lecture 6 higher order filters using inductor emulation
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/1.jpg)
Lecture 6
Higher Order Filters UsingInductor Emulation
![Page 2: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/2.jpg)
Inductor Emulation Using Two-port Network
GIC (General Impedance Converter)
GII (General Impedance Inverter)
![Page 3: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/3.jpg)
GyratorPositive Impedance Inverter
Floating inductor
![Page 4: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/4.jpg)
Gyrator Example
Gyration resistance=1/g1=1/g2=R
![Page 5: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/5.jpg)
Riordan Gyrator
![Page 6: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/6.jpg)
Example
For Gyration resistance=1kΩ
![Page 7: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/7.jpg)
Antoniou GIC
![Page 8: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/8.jpg)
Antoniou GIC
Inductance emulation is optimum in case of no floating inductorsi.e., LC high-pass filters
![Page 9: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/9.jpg)
Example
3rd Order LPF
6th Order BPF
![Page 10: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/10.jpg)
Bruton’s transformation
![Page 11: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/11.jpg)
FDNR
Bruton’s inductor simulation based on FDNR
Most suitable for LC LPF with minimum cap realization
![Page 12: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/12.jpg)
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
![Page 13: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/13.jpg)
Maximum signal (supply limited)
![Page 14: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/14.jpg)
Voltage swing scaling
![Page 15: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/15.jpg)
Power dissipation
For nth order
![Page 16: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/16.jpg)
• 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)
![Page 17: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/17.jpg)
• Example: low-pass filter
We compute the transfer function from VR to Vout: 1
1
RCs
sVV
R
out
From the theorem, we have 14
14 2222
2
fCRkTRf
VVfSfSR
outRout
.
The total noise power at the output:
CkT
uuu
CkTdf
fCRkTRP outn
0tan2
144 1
0 2222, (V2)
![Page 18: Lecture 6 Higher Order Filters Using Inductor Emulation](https://reader036.vdocuments.mx/reader036/viewer/2022062810/56815b83550346895dc985a4/html5/thumbnails/18.jpg)
Simple Example
Large R, Small C Large noise, parasitic sensitive
Large C, Small R Large power, large area