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ELEC-2005 Electronics in High Energy Physics Spring term: Integrated circuits and VLSI technology for physics

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### ELEC-2005Electronics in High Energy PhysicsSpring term: Integrated circuits and VLSI technology for physics

### ELEC-2005Electronics in High Energy PhysicsSpring term: Integrated circuits and VLSI technology for physics

Basic Analog Design

Giovanni Anelli

15 March 2005

Part II

Outline – Part II

- Noise in analog ICs
- Matching in analog ICs
- Operational Amplifier design examples
- Analog design methodology

Giovanni Anelli - CERN

Thermal noise in passive components

Thermal noise is caused by the random thermally excited vibration of the charge carriers in a conductor.

Power spectral density [ V 2 / Hz ]

R

R

There are no sources of noise in ideal capacitors or inductors. In practice, real components have parasitic resistance that does display thermal noise!

Giovanni Anelli - CERN

Noise sources in MOS transistors

Channel thermal noise: due to the random thermal motion of the carriers in the channel

1/f noise: due to the random trapping and detrapping of mobile carriers in the traps located at the Si-SiO2 interface and within the gate oxide.

Bulk resistance thermal noise: due to the distributed substrate resistance.

Gate resistance thermal noise: due to the resistance of the polysilicon gate and of the interconnections.

Giovanni Anelli - CERN

Noise in circuits

Noisycircuit

Noiseless circuit

To be independent from the gain of a given system, we use the concept of input-referred noise. This allows comparing easily the noise performance of different circuits (with different gains), and calculating easily the Signal-to-Noise Ratio (SNR).

At the input of our linear two-port circuit, we use two noise generator (one noise voltage source and one noise current source) to represent the noise of the system regardless the impedance at the input of the circuit and of the source driving the circuit.

Giovanni Anelli - CERN

Input-referred voltage noise

The MOS transistor is represented by its small-signal equivalent circuit. We can refer the noise sources inside the MOS transistor to the input, obtaining an input-referred voltage noise.

Channel thermal noise

Gate resistance thermal noise

Bulk resistance thermal noise

1/f noise

g ideally varies from 1/2 (w.i.) to 2/3 (s.i.)

Ka = 1/f noise parameter, technology dependent

Usually, the first two terms are the most important

Giovanni Anelli - CERN

Outline – Part II

- Noise in analog ICs
- Matching in analog ICs
- Operational Amplifier design examples
- Analog design methodology

Giovanni Anelli - CERN

The importance of matching

Yield of an N-bit flash Analog-to-Digital converter as a function of the comparator mismatch

Giovanni Anelli - CERN

Relative & absolute mismatch

D1

L1

D2

L2

Mismatch occurs for all IC components (resistors, capacitors, bipolar and MOS transistors)

Absolute mismatch

Relative mismatch

Giovanni Anelli - CERN

Mismatch in MOS transistors

IDS1

IDS2

VGS1

VGS2

Mismatch in physical parameters (Na, m, Tox) and layout dimensions (W, L) gives origin to mismatch in electrical parameters (VT, b and therefore ID)

Mismatch in Na, m, Tox

+

Mismatch in W and L

Parameter mismatch

I mismatch and V offset

Giovanni Anelli - CERN

The golden rule: Bigger is better!

Random effects “average out” better if the area is bigger. Therefore, for a given parameter P, we expect something like

Giovanni Anelli - CERN

Expected mismatch

AVth / tox ~ 1 mV·m / nm

From the literature

A ~ 1 to 3 %·m

Usually in a pair of identical transistors the two most important parameter subject to mismatch are the threshold voltage Vth and the current factor b

Mismatch can be treated as another source of noise. As in the noise case, different “mismatch” sources can be grouped into one adding the variances (not the standard deviations)

Giovanni Anelli - CERN

Differential pair mismatch

2I

INVERSION COEFFICIENT

The two transistors have the same drain current

I.C.

Giovanni Anelli - CERN

Current mirror mismatch

I

The two transistors have the same gate voltage

I.C.

INVERSION COEFFICIENT

Giovanni Anelli - CERN

Offset of a DP + Active CM

VDD

2I

RANDOM OFFSET (WORST CASE)

SYSTEMATIC OFFSET

The difference in the drain voltages of T1 and T2 gives origin a difference in the DC currents in the two branches.

“COMMON MODE” OFFSET

Due to mismatches in the transistors, a common mode signal at the input gives a non zero output voltage signal.

