Analog Filters for Telecommunications Active-RC Filters

183 Pages·2005·11.95 MB·English

Dipartimento di Ingegneria dell' Innovazione
Universita' degli Studi di Lecce

Andrea Baschirotto

[email protected]

Analog Filters for Telecommunications

Universita’ degli Studi di Bologna
June, 16th-17th, 2005

Active-RC Filters
A. Baschirotto, “Analog Filters for Telecommunications” 86
1st order cell
Filter Frequency Response
• First order cell
1+s(cid:2)(cid:1)
H(s) = A (cid:2) z
o
1+s(cid:2)(cid:1)
p
• Passive implementation
• Specific cases
1 s(cid:1)R(cid:1)C
H (s) = H (s) =
LP HP
1+s(cid:1)R(cid:1)C 1+s(cid:1)R(cid:1)C

• Zero power consumption
• Non-zero output impedance
• Useful for infinite input impedance block to be fed by this filtering stage
A. Baschirotto, “Analog Filters for Telecommunications” 87
Active-RC Filters
Basic building block: The integrator
C
v
i
v
o
R

1
H(s) = –
s(cid:1)R(cid:1)C

• The building block for ladder structures

A. Baschirotto, “Analog Filters for Telecommunications” 88
Active-RC Filters
1st order cell: Filter Frequency Response

R 1+s(cid:1)R (cid:1)C
2 1 1
H(s) = – (cid:1)
R 1+s(cid:1)R (cid:1)C
1 2 2
• The ratio R /R defines the dc-gain
2 1
• Their absolute values are defined by other parameters (noise, dynamics, etc ….)
• Non-zero power consumption due to the opamp
• Zero output impedance
• Output load (of following stages) can be driven
A. Baschirotto, “Analog Filters for Telecommunications” 89
2nd order cell (Biquadratic) cell
2 2
(s +s(cid:2)(cid:1) /Q +(cid:1) )
z1 z1 z1
H(s) =
2 2
(s +s(cid:2)(cid:1) /Q +(cid:1) )
p1 p1 p1
• Complex poles/zeros are present
(cid:1) A passive RC implementation is not possible (a regenerative loop is need to have
complex poles)

• Possible Active-RC implementations
(cid:1) Single-Opamp Biquad
(cid:1) Sallen&Key Biquadratic cell
(cid:1) Rauch Biquadratic cell
(cid:1) Multi-Opamp Biquad
(cid:1) Kerwin-Huelsman-Newcomb (KHN) Biquadratic cell
(cid:1) Tow-Thomas Biquadratic cell
A. Baschirotto, “Analog Filters for Telecommunications” 90
Single-Opamp Biquad
Sallen&Key Biquadratic cell

V Z `(cid:1)Z `
o 1 2
H(s) = =
V (Z +Z +Z `)(cid:1)Z `+Z (cid:1)Z
i 1 2 2 1 1 2

• The opamp is in a buffer configuration
• The opamp output swing is present at the opamp input nodes
(cid:1) The input stage may be critical
A. Baschirotto, “Analog Filters for Telecommunications” 91
Single-Opamp Biquad
Sallen&Key Biquadratic cell
• Low-pass frequency response Z1 = Z2 = R

C1 1
Z '=
1 s C
1
R R
vi
1
C2 vo Z '=
2 s C
2

1
H(s) =
2 2
1+ 2(cid:1)R(cid:1)C (cid:1)s+R (cid:1)C (cid:1)C (cid:1)s
2 1 2

1 1 C
(cid:1) = Q= (cid:1) 1
o
C (cid:2)C (cid:2)R 2 C
1 2 2
2 (cid:2)Q 1
C = C =
1 2
R(cid:2)(cid:1) 2 (cid:2)Q(cid:2)R(cid:2)(cid:1)
o o
• In-band maximally-flat frequency response for (Q= 2 2)
1 1
C1 = 2·C2 f = (cid:2)
p
2(cid:2)(cid:1) 2 (cid:2)R(cid:2)C
A. Baschirotto, “Analog Filters for Telecommunications” 92
Single-Opamp Biquad
Sallen&Key biquad
• Noise performance
C1
R R
vi
C2 vo

2 2
V = 2(cid:1)4(cid:1)k(cid:1)T (cid:1)R+V
n_out n_opamp

• Linearity performance
(cid:1) Good linearity for closed loop configuration
(cid:1) For out-of-band signal a 2·R-C prefilter increases out-of-band linearity
2
A. Baschirotto, “Analog Filters for Telecommunications” 93
Single-Opamp Biquad
Sallen&Key biquad
• Parasitic capacitance sensitivity
C
1
R R
v
i
v
o
C C
p p
C
2

• The transfer function is affected by the parasitic capacitance at the two nodes
A. Baschirotto, “Analog Filters for Telecommunications” 94
Single-Opamp Biquad
Sallen&Key Biquadratic cell
• Lowpass configuration: Design issue
C1
(cid:1) In the passband no current flows on the
R R
resistances (even if they are non vi
linear, non harmonic distortion C2 vo
results).

• Low pass Sallen and Key filter with real op-amp:
• A real op-amp used in CMOS monolithic
S&K filter is a transconductance op-amp

A. Baschirotto, “Analog Filters for Telecommunications” 95