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Selected Analog Electronic Circuits
Selected Analog Electronic Circuits
Dr. Lynn Fuller
Webpage: http://people.rit.edu/lffeee
ROCHESTER INSTITUTE OF TECHNOLOGYMICROELECTRONIC ENGINEERING
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 1
Webpage: http://people.rit.edu/lffeeeMicroelectronic Engineering
Rochester Institute of Technology82 Lomb Memorial DriveRochester, NY 14623-5604
Tel (585) 475-2035Email: [email protected]
MicroE webpage: http://www.microe.rit.edu
1-22-2011 Selected_Analog_Circuits.ppt
Selected Analog Electronic Circuits
INTRODUCTION
Analog electronic circuits are different from digital circuits in that the signals are expected to have any value rather than two discrete values. Primitive analog components include the diode, mosfet, BJT, resistor, capacitor, etc,. Analog circuit building blocks include single stage amplifiers, differential amplifiers, constant current sources, voltage references, etc. Basic analog electronic ciruits include the operational amplifier, inverting amplifier, non-inverting
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 2
sources, voltage references, etc. Basic analog electronic ciruits include the operational amplifier, inverting amplifier, non-inverting amplifier, integrator, bistable multivibrator, peak detector, comparator, RC oscillator, etc. Mixed-mode analog integrated circuits include D-to-A, A-to-D, etc.
This document will introduce some selected analog electronic circuits.
Selected Analog Electronic Circuits
OUTLINE
Wien Bridge OscillatorMultiplier ChipConstant PowerConstant TemperatureActive Filters
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 3
Active FiltersOperational Transconductance AmplifiersSwitched Capacitor CircuitsReferencesHomework
Selected Analog Electronic Circuits
WIEN BRIDGE OSCILLATOR CIRCUIT
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 4
CMOS Analog Circuit Design, Phillip Allen, Douglas Holbert, Holt, Rinehard and Winston. 1987, pg 637-639.
Selected Analog Electronic Circuits
LOOP GAIN OF WIEN BRIDGE OSCILLATOR
Let R1 = R2 = R andC1 = C2 = C
Loop gain G(s) =
K s/RC
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 5
CMOS Analog Circuit Design, Phillip Allen, Douglas Holbert, Holt, Rinehard and Winston. 1987, pg 637-639.
s2 + s 3/RC + (1/RC)2
Loop gain G(jw) = jw K/RC
(jw)2 + jw 3/RC + (1/RC)2
If jw = 1/RC and K = 3 then Loop gain = 1+j0and circuit will oscillatewhen loop is closed
Selected Analog Electronic Circuits
WAVEFORM GENERATOR
CR
-
Rf
CR
+
+V
R2R1 VT Rf
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 6
-
+Vo3Vo2
R-
+Vo1-
+
C
-V
RVo1 – SQUARE WAVE
Vo2 – TRIANGLE WAVE
Vo3 – SINE WAVE (approximation)
Selected Analog Electronic Circuits
SPICE RESULTS WAVEFORM GENERATOR CIRCUIT
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 7
Selected Analog Electronic Circuits
WAVEFORM GENERATORS
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 8
Selected Analog Electronic Circuits
MULTIPLIER
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 9
Selected Analog Electronic Circuits
MULTIPLIER AND DIVIDER CONFIGURATION
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 10
Selected Analog Electronic Circuits
INTERNAL CIRCUIT SCHEMATIC FOR THE MULTIPLIER
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 11
CMOS Analog Circuit Design, Phillip Allen, Douglas Holbert, Holt, Rinehard and Winston. 1987, pg 637-639.
Selected Analog Electronic Circuits
MULTIPLIER CHIP APPLICATIONS
MultiplierSquarerDividerSquare Rooter
Constant Power Controller
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 12
Constant Power ControllerConstant Temperature ControllerVoltage Controlled AmplifierLinear AM ModulatorVoltage to Frequency ConverterRMS to DC Converter
Selected Analog Electronic Circuits
GAS FLOW SENSOR
Upstream Polysilicon
Resistor
Polysilicon heater
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 13
Constant heat (power in watts) input and two temperature measurement resistors, one upstream, one downstream. At zero flow both sensors will be at the same temperature. Flow will cause the upstream sensor to be at a lower temperature than the down stream sensor.