Vin

T1

T2

Vout

T3

T4

Giovanni Anelli - CERN

Outline – Part II

- Noise in analog ICs
- Matching in analog ICs
- Operational Amplifier design examples
- Op Amp application examples
- Single-Stage Op Amps
- Two-Stage Op Amps
- Fully Differential Op Amps
- Feedback and frequency compensation
- Analog design methodology

Giovanni Anelli - CERN

The ideal op amp

An op amp is basically a voltage-controlled voltage source

Vin +

Rout

Rin

Vout

Vin -

The op amp is ideal when

A0 = Rin = ∞, Rout = 0

Giovanni Anelli - CERN

Op amp application examples

NONINVERTING CONFIGURATION

INVERTING CONFIGURATION

R2

Vin

Vout

Vin

Vout

R1

R2

BUFFER

R1

Vin

Vout = Vin

The above equations are valid only if the gain A0 of the op amp is very high!

Giovanni Anelli - CERN

Single-stage Op Amp

VDD

The differential pair + active current mirror scheme we have already seen is a single stage op amp. Several different solutions can be adopted to make a Single-stage amplifier. If high gains are needed, we can use, for example, cascode structures.

With single-stage amplifiers it is difficult to obtain at the same time high gain and voltage excursion, especially when other characteristics are also required, such as speed and/or precision.

Two-stage configurations in this sense are better, since they decouple the gain and voltage swing requirements.

T7

T8

T5

T6

Vout

Vb1

Vb1

T4

T3

T2

T1

Vin

ISS

Giovanni Anelli - CERN

Two-stage Op Amp

VDD

T6

T7

T8

Vout

Vin -

T1

T2

Vin +

Rb

T5

T3

T4

The second stage is very often a CSS, since this allows the maximum voltage swing.

The output voltage swing in this case is VDD - |2VDS_SAT|

Giovanni Anelli - CERN

Two-stage Op Amp

VDD

T3

T4

In this case we kept the differential behavior of the first stage, and is the current mirror T7-T8 which does the differential-to-single ended conversion. The output is still a CSS.

T5

Vb

T6

T2

T1

Vin

Vout

ISS

T7

T8

Giovanni Anelli - CERN

Fully Differential Op Amp

VDD

To increase the gain, we can again make use, in the first stage, of cascode structures.

T8

T7

Vb3

Vb3

T6

T5

Vb2

Vb2

T9

T10

Vb1

Vb1

T4

T3

Vout1

Vout2

T2

T1

Vin

T11

T12

Vb4

ISS

Vb4

Giovanni Anelli - CERN

Feedback

+

e

Vin

A(s)

Vout

F(s)

- A(s) is the open loop transfer function
- F(s) is the feedback network transfer function
- G(s) is the closed loop transfer function
- A(s)F(s) is the loop gain
- If the feedback is negative, the loop gain is negative
- For |Gloop(s)| >> 1, we have that

Giovanni Anelli - CERN

Properties of negative feedback

- Negative feedback reduces substantially the gain of a circuit, but it improves several other characteristics:
- Gain desensitization: the open loop transfer function is generally dependent on many varying quantities, given by the active components in the circuit. Using a passive feedback network, we can reduce the dependence of the gain variation on the variations of the open loop transfer function.
- Reduction of nonlinear distortion
- Reduction or increase (depending on the feedback topology) of the input and output impedances by a factor 1-Gloop.
- Increase of the bandwidth

Giovanni Anelli - CERN

Bode diagrams

Many interesting properties of the frequency behavior of a given circuit can be obtained plotting the module and the phase of the Transfer Function as a function of the frequency. These plots are called Bode diagrams. In the general case, a transfer function is given by the ratio between two polynomials. The roots of the numerator polynomial are called zeros, the roots of the denominator polynomials are called poles. For example, in the case of alow-pass filter with RC = 1 ms, the Bode diagrams look like:

Giovanni Anelli - CERN

Bandwidth increase with feedback

+

|G(s)|

Vin

Vout

A0

A(s)

- f

w

w0

w0(1+fA0)

GBWP

The gain-bandwidth product does not change with feedback!

