 Introduction to Microelectronics
42008 Kenneth R. Laker updated 07Dec09 KRL
Practical Lowpass Filter SpecificationKey specs:1.2. A
max
3.4. A
min
f B=P /2
f S=S /2
Filter cost increases!1. A
max -> lower
2. Amin
-> larger3. -> larger4. -> 1 S /P
Passband Stop-band
Amax
Amin
Transition band
0
0 P Sz1 z2
selectivity factor = S
P
P
|G| (dB)
ESE319 Introduction to Microelectronics
52008 Kenneth R. Laker updated 07Dec09 KRL
G s=aM sz1sz2........szM s p1s p2........s pN
=>
MatLab is a good tool for this task.
Filter Approximation – Design G(s)
|G|
ESE319 Introduction to Microelectronics
62008 Kenneth R. Laker updated 07Dec09 KRL
Practical Bandpass Filter Specification
SL
PL=SU
PU
SL
PL≠SU
PU
Symmetric bandpass filter
Transition bands
Passband
0 Amax
Amin
Upper Stop-band
Lower Stop-band
SL PL PU SU
SLPL0
Q=PU−PL
0
|G| (dB) Selectivity factors
ESE319 Introduction to Microelectronics
72008 Kenneth R. Laker updated 07Dec09 KRL
Cascade Filter DesignIf N = odd
(N- 1)/2
If N = even
G s=aM s
MaM−1 sM−1....a1 sa0
sNbN−1 sN−1....b1 sb0
=a10 sa00sb10
∏ a2i s2a1i sa0i
s2b1i sb0i=∏G i s
i = 1i = 1 i = 0
(N- 1)/2
G s=aM s
MaM−1 sM−1....a1 sa0
sNbN−1 sN−1....b1 sb0
=∏ a2i s2a1i sa0i
s2b1i sb0i=∏G i s
i = 1
N/2
i = 1
N/2
....G1(s) G2(s) G3(s) GN/2(s)Vin
VoutVo1
Vo2Vo3 Vo(N-1)/2
N = odd => G1(s) 1st order
N = even => G1(s) 2nd order
ESE319 Introduction to Microelectronics
82008 Kenneth R. Laker updated 07Dec09 KRL
2nd order low-pass (LP)
G s=a0
s2s0
Q0
2
∣G j0 ∣=a002
G s=a2 s
2
s2s0
Q0
2
∣G j∞∣=a22nd order bandpass (LP)
2nd order high-pass (LP)
G s=a1 s
s2s0
Q0
2
∣G j0∣=a1Q0
j
j
0
0
0
2Q
0
2Q
0
0
X
X
X
X
O
Oo
j
0
0
2Q
0
X
X
z1=∞z 2=∞
z1=0z 2=0
z 2=∞z1=0
max
|G|a002
0max
max=01− 12Q2
∣a0∣Q
021− 1
4Q2
|G|
0
∣a2∣
max=0/1− 12Q2
∣a2∣Q /1− 14Q2
00
|G|
Gmax
Gmax
0.707 Gmax
a1Q /0
a1Q /20
0 00/Q
1 2
12=02
Gmax
Filter Type s-plane zeros/poles |G|
ESE319 Introduction to Microelectronics
92008 Kenneth R. Laker updated 07Dec09 KRL
2nd order Notch (N)
|G|
|G|
|G|
0
0
0
2nd order LP Notch (LPN)
2nd order HP Notch (HPN)
G s=a2s2N
2
s2s0
Q0
2
N0
∣G j0 ∣=∣a2∣N2
02
∣G j∞∣=∣a2∣
G s=a2s2N
2
s2s0
Q0
2
N0
∣G j0 ∣=∣a2∣N2
02
∣G j∞∣=∣a2∣
X
X
X
X
X
X
O
O
O
O
O
O
j
j
j
0
0
0
0
0
0
0
0
0
0
0
N
N
N
N
N
N
max
max
0
2Q
0
2Q
0
2Q
Gmax
Gmax
∣a2∣
∣a2∣
∣a2∣
∣a2∣N2
02
∣a2∣N2
02
∣a2∣N2
02
∣a2∣2
1 2
12=02
Filter Type s-plane zeros/poles |G|
