announcements troubles with assignments… –assignments are 20% of the final grade –exam...
Post on 19-Dec-2015
218 views
TRANSCRIPT
![Page 1: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/1.jpg)
Announcements• Troubles with Assignments…
– Assignments are 20% of the final grade– Exam questions very similar (30%)
• Deadline extended to 5pm Fridays, if you need it.– Place in my mailbox (rm 217), or under my door (rm
222)– Any later than that will not be graded
• Come and talk to me if you need help.• mid-term: Thursday, October 27th
![Page 2: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/2.jpg)
Adam Riess, Brian Schmidt and Saul Perlmutter
![Page 3: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/3.jpg)
Lecture 10 Overview
• Transistors (continued)
• The common-emitter amplifier
• Amplifier parameters
• Black box amplifier models
![Page 4: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/4.jpg)
Summary of useful equations
• Basic DC operating conditions:
CCCCC
VVSC
CE
BC
CBE
RIVV
eII
II
II
III
TBE
/
1
• Add a small signal:
T
Cm
bembeT
Cc
V
Ig
vgvV
Ii
mme
bee
mb
be
ggi
vr
gi
vr
1
![Page 5: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/5.jpg)
Using small signal models
1) Determine the DC operating conditions (in particular, the collector current, IC)
2) Calculate small signal model parameters: gm, rπ, re
3) Eliminate DC sources: replace voltage sources with shorts and current sources with open circuits
4) Replace BJT with equivalent small-signal model. Choose most convenient depending on surrounding circuitry
5) Analyze
e.g. Tmodel
![Page 6: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/6.jpg)
Voltage gain with small signal model
Find the gain using a small signal model:
vbe vbe
+
-
+
-
ic
re
RC
Cmbe
c
mme
e
C
ee
Ce
be
c
eebe
CeCe
Ccc
Rgv
v
ggr
r
R
ri
Ri
v
v
riv
RiRi
Riv
gain voltageso
1
gain Voltage
ic
vc
eliminate DC sources and apply T-model
![Page 7: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/7.jpg)
How to build a Real Common emitter amplifier
• Why bother with 2 voltage supplies? • Use a voltage divider R2/R1 to provide base-emitter voltage to correctly bias the transistor.
![Page 8: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/8.jpg)
DC condition: the voltage divider
• The voltage divider should provide sufficient voltage to place the transistor in active mode (base-emitter forward biased):
Cbb I
RR
V10
21
V6.0
V6.0
EEB
EBBE
RIV
VVV
• Current through resistors should be >10 times base current for stability
BB
EE
BBB
V
RI
RR
R
RR
RVV
V6.0 so
now
21
1
21
1
![Page 9: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/9.jpg)
Amplifier specifications
• What other parameters of an amplifier do we care about?– Voltage gain– Dynamic range– Frequency response (bandwidth)– Input impedance– output impedance
![Page 10: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/10.jpg)
Voltage Gain• Voltage gain• Use small signal model (short Voltage sources and capacitors)
1 since
)(
CeCcc
Eeeb
RiRiv
Rriv
Ee
C
b
c
in
out
Rr
R
v
v
v
v
E
C
b
c
R
R
v
v
voltage gain
usually re<<RE
• Voltage gain is only defined by resistors RC and RE
ground
ground
αie
![Page 11: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/11.jpg)
Frequency response (Bandwidth)
• Normally interested in providing a small, AC signal to the base
• Use capacitors to remove ("block") any low frequency (DC) component ("capacitively couple the signal to the base") which could affect the bias condition
• C1 forms a high-pass filter with R1in parallel with R2 (Assuming the AC impedance into the base is large).
• Cut off frequency ω0=1/RC, so to remove frequencies <fmin:
21
21min
1
2
1
RRRR
f
C
![Page 12: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/12.jpg)
Frequency response (Bandwidth)
• Also worthwhile to place a capacitor on the output
• C2 forms a high pass filter with RL.
• Cut off frequency ω0=1/RC, so to remove frequencies <fmin:
LRfC
min2 2
1
![Page 13: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/13.jpg)
Dynamic Range
• Maximum voltage output = Vbb
• Minimum = 0• Beyond this the signal becomes 'clipped' or distorted• To get the maximum possible voltage swing, both positive and negative, set VC=0.5 VBB • Maximum 'dynamic range'
VC
![Page 14: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/14.jpg)
rb
rOUT
Input impedance• Consider the circuit without the voltage divider resistors. What's the small signal (AC) input impedance at the base, rb?
