Lecture 6
Higher Order Filters Using
Inductor Emulation
Inductor Emulation Using Two-port Network
GIC (General Impedance Converter)
GII (General Impedance Inverter)
Gyrator
Positive 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 inductors
i.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
Minimum signal (noise limited)
• 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
Vn2 = Sv(f) = 4kTR, f  0,
where k = 1.381023 J/K is the Boltzmann constant and Sv(f) is expressed in V2/Hz.
• Example: low-pass filter
We compute the transfer function from VR to Vout:
Vout
s   1
VR
RCs  1
2
V
1
From the theorem, we have Sout  f   S R  f  out  f   4kTR 2 2 2 2
.
VR
4 R C f  1
The total noise power at the output:

Pn,out  0
4kTR
2kT
kT
1 u  
df

tan
u

u0 C
C
4 2 R 2C 2 f 2  1
(V2)
Simple Example
Large C, Small R
Large power, large area
Large R, Small C
Large noise, parasitic sensitive