Seminar: Moderne Methoden der analogen MOSSchaltungstechnik 5' Noise in lowvoltage circuits

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Seminar Moderne Methoden der analogen
MOS-Schaltungstechnik5. Noise in low-voltage
circuits

• Eugenio Di Gioia

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Noise in MOS Transistors

• Flicker (1/f) Noise
• Modeled as voltage source in series with the gate
• Inversely proportional to the frequency
  (important al low frequencies)
• Inversely proportional to the MOS area (large
  transistors have less Flicker noise)
• Inversely proportional to the specific
  capacitance COX
• It is caused from charge carriers trapped at the
  interface between silicon and oxide or
  fluctuation in the mobility of the charge
  carriers
• k is process-depending (about 10-25 V2F)

Design of Analog CMOS ICs B. Razavi
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Noise in MOS Transistors

• Thermal Noise
• Modeled as current source in parallel between
  drain and source
• It is due to the resistive channel
• Its spectrum is white (the same at all
  frequencies)
• ? is about 2/3
• The exact formula is
• but for long-channel transistors it is

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Noisy MOS
Thermal
Flicker
Output-referred
Input-referred
The input-equivalent noise current source was
neglected
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Noisy Common Source (passive load)
Total output voltage noise
Total input voltage noise
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Noisy Common Source (active load)
Total output voltage noise
Total input voltage noise
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Noisy Common Source (active load)

• Considering only the thermal noise
• Small gm2 reduces the total noise
• In saturation and
• W2/L2 should be small. By keeping the current
  constant this increases Vov2 (reduction of the
  output swing)
• If gm1gm2

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Cascode amplifier
M2 is source degenerated through ro1 Gain form G2
to output AV2-ROUT/r01
Gain from G1 to output AV-gm1ROUT
Output-referred voltage noise
Input-referred voltage noise
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Cascode amplifier
The noise contribution of M2 can be neglected ?
Only M1 is noisy
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Cascode amplifier with passive load
M1
RL
M2
If RL is large its noise contribution can be
neglected
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Active Cascode
Gain G2/output
Input-referred
Can be neglected if A3ltltgm1r01
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Folded Cascode
Output-referred voltage noise
Gain G1/output
Gain G3/output
Gain G2/output
Input-referred voltage noise
More noise than cascode because of the M3-term!
M1
M2
M3
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Differential pair with passive loads
Noise analysis

• The noise contribution of M3 can be neglected
  (symmetry)
• For noise analysis node X is not virtual ground!
  (uncorrelated sources)

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Differential pair with passive loads
Noise equivalent circuit
Superposition principle all uncorrelated noise
sources are considered separately. The output
noise power will be added.
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Differential pair with passive loads
Noise of Transistor M1
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Differential pair with passive loads
Noise of Resistor R1
Annahme
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Differential pair with passive loads
Noise of Transistor M2
Because of the symmetry
Noise of Resistor R2
Because of the symmetry
Total output noise
Total input referred noise

• Input-referred noise power is doubled compared
  to single ended Common-Source
• Input signal power is four times larger
• SNR is improved by 3 dB

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OTA circuits (1) Two-Stage
Two-stage OTA
Total transconductance
M1
M2
M3
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OTA circuits (2) OTA with current gain

• One-stage solution only the output node has a
  high impedance
• The current mirror has a gain B
• Mirror pole sp2gm2/(Cgs2Cgs3) (high frequency)
• The PM is high only if sp2gtgtsu
• Low-voltage suitable
• Transconductance (but not voltage gain) is
  larger than standard single stage but smaller
  than two-stage OTA

Same voltage gain as 1-stage!
B 2 to 4
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OTA circuits (2) OTA with current gain
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OTA circuits (3) current starving

• One-stage solution only the output node has a
  high impedance
• Mirror pole sp2gm2/(Cgs2Cgs3)
• M2 has less current than M1
• This reduces gm2 and thus sp2
• Compromise between single-stage and two-stage
• Low-voltage suitable
• Transconductance and voltage gain are larger
  than single stage

B 2 to 4
A 0.5 to 0.9
A 0.8-V, 8-µW, CMOS OTA with 50-dB Gain and
1.2-MHz GBWin 18-pF Load L. Yao, M. Steyaert
and W. Sansen
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OTA circuits (3) current starving
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OTA circuits (3) current starving
Gain G4/Input
Gain G2/input
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OTA circuits (3) current starving
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Example noise analysis
Equivalent noise model
Active-RC Low pass filter
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Output noise voltage (1)

• Assumption all equivalent noise sources are
  uncorrelated
• Principle of superposition
• Effect of In1, Inf and In- (opamp -Terminal)

Integration impedance
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Output noise voltage (1)

• Low pass behavior
• 3-dB frequency

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Output noise voltage (2)

• Effect of In, Vn2 and Vn (opamp Terminal)

Gain of the opamp in non-inverting configuration
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Output noise voltage (2)
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Total output noise
Bode diagram of the noise transfer functions
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Calculation of the noise sources
Passive elements Rf100 kO Cf160 pF R110
kO R29.1 kO
opamp equivalent noise sources
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Output noise voltage (2)
Seite 27
für f0
Seite 29
für f0
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The End