Downstream
Polysilicon Resistor
GAS
Selected Analog Electronic Circuits
GAS FLOW SENSOR
R2R1
UpstreamResistor Sensor
DownstreamResistor SensorHeater
Diode Temperature Sensor
600o
hm
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 14
Selected Analog Electronic Circuits
FLOW SENSOR ELECTRONICS
+6 Volts
+
Constant Power Circuit for the Heater
R210 OHMDownstream
Resistor
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 15
Gnd-6 Volts
Vout+-
Vout near Zero so thatit can be amplified
R1
AD534
UpstreamResistor
STOPPLAY
Selected Analog Electronic Circuits
ANEMOMETER
A single resistor with enough power dissipation will self heat to some value. At this elevated temperature the resistance normally increases. As fluid flows across the resistor the heat is carried away. King’s law gives a relationship between the fluid velocity and fluid temperature, power in the heater and the temperature of the heater. If the temperature of the heater is kept constant and the fluid temperature is known the fluid velocity can be found from the power to the heater. (calibration parameters a, b, n)
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 16
Units of flow:sccm = standard cubic cm per min.Slm = standard liter per min.
R Flow = vf x Area
fluid temperature is known the fluid velocity can be found from the power to the heater. (calibration parameters a, b, n)
Vf
Power(Ts – Tf)
b
- a
1/n
=
King’s Law
Selected Analog Electronic Circuits
ANEMOMETER CHARACTERIZATION
I
V1 2 3 4
-4 -3 -2 -1
-0.002
0.0040.0030.002
ColdHot
Resistive Heater on DiaphragmWith integrated diode temperature sensor
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 17
-0.002-0.003-0.004
L,W,xj do not change, µn and µp changes with temperature, n and p does not change much in heavy doped semiconductors (that is, n and p is determined by doping)
R = ρ L/(W xj) ohmsρ = 1/( qµnn + qµpp)
Diode Temperature Measurement
Selected Analog Electronic Circuits
ANEMOMETER CHARACTERIZATION
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 18
Vf
Power(Ts – Tf)
b
- a
1/n
=
Selected Analog Electronic Circuits
AD534 CONSTANT TEMPERATURE CIRCUIT
+9 Volts
I
Setpoint
+ Heater
+-
V
1000
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 19
AnalogDividerUsingAD534
Gnd
+-
Heater
10 Ω
-+
R=V/I
I
Selected Analog Electronic Circuits
WHEATSTONE BRIDGE CONSTANT TEMP CIRCUIT
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 20
Selected Analog Electronic Circuits
POWER OUTPUT STAGE
-Vo
Vin
+V
+V
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 21
+VinRload
-V
-V
Selected Analog Electronic Circuits
OPERATIONAL AMPLIFIER DC CHARACTERIZATION
Vout
+V=+6
Vin
+
- Slope = Gain
Vout
+6
0
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 22
Vout
-V=-6
+
Set up the HP 4145 to sweep the Vin from -20 mV to +20 mVin 0.001V steps. Measure Gain and Input offset voltage.
Vin
-20mV +20mV0Vos
-6
0
Selected Analog Electronic Circuits
MEASURED OPEN LOOP DC GAIN
Vout
+6v
-6v
+
-
100k
1k
Vi
SMU1
SMU2
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 23
-6v
Gain = slope x 100
= 66,000
= 96 dB
Selected Analog Electronic Circuits
FREQUENCY RESPONSE OF AN OP AMP
Vout
+6v
-6v
+
-
100k
100k
1k
+V
C1
Vin
Rb
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 24
Adjust Rb to give Vout = zero with Vin = zero, Then use a network analyzer to collect data for Gain vs Frequency
-V
Selected Analog Electronic Circuits
NETWORK ANALYZER
Quick Measurement Setup for 3577A Network Analyzer (by Jirachai Getpreecharsawas)
Magnitude Plot:
1. Press INPUT button and select input A2. Press DISPLY FCTN button and select LOG MAG3. Press FREQ button and select STOP FREQNote: Other options are also available.4. Press AMPTD button and adjust the amplitude if necessary, say –20 dBm5. Press RES BW and select an appropriate frequency resolution, say 100 Hz
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 25
Note: Sweep time might need to be adjusted so that it is higher than the settling time required for each Res BW, see table* below.
