Download The current source The Active Current Source

The current source
R
+
I
Vref
Thevenin
Norton
I=
Vref
R
R
4kT
R
•Minimum noise equals:
DC current through resistor gives an increase of 1/f noise
(granular structure)
•Accuracy of source also determined by the accuracy of R
•Output impedance mostly too low
Use active V
I converter
Reference Sources
A. van Staveren and W.A. Serdijn
37
The Active Current Source
Vref
+
-
-
+
I
R
• Output impedance is ………
• What about the noise?
Reference Sources
A. van Staveren and W.A. Serdijn
38
1
Nullor implemented by one CE stage
I
Vref
R
• I = -(Vref - VBE)/R
• Temperature behavior VBE found in I (how to solve?)
• Output impedance:
β f ro − R
rout = r0 + R + R ⋅
rb + rπ + R
• If R >> rπ and R >> rb
rout = ( β f + 1)r0
Reference Sources
A. van Staveren and W.A. Serdijn
39
Plot of the output impedance vs R
rout
ro
0.7(βf+1)
(βf+1)
1
R
rπ
2
VR = I ⋅ R = I ⋅ 2rπ = 2 β
kT
q
β f = 100,
kT
= 25 mV
q
VR=5V
• Lower βf reduces VR but also rout
• Better nullor approximation helps (ro must be increased)
Reference Sources
A. van Staveren and W.A. Serdijn
40
2
Noise behavior of active current source
4kTrb
2qIC
2qIB
rb
1
4kT( + 2 )
2qIC
2qIB
R R
Sout =
+ r
+
(1+βfR )2 (1+ π )2
(1+rπ )2
rπ
βfR
βfR
I
R
II
I
II
III
infinite
Sout
4kT/R
R
III
0
2qIB
0 (4kT/R)
Only base
shot noise
remains
Reference Sources
A. van Staveren and W.A. Serdijn
41
Plot of noise vs R
Sout
2qIc
1
2/βf
1/βf
1
2
R
rπ
If contribution of 2qIC plus 4kT/R equals 2qIB, then
2β
VR = 5 V and Sout = 4qIB
R= gm f
Lowering βf for reducing VR does not help also, as:
Sout = 8kT I/VR
= 2·2qIB
The lower VR the higher the noise
Reference Sources
A. van Staveren and W.A. Serdijn
42
3
Current source demo
25 V
10kΩ
Switch open:
R2
Sout ≈ 4kT 2 + 4kTR2 + 2qI B R22
R1
10kΩ
R1
Q1 βf = 200
1 mA
15kΩ
vn ,out ≈ 22 nV / Hz = −33 dBµV
+
10kΩ V
analyzer
R2
-
Switch closed:
S out ≈ 0 + 4kTR2 + 2qI C R22
vn ,out ≈
nV / Hz =
Reference Sources
A. van Staveren and W.A. Serdijn
dBµV
43
Current sources in 1V circuits
Output impedance:
VR relatively small
1V
rout
• Reduction of the DC loop gain
accuracy
• Does not need to cost bandwidth
as pole also shifts
rπ
Noise:
VAF
rout= I
C
1V
2qIC
• Noise of the active part
approximately doubles
2qIC
Reference Sources
A. van Staveren and W.A. Serdijn
44
4
Saturating transistors
IC
IB
VBC
VCE
VBE
• Transistor saturates if IC/IB < βF
• Collector-emitter voltage is the difference
of VBE and VBC
1
1+
1 + IC / I B
βr
kT
VCE =
ln
I
q
1− C
PTAT
IBβ f
LM
MM
MN
b
g OP
PP
PQ
• For IC/IB = βf denominator equals zero
VCE not determined
• VCE reduces for larger βr (saturation voltage reduces)
• VCE reduces for larger IC/IB (deeper saturation)
Reference Sources
A. van Staveren and W.A. Serdijn
45
Influence of layout on Vsaturation (I)
C
B
E
I
II
• electron at I has a larger
chance on recombination
than electron at II
Bad for βr
Take care of a large βr
C
I
B
E
II
• Most of the electrons have
a short way to go
Less recombination
βr increases
General: Collector and emitter overlap should be as large as possible
Reference Sources
A. van Staveren and W.A. Serdijn
46
5
The current mirror
Iin
+
-
-
+
(n)
Mirror used for:
• biasing purposes
• current-gain stages
• buffering (cascode)
Iout
(m)
Transfer :
Iin
Iout
Again nullor can be implemented by wire
=
m
n
standard current mirror
Reference Sources
A. van Staveren and W.A. Serdijn
47
Signal-to-noise ratio and dynamic
range of a current mirror
• SNR is the ratio of smallest and largest signal that can be processed
at the same time
• DR is ratio of smallest and largest signal that can be processed,
not necessarily at the same time
• Noise power proportional to collector current (2qIC)
• Signal power proportional to the square of IC (IC2)
For IC=1 nA
and B=10 kHz
P,S
Psignal
SNR
Snoise
DR
SNR = 52dB
DR → ∞
I
Reference Sources
A. van Staveren and W.A. Serdijn
48
6
Peaking current source
Derived from current mirror
ln
FG I IJ = lnFG I IJ − I R
H I K H I K kT / q
2
1
S2
S1
1
I1
1
R2
I2
R1
dI C 2
=0
dI C1
for R ⋅ I C1 =
kT
q
Q2
Q1
• Source I1 can be implemented by a resistor
• R1 relatively low ohmic and accurate
a broad resistor
• R2 relatively high ohmic and not very accurate
a small resistor
• What about PSSR ?
Reference Sources
A. van Staveren and W.A. Serdijn
VR1 =
kT
q
49
T = 300 K
R1=50 Ω
R1=100 Ω
Reference Sources
A. van Staveren and W.A. Serdijn
50
7
Peaking current source vs Current mirror
510µA
R1
8.2 kΩ
200µA 200µA
R2
21 kΩ 200µA
50 Ω
Q1
Qp2
Q2
Qp1
• 50 must be accurate
• 8k2 does not need to be accurate
• 21k must be accurate
Reference Sources
A. van Staveren and W.A. Serdijn
51
R1, R2 : 70%, 100% 130%
Current mirror
Peaking current source
Reference Sources
A. van Staveren and W.A. Serdijn
52
8
Conclusion/Summary
• Several configurations of voltage and current sources discussed
• Current level is the performance determining quality,
not a 1V constraint
• Circuit design is hampered by 1V criterion
Reference Sources
A. van Staveren and W.A. Serdijn
other topologies
53
9