Lecture 6 Higher Order Filters Using Inductor Emulation.
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Transcript of Lecture 6 Higher Order Filters Using Inductor Emulation.
Lecture 6
Higher Order Filters UsingInductor Emulation
Inductor Emulation Using Two-port Network
GIC (General Impedance Converter)
GII (General Impedance Inverter)
GyratorPositive Impedance Inverter
Floating inductor
Gyrator Example
Gyration resistance=1/g1=1/g2=R
Riordan Gyrator
Example
For Gyration resistance=1kΩ
Antoniou GIC
Antoniou GIC
Inductance emulation is optimum in case of no floating inductorsi.e., LC high-pass filters
Example
3rd Order LPF
6th Order BPF
Bruton’s transformation
FDNR
Bruton’s inductor simulation based on FDNR
Most suitable for LC LPF with minimum cap realization
Filter Performance & Design Trade-offs
Transfer function (ω0 , Q or BW, Gain, out-of-band attenuation, etc.)
Sensitivity (component variations, parasitics)
Dynamic range (DR)Maximum input signal (linearity)Minimum input signal (noise)
Power dissipation & Area
Maximum signal (supply limited)
Voltage swing scaling
Power dissipation
For nth order
• Thermal noise of a resistor
The thermal noise of a resistor R can be modeled by a series voltage source, with the
one-sided spectral density
2nV = Sv(f) = 4kTR, f 0,
where k = 1.3810 23 J/K is the Boltzmann constant and Sv(f) is expressed in V2/Hz.
Minimum signal (noise limited)
• Example: low-pass filter
We compute the transfer function from VR to Vout: 1
1
RCs
sV
V
R
out
From the theorem, we have 14
14 2222
2
fCRkTRf
V
VfSfS
R
outRout
.
The total noise power at the output:
C
kT
u
uu
C
kTdf
fCR
kTRP outn
0tan
2
14
4 1
0 2222, (V2)
Simple Example
Large R, Small C Large noise, parasitic sensitive
Large C, Small R Large power, large area