* Instruction Manual for 3577A Network Analyzer, pp 4-62.6. If applicable, press SWEEP TYPE button and select LOG FREQ SWEEP to
display x-axis (freq) in log scaleNote: You might need to readjust the frequency range again by pressing FREQ button
! Tip: Turning the knob will move the Marker along the trace (data readout).
Phase Plot:
1. Press TRACE 2 button2. Press INPUT button and select input A3. Press DISPLY FCTN button and select PHASE4. If needed, adjust the frequency range using FREQ button
Network Analyzer
Obtain a plot using software Agilent Data Capture 2:
1. Go to Programs > Agilent IntuiLink > IntuiLink Data Capture Application2. Click Instrument tab, choose 3577A if not selected, accept default setting, and click OK.3. Click Get Data icon, the 2nd icon from the right, to open a plot window if no plot shown
Selected Analog Electronic Circuits
AC TEST RESULTS
ROCHESTER INSTITUTE OF TECHNOLOGY
MICROELECTRONIC ENGINEERING LFF OPAMP.XLS FILE3B
LOT F960319 OPAMP TEST RESULTS - 1-29-97
Frequency Gain Vout Vin
hZ dB V mV
1 73.9794 10 2
5 73.53387 9.5 2
100 73.33036 9.28 2
200 70.31748 6.56 2
300 67.53154 4.76 2
400 65.48316 3.76 2
Op Amp Frequency Response
60
70
80GBP = 500,000 Hz
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 26
500 63.97314 3.16 2
600 62.41148 2.64 2
700 61.51094 2.38 2
800 60.34067 2.08 2
900 59.46256 1.88 2
1000 58.68997 1.72 2
1100 58.0618 1.6 2
1200 57.50123 1.5 2
1300 57.14665 1.44 2
1400 56.5215 1.34 2
1500 56.1236 1.28 2
1600 55.56303 1.2 2
50000 20 0.02 2
500000 0 0.002 2
10000000 -20 0.0002 2
-20
-10
0
10
20
30
40
50
1 10 100 1000 10000 100000 1000000 10000000
Frequency Hz
Gain
dB
Selected Analog Electronic Circuits
LOW PASS FILTER
Vout
R2
-+
R1
C2
Vin
Derive an expression for Vo/VinPlot 20Log10 (Vo/Vin) vs frequencyVerify using SPICEVerify by building the circuit
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 27
Vo/Vin = -R2/R1 1
1 + j ω/ω1
ω = 2 π fω1 = 1/R2C2 f
1
SR2C2 + 1
Selected Analog Electronic Circuits
HIGH PASS FILTER
Vout
R2
-+
R1C1Vin
Derive an expression for Vo/VinPlot 20Log10 (Vo/Vin) vs frequencyVerify using SPICEVerify by building the circuit
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 28
Vo/Vin = -R2/R1 j ω/ω1
1 + j ω/ω1
ω = 2 π fω1 = 1/R1C1
f
SR1C1
SR1C1 + 1
Selected Analog Electronic Circuits
GENERAL FILTER
Vout-+
C2
Vin
R2C1R1
Derive an expression for Vo/VinPlot 20Log10 (Vo/Vin) vs frequencyVerify using SPICEVerify by building the circuit
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 29
Vo/Vin = -R2/R1 = -R2/R1 1 + j ω/ω1
1 + j ω/ω2
ω = 2 π fω1 = 1/R1C1, ω2 = 1/R2C2
SR1C1 + 1
SR2C2 + 1
Selected Analog Electronic Circuits
COMBINATIONS OF FILTERS
Vo/Vin = -R2/R1
Generalω1, ω2
Generalω3, ω4
Two General Filters in series1 + j ω/ω1
1 + j ω/ω2
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 30