• Including voltage divider resistors in parallel
• Input signal sees a total input impedance rIN= R1 // R2 // rb
RB
![Page 15: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/15.jpg)
rb
ROUT
Output impedance
Co
Co
o
oOUT R
i
Ri
i
vr
![Page 16: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/16.jpg)
• If RL=10kΩ and we want a low frequency cutoff of 20Hz, What is C2?• If VBB=15V and IC=2mA what is the output impedance?
Co
Co
o
oOUT R
i
Ri
i
vr
BBC VV 5.0
LRfC
min2 2
1
21
21min
1
2
1
RRRR
f
C
E
C
b
c
R
R
v
v
BB
EE
V
RI
RR
R V6.0
21
1
Cbb I
RR
V10
21
DC condition
Frequency responseImpedance Gain/Dynamic range
![Page 17: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/17.jpg)
• Why do we care about the input and output impedance?
• Simplest "black box" amplifier model:
Impedances
RIN
ROUT
VIN AVINVOUT
• The amplifier measures voltage across RIN, then generates a voltage which is larger by a factor A
• This voltage generator, in series with the output resistance ROUT, is connected to the output port.
• A should be a constant (i.e. gain is linear)
![Page 18: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/18.jpg)
• Attach an input - a source voltage VS plus source impedance RS
Impedances
RIN
ROUT
VINAVIN
VOUT
• Note the voltage divider RS + RIN.
• VIN=VS(RIN/(RIN+RS)
• We want VIN = VS regardless of source impedance
• So want RIN to be large.
• The ideal amplifier has an infinite input impedance
VS
RS
![Page 19: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/19.jpg)
• Attach a load - an output circuit with a resistance RL
Impedances
• Note the voltage divider ROUT + RL.
• VOUT=AVIN(RL/(RL+ROUT)
• Want VOUT=AVIN regardless of load
• We want ROUT to be small.
• The ideal amplifier has zero output impedance
RIN
ROUT
VINAVIN VOUTVS
RS
RL
![Page 20: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/20.jpg)
Operational Amplifier
• Integrated circuit containing ~20 transistors
![Page 21: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/21.jpg)
Operational Amplifier
• An op amp is a high voltage gain amplifier with high input impedance, low output impedance, and differential inputs.• Positive input at the non-inverting input produces positive output, positive input at the inverting input produces negative output. • Can model any amplifier as a "black-box" with a parallel input impedance Rin, and a voltage source with gain Av in series with an output impedance Rout.
![Page 22: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/22.jpg)
Ideal op-amp• Place a source and a load on the model
• Infinite internal resistance Rin (so vin=vs).• Zero output resistance Rout (so vout=Avvin).• "A" very large• No saturation• iin=0; no current flow into op-amp
-
+
voutRL
RS
So the equivalent circuit of an ideal op-amp looks like this:
![Page 23: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/23.jpg)
Schematics An amplifier will not work without a power supply. And a more complete diagram looks like the figure below, which also indicates the standard pin configuration.
-
+
out
V+
V-
2
3
4
6
7 1
4 5
8
top view
PinFunction
2 Inverting input
3 Non-inverting input
4 V- supply
6 Output
7 V+ supply
![Page 24: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/24.jpg)
Measuring Impedances
• Assuming you can only vary RL and RS, how would you measure the input and output impedances of the amplifier?
RIN
ROUT
VINAVIN VOUTVS
RS
RL
![Page 25: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/25.jpg)
Measuring Impedances
• With the black box model, it is simple to measure the input and output impedances of an amplifier
• To measure the input impedance, vary RS until the output voltage has dropped to half ; then RS=RIN= input impedance
•To measure the output impedance, vary RL until the output voltage has dropped to half ; then RL=ROUT= output impedance
RIN
ROUT
VINAVIN VOUTVS
RS
RL
![Page 26: Announcements Troubles with Assignments… –Assignments are 20% of the final grade –Exam questions very similar (30%) Deadline extended to 5pm Fridays, if](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d375503460f94a0f419/html5/thumbnails/26.jpg)
Cascaded Amplifiers
• Easiest way to increase amplification is to link amplifiers together
RIN1
ROUT1
VIN1A1VIN1 VOUT1 RIN2
ROUT2
VIN2A2 VIN2 VOUT2
• Ideal amplifiers; VOUT2=A1A2VIN1
• In reality, take account of voltage divider action due to input and output impedances