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OscillatorsFixed Frequency, Controlled Power•Transmitters•Receivers/Tuners•Clock Circuits
Av
B(j)
+
+ VoutVin 1out v
in v
V A
V A B s
System poles @ AvB(s) = 1
Barkhausen Criteria
System poles @ AvB(s) = 1
Pole in RHP: Oscillation amplitude grows until amplifier starts to clip, then Av’ < Av .
0
Root locus for Av’ < Av
'0( ) 1 (Stable Oscillation)vA B j
0( ) 1 0vA B j
Oscillator Design
Av
B(j)
+
+ VoutVin
Common Base:rin = re
Av = Rc’/re
Common Emitter:rin = (+1)re
Av = -Rc’/re
Frequency Selective Feedback Network
LC NetworkQuartz Crystal
Amplifier GainAv = + Rc’/re
re = 26 mV/IE (from DC Analysis)
Rc’ : Parallel Combination of 1. Transformed Load: RL’ = RL/v
2
2. Parasitic Loading (finite Q): Rcoil = QuXT 3. Feedback Network: Re’ = . . . . .4. Collector Dynamic (AC) Resistance: rc ~ 20 k5. Any other resistances in Collector Circuit
Hartley Oscillator(common base, autotransformer feedback)
E
C1 2
'2
ov
LL
v
n
n n
RR
21
2 1
2
1 2
||
||e E
e E F
nB
n n
r RB
r R R
B B B
'2
1
||e E Fe
r R RR
B
R1
R2
R3R4
RL
n1
n2 n3
CT
LT , Qu
BPBP
VCC
, rc
+ -
R2R3
IB
VCC
R1IC IB
R3 re
IE IB
ie
1 ei
rc
R4
n2
n1
+ ve
-
B
C
E
B
CE
re
2
1 2
3L L
n nR R
n
P T uR X Q
Hartley Oscillator
0.026e
E
vr
I
DC Equivalent
AC Equivalent
R3 re
ie
1 ei
rc RP 'LR
R4
n2
n1
+ ve
- B
CE
32
4 3
e
e
R rB
R R r
11
1 2
nB
n n
+ vc
-
B1vcve = B1B2vc
4 3F eR R R r
R3 re
ie
1 ei
rc RP LR+ ve
- B
CE + vc
-
B=B1B2
21
FF
RR
B
ve = Bvc
Ideal
re
ie
1 ei
rc RP 'LR
+ ve
- B
CE + vc
-
B
FR
ve = Bvc
re
ie
1 ei
+ ve
- B
CE+ vc
-
Bve = Bvc
' 'c c P L FR r R R R
1 1e
c c e ce
vv R i R
r
1 1c c c
v c ee e e
v R RA R i
v r r
Note: any additional resistance placed across the tank circuit must be included as an additional parallel contribution.
B
AV
Barkhausen: is AVB > 1 ? Book Example :f = 1 MhzIC ~ IE = 1 man1 = 10, n2 = 100, n3 = 5 (subscripts changed)
LT = 53 uH, Qu = 50, XT = 333 RL = 50 R3 = 1 kR4 = 0 therefore, B2 = 1rc = 50 k
R1
R2
R3R4
RL
n1
n2 n3
CT
LT , Qu
BPBP
VCC
, rc
re
2626
1e
mVr
mA
11
1 2
2
2
1
10.091
110
5024.2
5 110
0 1 263
50 333 16.7
2.2
L
F
P u T
C c L F P
nB
n n
R k
kR k
B
R Q X k
R r R R R k
220084.6 38.5
26VA dB 84.6 0.091 7.7 1VA B
Maximum Power Considerations
The maximum 0-pk collector AC voltage is:
0 .001 2200 2.2pk C CV I R A V
220 2.21 1
0.12 2 24.2
pkMAX
L
V VP mW
R k
The maximum power to the load is:
VCC was not given for this problem, but we can determine a minimum value required to prevent saturation at max power by recalling that . . .
, ,
, ,
2.2 1 2.2
1 2.2 3.2
CEc opt CE MIN c C
C
CC MIN E CE MIN
VR V R I k mA V
I
V V V V V V