2nd Order low-pass, high-pass, bandpass, bandrejection and all pass filter
ω1, ω2 ω3, ω4
Vo/Vin = -R2R4/R1R3 1 + j ω/ω1
1 + j ω/ω2
1 + j ω/ω3
1 + j ω/ω4
Selected Analog Electronic Circuits
SKETCH OF VARIOUS FILTER FREQUENCY RESPONSE
ω1 = ω3 < ω2 = ω4
ω2 = ω4 < ω1 = ω3
Vo/Vin = -R2R4/R1R3 1 + j ω/ω1
1 + j ω/ω2
1 + j ω/ω3
1 + j ω/ω4
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 31
ω2 = ω4 < ω1 = ω3
ω1 < ω2 < ω4 < ω3
ω2 < ω1 < ω3 < ω4
Selected Analog Electronic Circuits
OPERATIONAL TRANSCONDUCTANCE AMPLIFIER
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 32
Selected Analog Electronic Circuits
OPERATIONAL TRANSCONDUCTANCE AMPLIFIER
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 33
National Semiconductor
LM13700
Selected Analog Electronic Circuits
OPERATIONAL TRANSCONDUCTANCE AMPLIFIER
+V
M3 M4
12/30 12/30
CMOS Realization
2
Va +
V- Ibias
V+
VbIout
- M3 M4
12/30
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 34
-V
Vin+Vin-
M1 M2
M5
12/30
12/30 12/305
1
4
V- Ibias
Va +
Vb
Iout
- Ibias
Iout
gm(Va-Vb) Vref
Note: gm is set by Ibias
Selected Analog Electronic Circuits
BIQUAD FILTER
+
Ibias1
V+
-
+
V+
Vout-
+
V+
-
gm1 gm3gm2
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 35
VC
V- Ibias1 V- Ibias3
VA +
V- Ibias5
V+
-
V- Ibias2
C2
C1
VB +
V- Ibias4
V+
-gm4
gm5
Selected Analog Electronic Circuits
BIQUAD FILTER
Vout = (s2C1C2Vc + s C1 gm4 Vb + gm2 gm5 Va)/(s2C1C2+ sC1gm3+gm2gm1)
This filter can be used as a low-pass, high-pass, bandpass, bandrejection and all pass filter. Depending on the C and gm values a Butterworth, Chebyshev, Elliptic or any other configuration can be achieved
For example: let Vc=Vb=0 and Va=Vin, also let all g be equal, then
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 36
For example: let Vc=Vb=0 and Va=Vin, also let all gm be equal, then
Vout = Vin / (s2C1C2/ gmgm + sC1/gm + 1)
which is a second order low pass filter with corner frequency at
ωc = gm / C1C2 and Q = C2/C1
Selected Analog Electronic Circuits
ELLIPTIC FILTER
+
V- Ibias
V+
-
+
Ibias
V+
Vout-
+
V+
-
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 37
VC=Vin/31
V- Ibias V- Ibias
Vin +
V- Ibias
V+
-
V- Ibias
C2
C1
R2R1
1500
50
VinVA
Selected Analog Electronic Circuits
COMPARISON OF DIFFERENT FILTER DESIGNS
Butterworth
gainLowpass Filters
Butterworth is flat in the band pass region, has the least steep transition to band stop region
Chebychev is not flat in the band pass region, has a
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 38
EllipticChebychev
frequencyElliptic is flat in the band pass region, has the steepest transition to band stop region but has some gain in the band stop region
band pass region, has a steeper transition to band stop region than Butterworth
Selected Analog Electronic Circuits
SWITCHED CAPACITOR CIRCUITS
Switched capacitor circuits makes use of analog switches and capacitors to replace resistors.
