Bandgap References - 國立中興大學cc.ee.nchu.edu.tw/~aiclab/teaching/AIC/lect11.pdf · Bandgap References 類比電路設計 ... reference generators in CMOS technology, focusing

Ching-Yuan Yang

National Chung-Hsing UniversityDepartment of Electrical Engineering

Bandgap References

(3349)

Ching-Yuan Yang / EE, NCHUAnalog Circuit Design 11-1

ReadingB. Razavi Chapter 11.

IntroductionAnalog circuits incorporate voltage and current references extensively. Such references

are dc quantities that exhibit little dependence on supply and process parameters and a

well-defined dependence on the temperature. In this lecture, we deal with the design of

reference generators in CMOS technology, focusing on well-established bandgap

techniques.

In most applications, the required temperature dependence assumes one of three forms:

(1) proportional to absolute temperature (PTAT);

(2) constant-Gm behavior;

(3) temperature independent.

In addition, several parameters of reference generators, such as output impedance,

output noise, and power dissipation, may be critical as well.

Overview


Current-mirror biasing using (a) an ideal current source, (b) a resistor.

Simple circuit to establish supply-independent currents.

Te output current is quite sensitive to VDD:

How do we generate IREF independent of the supply voltage?

Supply-independent biasing

In order to arrive at a less sensitive solution, we postulate that the circuit must bias itself, i.e. , IREFmust be somehow derived from Iout.

If M1-M4 operate in saturation and = 0, then Iout = KIREF, and hence can support any current level.

( )( )1

2

11 //

/1 LWLW

gRVI

m

DDout +

=


Addition of RS to define the currents Alternative implementation eliminating body effect

The current is independent of the supply voltage (but still a function of process and temperature).

Assuming = 0, then Iout = IREF and VGS1 = VGS2 + ID2RS

SoutTHNoxn

outTH

Noxn

out RIVLWKC

IVLWC

I++=+ 21 )/(

2)/(

2

Neglecting body effect, we have SoutNoxn

out RIKLWC

I=

11)/(

2

2

2111

)/(2

=

KRLWCI

Snoxnout

.

Supply-independent biasing

That is,


Supply-independent biasing (contd)Addition of RS to define the currents (assuming 0). Determine Iout /VDD.

R1 = ro1 || (1/gm1), R3 = ro3 || (1/gm3)

143

4 RVgRI

rVV X

mouto

XDD =+

The equivalent transconductance of M2 and RS is 2222

222 )( oSmbmoS

om

X

outm rRggrR

rgVIG

+++==

Thus, ( )

1

341424

11

= Rg

RrGrVI

momoDD

out 0, if ro4 = .


Supply-independent biasing (contd)

Addition of RS to define the currents

Addition of start-up device

An important issue in supply-independent biasing is the

existence of degenerate bias points. For example, if all

the transistors carry zero current when the supply is

turned on, they may remain off indefinitely because the

loop can support a zero current in both branches.In other words, the circuit can settle in one of twodifferent operating condition

The diode-connected device M5 provides a current path from VDD through M3 and M1 to ground upon start-up.

This technique is practical on if VTH1 +VTH5 + |VTH3| < VDDand VGS1 +VTH5 + |VGS3| > VDD, the latter to ensure M5remains off after start-up.


Temperature-independent reference

How to generate a quantity that remains constant with temperature?

If two quantities having opposite temperature coefficients (TCs) are added with proper weighting, the result displays a zero TC.

- Ex. VREF = 1V1 + 2V2, with zero TC, i.e., 1V1/T + 2V2/T = 0.


Negative-TC voltageFor a bipolar device, where IC = IS exp(VBE /VT), where VT = KT /q.The saturation current IS is proportional to kTni2, where denotes the mobility of

minority carries and ni is the intrinsic minority carrier concentration of silicon.

Temperature dependence: 0Tm, and ni2 T3exp[Eg/(KT)], where m 3/2 and

Eg 1.12eV is the bandgap energy of silicon.

Find TC of VBE: since VBE = VT ln(IC /IS) and , then

With VBE 750mV and T = 300oK, VBE /T 1.5mV/oK.

The temperature coefficient of VBE itself depends on the temperature, creating error in constant reference generation if the positive-TC quantity exhibits a constanttemperature coefficient.

kTE

bTI gmS

= + exp4

( )

+

+=

++

243 expexp4

kTE

kTE

bTkTE

TmbTI ggmgmS ( ) TgTS

S

T VkTE

TVm

TI

IV

24 ++=

( )T

qEVmVTI

IV

II

TV

TV gTBES

S

T

S

CTBE /4ln+

=

=


Positive-TC voltage

Generation of PTAT voltage

Another type

( )mnqk

TVBE ln=

If IS1 = IS2, and the base currents are negligible, then

Thus, VBE exhibits a positive temperature coefficient:

The TC is independent of temperature or behavior of

collector currents.

nVIIV

InIVVVV T

ST

STBEBEBE lnlnln

2

0

1

021 ===

nqk

TVBE ln=


Bandgap referenceDevelop a reference having a nominally zero TC:

Let VREF = 1VBE1 + 2(VT lnn), where VT lnn is the difference between the base-emitter voltage of the two bipolar transistors operating at different current densities.

How to choose 1 and 2?

Since at room temperature VBE /T 1.5mV/oK whereas VT /T +0.087mV/oK,

we set 1 =1, and choose (2lnn)(VT /T) = 1VBE /T = 1.5mV/oK, then 2 lnn

17.2,indicating that for zero TC: VREF VBE1 + 1.72VT 1.25V.

Conceptual generation of temperature-independent voltage

Two modifications:

A mechanism must be added to guarantee VO1 = VO2.