ESE319 Introduction to Microelectronics
102008 Kenneth R. Laker updated 07Dec09 KRL
vO t =K v I t−td ⇒T j=∣T j∣e j tdIdeal transmission: ∣T j∣=K
j=− t d
=−d jd
=t dGroup Delay
2nd order All-Pass (AP)
G s=a2s2−s
0
Q0
2
s2s0
Q0
2
∣G j0 ∣=∣G j∞∣=∣a2∣
|G|
∣a2∣
0
j
00
0
X
X
O
O0
2Q0
2Q
0 0
−
−2
ESE319 Introduction to Microelectronics
112008 Kenneth R. Laker updated 07Dec09 KRL
Delay Equalization Concept
DelayEqualizerDE
Total Equalized Delay tot =CDE
Cable or Filter tot =CDE
DelayEqualizer
Cable or Filter
equalized data
delay distorted
data
ESE319 Introduction to Microelectronics
122008 Kenneth R. Laker updated 07Dec09 KRL
OP Amp Building Blocks
vO t =−1CR∫v I t dt0
t
V o sV i s
=−1sCR
=−int
s
int=1CR
Inverting Integrator Summer
V =−R fR1
V 1R3
R2R31
R fR1
V 2.
R2R2R3
1R fR1
V 3
v¿
v−¿
ESE319 Introduction to Microelectronics
132008 Kenneth R. Laker updated 07Dec09 KRL
Two-Integrator-Feedback-Loop Active FilterV hp s=
K s2
s2s0
Q 02V is=
K
1 1Q
0
s02
s2
V is
V hp s=−V hp s1Q
0
s −V hp s02
s2K V i s
V i
V hp−0
sV hp=V bp
02
s2V hp=V lp
V hp −0
sV hp
02
s2V hp
−0
s−0
s
−0
s −0
s
-1
K
1Q
=>
02
s2V hp
−0
s V hp
V iV hp
1 /Q
−1
Kint=1CR
=0
V hp sV hps 1Q
0
s V hp s02
s2=K V i s=>
02
s2V hp 0
2
s2V hp−0
sV hp
−0
sV hp
ESE319 Introduction to Microelectronics
142008 Kenneth R. Laker updated 07Dec09 KRL
Feedback Equations
V hp=− 1Q 0
s 02
s2 V hpK V i
Ghp s=V hp
V i=
K
1 1Q
0
s02
s2
=K s2
s20
Qs0
2
ESE319 Introduction to Microelectronics
152008 Kenneth R. Laker updated 07Dec09 KRL
Feedback Equations IIV hp
V i=
1
K 1Q
0
s02
s2
=K s2
s20
Qs0
2High Pass Output:
Bandpass Output:V bp
V i=−0
sV hp
V i=−
K0 s
s20
Qs0
2
Lowpass Output:V lp
V i=−0
sV bp
V i=
K02
s20
Q s02
ESE319 Introduction to Microelectronics
162008 Kenneth R. Laker updated 07Dec09 KRL
ESE319 Introduction to Microelectronics
172008 Kenneth R. Laker updated 07Dec09 KRL
Implementation
Inverting Integrators
Summing Amp
V hp=−0
2
s2V hp−
1Q
0
sV hpK V i
R3
R2
R f
R1
R RC C
V hp
V bp
V lpV i
−0
sV hp=V bp
02
s2V hp=V lp
V hp=−R fR1 0
2
s2 V hpR2
R2R3 1 R fR1 −0
s V hpR3
R2R3 1 R fR1 V i
ESE319 Introduction to Microelectronics
182008 Kenneth R. Laker updated 07Dec09 KRL
Implementation II
V hp=−02
s2 V hp−2R2R2R3 0
s V hp2R3R2R3
V i
R f=R1Set: And compare terms:
V hp=−02
s2 V hp−1Q 0
s V hpKV i
R3R2
=2Q−1Q=R2R32R2
⇒Q=12 1 R3R2 =>
circuit symbolic Eq.
spec/numerical Eq.