Saves space compared to using resistors
Low pass filter, filters out high frequency switching artifacts
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 39
Selected Analog Electronic Circuits
SWITCHED CAPACITOR EQUIVALENT RESISTOR
I
CV1
+
-
S2S1
V2
+
-
I
V2
+
-
V1
+
-
R
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 40
I = Cfs (V1-V2) I = (1/R) (V1-V2)
S1 closed C charges to V1, charge transferred is Q = CV1
S1 is opened
S2 is closed C charges to V2, charge transferred is Q = CV2
if the switches operate at a switching frequency fs, then I = Qfs = Cfs(V1-V2)
and Req = 1/(Cfs)
Selected Analog Electronic Circuits
SWITCHED CAPACITOR CIRCUITS
Req = 1/(Cfs)
1. The sampling frequency fs must be much higher than the signal frequencies 2. The voltages at node 1 and 2 must be unaffected by switch closures.3. The switches are ideal.4. S1 and S2 are not both on at same time. (use non overlapping clocks)
I
V2
+
V1
+R
I
+ S2 +S1
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 41
Req = 1/(Cfs)
I = (1/R) (V1-V2)
V2
-
V1
-V1
+
-
S2
CV2
+
-
S1
Example: for audio applications with frequencies up to 10KHz, we select switch frequency of 500KHz, for a 1 MEG ohm resistor we find that
C = 1/ (500K 1MEG) = 2 p/F
If Xox = 4000 Å, then the capacitor will be about 150 µm by 150 µm
Selected Analog Electronic Circuits
LMF100 SWITCHED CAPACITOR FILTER CHIP
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 42
Selected Analog Electronic Circuits
CHEBYCHEV FILTER EXAMPLE USING LMF100
From LMF100 Data Sheet
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 43
Selected Analog Electronic Circuits
SWITCHED CAPACITOR AMPLIFIER
VinCf
-Vo
ΦΦΦΦ1
ΦΦΦΦ1 ΦΦΦΦ2
Q = CV
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 44
Cx+
Vo
Vo = - Vin Cx/Cf
Selected Analog Electronic Circuits
CAPACITOR SENSOR TO DC VOLTAGE
Cf
-Vo
ΦΦΦΦ1
ΦΦΦΦ1 ΦΦΦΦ2
Q = CV
Low PassFilter
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 45
Vin Cx+
Vo
Vo = - Vin Cx/Cf
Filter
Selected Analog Electronic Circuits
CAPACITANCE MEASUREMENT CIRCUIT SIMULATION
Cf
Cx
SPICE SIMULATION
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 46
Vo = - Vin ((((Cx-CA) / Cf
Selected Analog Electronic Circuits
REFERENCES
1. Switched Capacitor Circuits, Phillip E. Allen and Edgar Sanchez-Sinencio, Van Nostrand Reinhold Publishers, 1984. 2. “Active Filter Design Using Operational Transconductance Amplifiers: A Tutorial,” Randall L. Geiger and Edgar Sanchez-Sinencio, IEEE Circuits and Devices Magazine, March 1985, pg. 20-32. 3. Microelectronic Circuits, 5th Edition, Sedra and Smith4. CMOS Analog Circuit Design, Phillip Allen, Douglas Holbert, Holt, Rinehard and Winston, 1987, pg 637-639.
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 47
and Winston, 1987, pg 637-639.5. “Asingle-Supply Op-Amp Circuit Collection”, Texas Instruments, Application Report SLOA058-November 2000.6. “Op Amp Circuit Collection”, National Semiconductor, Application Note 31, September 2002.
Selected Analog Electronic Circuits
HOMEWORK – SELECTED ANALOG CIRCUITS
1. Create one good homework problem and the solution related to the material covered in this document. (for next years students)2. Design a high pass filter to have a gain of 100 and corner frequency of 10Mhz.3. You have a 10pf switched capacitor equivalent resistor. What frequency is required to give an equivalent resistance of 10Mohm.
© January 22, 2011 Dr. Lynn Fuller, Professor
Rochester Institute of Technology
Microelectronic Engineering
Page 48
frequency is required to give an equivalent resistance of 10Mohm.4. Design a bandpass filter to pass frequencies of 2K to 10Khz.