Giovanni Anelli - CERN

Stability Criteria

+

|fA(s)|

GREEN: STABLERED: UNSTABLE

Vin

Vout

A(s)

- f

w

fA(s)

w

- 90

Barkhausen’s Criteria

- 180

|fA(jw1)| = 1

fA(jw1) = - 180

Giovanni Anelli - CERN

Phase Margin

We have seen that to ensure stability |fA(s)| must be smaller than 1 before fA(s) reaches - 180. But, in fact, to avoid oscillation and ringing, we must have a bit more margin.We define phase margin (PM) the quantity 180 + fA(w1), where w1 is the gain crossover frequency. It can be shown that, to have a stable system with no ringing (for small signals) we must have PM > 60. If we want to have an amplifier which responds to a large input step without ringing, PM must be even higher.

|fA(s)|

|fA(s)|

w

w

SMALL PM

LARGE PM

fA(s)

fA(s)

w

w

- 180

- 180

Giovanni Anelli - CERN

Frequency Compensation

RED: BEFORE COMPENSATIONGREEN: AFTER COMPENSATION

Single-pole op-amps would always be stable (the phase does not go below - 90). But a typical op-amp circuit always contains several poles (and zeros!). These op-amps can easily be unstable, and they need therefore to be compensated. This is generally done lowering the frequency of the dominant pole.

|fA(s)|

fA(s)

- 90

- 180

Giovanni Anelli - CERN

Outline – Part II

- Noise in analog ICs
- Matching in analog ICs
- Operational Amplifier design examples
- Analog design methodology

Giovanni Anelli - CERN

Analog design methodology

Define specifications

Extract schematic from layout

Choose architecture

Layout Versus Schematic (LVS) check

Simulate schematic

Extracted schematic simulations

Simulate schematic varying T, VDD, process parameters

BLOCK DONE!

In a complex design, this will be repeated for every block of the design hierarchy.

Masks layout

Design Rules Check (DRC)

Giovanni Anelli - CERN

Analog design trade-offs

NOISE

LINEARITY

POWER DISSIPATION

GAIN

ANALOG DESIGN OCTAGON

INPUT/OUTPUT IMPEDANCE

SUPPLY VOLTAGE

VOLTAGE SWINGS

SPEED

Giovanni Anelli - CERN

Bibliography

Books:

B. Razavi, Design of Analog CMOS Integrated Circuits, McGraw-Hill International Edition, 2001.

P.R. Gray, P.J. Hurst, S.H. Lewis, R.G. Meyer, Analysis and Design of Analog Integrated Circuits, J. Wiley & Sons, 4th edition, 2001.

R. Gregorian, Introduction to CMOS Op-Amps and Comparators, J. Wiley & Sons, 1999.

R.L. Geiger, P.E. Allen and N.R. Strader, VLSI Design Techniques for Analog and Digital Circuits, McGraw-Hill International Edition, 1990.

D.A. Johns and K. Martin, Analog Integrated Circuit Design, J. Wiley & Sons, 1997.

Y. Tsividis, Operation and Modeling of The MOS Transistor, 2nd edition, McGraw-Hill, 1999.

K. R. Laker and W. M. C. Sansen, Design of Analog Integrated Circuits and Systems, McGraw-Hill, 1994.

C. D. Motchenbacher and J. A. Connelly, Low Noise Electronic System Design, John Wiley and Sons, 1993.

A. L. McWhorter, Semiconductor Surface Physics, University Pennsylvania Press, 1956, pp. 207-227.

Z.Y. Chang and W.M.C. Sansen, Low-noise wide-band amplifiers in bipolar and CMOS technologies, Kluwer Academic Publishers, 1991.

Papers:

K. R. Lakshmikumar, R. A. Hadaway and M. A. Copeland, "Characterization and Modeling of Mismatch in MOS Transistors for Precision Analog Design", IEEE Journal of Solid-State Circuits (JSSC), vol. 21, no. 6, December 1986, pp. 1057-1066.

Behzad Razavi, “CMOS Technology Characterization for Analog and RF Design", JSSC, vol. 34, no. 3, March 1999, p. 268.

M.J.M. Pelgrom et al., “Matching Properties of MOS Transistors”, IEEE JSSC, vol. 24, no. 10, 1989, p. 1433.

M.J.M. Pelgrom et al., “A 25-Ms/s 8-bit CMOS A/D Converter for Embedded Application”, IEEE JSSC, vol. 29, no. 8, Aug. 1994 , pp. 879-886.

R. W. Gregor, "On the Relationship Between Topography and Transistor Matching in an Analog CMOS Technology", IEEE Transactions on Electron Devices, vol. 39, no. 2, February 1992, pp. 275-282.

Giovanni Anelli - CERN

Basic Analog Design

Giovanni Anelli

15 March 2005

Part II

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