V hp=−R fR1 0
2
s2 V hpR2
R2R3 1 R fR1 −0
s V hpR3
R2R3 1 R fR1 V i
ESE319 Introduction to Microelectronics
192008 Kenneth R. Laker updated 07Dec09 KRL
K – Q DependenceR3R2
=2Q−1
K=2R3R3R2
=2R3R2
1R3R2
= 2 2Q−112Q−1
=2− 1Q
Only Q or K can be the independent variable!
From previous slide: K=2 R3R2R3
ESE319 Introduction to Microelectronics
202008 Kenneth R. Laker updated 07Dec09 KRL
Design Equations
R f=R1
R3R2
=2Q−1
KQ=R3R2
=2Q−1⇒K=2− 1Q
RC= 10
Given , choose C, calculate R
Choose Rf, Calculate R1 or vice-versa.
Given Q, choose R2, calculate R3 or vice-versa.
K is fixed by choice of Q.
We have two independent parameters ( and Q, or K) and threeindependent components (C, Rf (or R
1), and R2(or R
3)).
0=2 f 0
0
ESE319 Introduction to Microelectronics
212008 Kenneth R. Laker updated 07Dec09 KRL
RestrictionsSince
When Q = 1/2:
V hp
V i=
K s2
s22002=
K s2
s0 2
We have 2 real and equal poles.
For Q > 1/2, we are restricted to complex conjugate poles.
K=2− 1Q 0⇒Q1/2
ESE319 Introduction to Microelectronics
222008 Kenneth R. Laker updated 07Dec09 KRL
Adding Finite Zeros – (Notches)To be able to create notches in the response, we need anothersumming amplifier:
Where the weighted inputs come from the highpass,bandpass, and lowpass outputs of the feedback circuit.
V hp
V bp
V lp
V o
ESE319 Introduction to Microelectronics
232008 Kenneth R. Laker updated 07Dec09 KRL
Notch CreationAll the output point transfer functions contain the samedenominator, so only the numerator terms will be affected:
G s=− RFRH V hpRFRBV bp
RFRLV lp
G s=−KRF /RH s
2−RF /RB0 sRF /RL02
s20 /Q s02
For a notch at , no connection is made to Vbp, i.e. =N
RL
RFRHRB
V hp
V bp
V lp
V o
RB=∞
ESE319 Introduction to Microelectronics
242008 Kenneth R. Laker updated 07Dec09 KRL
ESE319 Introduction to Microelectronics
252008 Kenneth R. Laker updated 07Dec09 KRL
“Big Picture” Filter Design Tasks1. Design G(s) from filter specs.2. Determine filter structure (block diagram) to realize G(s).3. Determine filter circuit(s) to implement structure.4. Determine component values.
Filter Design CAD Tools on the Market1. MatLab - Mathworks2. FILTER PRO – Texas Instruments3. Aktiv Filter – New Wave Instruments4. Filter Lab – Microchip5. Filter Wiz Pro – Schematica6. FilterCAD – Linear Technology
ESE319 Introduction to Microelectronics
262008 Kenneth R. Laker updated 07Dec09 KRL
ESE319 Introduction to Microelectronics
272008 Kenneth R. Laker updated 07Dec09 KRL
ESE319 Introduction to Microelectronics
282008 Kenneth R. Laker updated 07Dec09 KRL
ESE319 Introduction to Microelectronics
292008 Kenneth R. Laker updated 07Dec09 KRL
R2n=R fn=R1n=10
ESE319 Introduction to Microelectronics
302008 Kenneth R. Laker updated 07Dec09 KRL
ESE319 Introduction to Microelectronics
312008 Kenneth R. Laker updated 07Dec09 KRL
ESE319 Introduction to Microelectronics
322008 Kenneth R. Laker updated 07Dec09 KRL
(MFM)