Since lnn = 1.72 translates to a prohibitively large n, the

term RI = VT lnn must be scaled up by a reasonable factor.


where VBE = VBE1 VBE2 = VT lnn.

For a zero TC, we have (1 + R2/R3)lnn 17.2.

For example, we may choose n = 31 and R2/R3 = 4.

Note these results do not depend on the TC of the resistors.

Actual implementation of bandgap reference

( ) ( )

++=+

+=

3

2223

32 1ln R

RnVVRRRVVV TBEBEBEout


What happens to the temperature coefficient of VBE if the collector currents

are PTAT?

Since VBE = VT ln(IC /IS), we have

Since IC1 = IC2 (VT lnn)/R3 IC /T

(VT lnn)/(R3T) = IC /T,

we have

indicating that the TC is slightly less negative than 1.5mV/oK at T = 300oK.

Collector current variation

+

=

TI

ITI

IV

II

TV

TV S

S

C

CT

S

CTBE 11ln

( )T

qEVmVTI

IV

TV

II

TV

TV

gTBE

S

S

TT

S

CTBE

/3

ln

+=

+

=


Compatibility with CMOS technology

Realization of a pnp bipolar transistor in CMOS technology.

Circuit implemented with pnp transistors

The p-type substrate acts as the collector

and it is inevitably connected to the most

negative supply (usually ground).


OP amp offset and output impedance

Effect of op amp offset on the reference voltage

If A1 is large, VBE1 VOS VBE2 + R3 IC2 and

Vout = VBE2 + (R3 + R2)IC2. Thus,

The key point is that VOS is amplified by 1 + R2/R3,

introducing error in Vout. More importantly, VOS itself varies with temperature,

raising the temperature coefficient of the output voltage.

( )

( )OSTBE

OSBEBEBEout

VnVRRV

RVVVRRVV

++=

++=

ln13

22

3

21232


R1 and R2 are ratioed by a factor of m, producing I1 mI2.

Neglecting base currents and assuming A1 is large, we

have VBE1 + VBE2 VOS = VBE3 + VBE4 + R3I2 and

Vout = VBE3 + VBE4 + (R3 + R2)I2. It follows that

The effect of the offset voltage is reduced by increasing the

first term in the square brackets.

The implementation is not feasible in a standard

CMOS technology because the collectors of Q2 and

Q4 are not grounded. We modify the series combination

of the diodes as illustrated in Fig.(a), converting to one

of the diodes to an emitter follower.

Reduction of the effect of op amp offset

Biased by PMOS current sources

( ) ( )3

2343ln2

RVmnVRRVVV OSTBEBEout

+++=

( )[ ]OSTBE VmnVRRV

++= ln212

3

2


Reduction of the effect of op amp offset (contd)

Reference generator incorporating two series base-emitter voltage

Discussion:

Advantage:

The op amp experiences no resistive loading.

Disadvantage:

The mismatch and channel-length modulation

of the PMOS devices introduce error at the

output.

Since Q2 and Q4 have a finite current gain ,

they generate an error in the emitter currents

of Q1 and Q3 and introduce error at the output.


Feedback polarity

The negative feedback factor is given by

The positive feedback factor is given by

To ensure an overall negative feedback, P must be less than N, preferably by

roughly a factor of two so that the transient response remains well-behaved with

large capacitive loads.

232

32

/1/1

RRgRg

m

mN ++

+=

11

1

/1/1

Rgg

m

mP +=


Bandgap reference

Bandgap reference VREF = VBE + VT lnn, then .

Setting and ,

we have

Thus, we obtain

The reference voltage exhibiting a nominally-zero TC is given by a few fundamental

numbers: the bandgap voltage of silicon (Eg /q), the temperature exponent of mobility

(m), and the thermal voltage (VT).

The term bandgap is used here because as T 0, VREF Eg /q.

nTV

TV

TV TBEREF ln+

=

0=

T

VREF ( )T

qEVmVT

V gTBEBE /4 +=

( )n

TV

TqEVmV TgTBE ln

/4=

+

( ) TgREF VmqE

V ++= 4


Supply dependence and start-up

The output voltage is relatively independent of the supply voltage so long as the

open-loop gain of the op amp is sufficiently high.

The circuit may require a start-up mechanism because if VX and VY are equal to

zero, the input differential pair of the op amp may turn off.

The supply rejection of the circuit typically degrades at high frequencies owing to

the op amps rejection properties, often mandating supply regulation.


Curvature in temperature dependence of a bandgap voltage

Bandgap voltages exhibit a finite curvature,

i.e., their TC is typically zero atone temperature

and positive or negative at other temperatures.

The curvature arises from temperature variation of base-emitter

voltages, collector currents, and offset voltages.

Variation of the zero-TC temperature for differences samples

Many curvature correction techniques have been devised

to suppress the variation of VREF in bipolar bandgap

circuits but they are seldom used in CMOS counterparts.

This is because, due to large offsets and process variations,

samples of a bandgap reference display substantially different

zero-TC temperatures (right Figure) ,making it difficult to correct the curvature reliably.

Curvature correction


PTAT current generation

Generation of a PTAT current Generation of a PTAT current using a simple

amplifier

M1 = M2, M3 = M4 ID1 = ID2 VX = VY

In practice, due to mismatches between the transistors

and the TC of R1, the variation of ID5 deviates from the

ideal equation.

121

lnR

nVII TDD ==


PTAT current generation (contd)

Generation of a temperature-independent voltage

M1 = M2, M3 = M4 = M5, the output equals

If VREF /T = 0 , we can find the required reference value.

In reality, mismatches of the PMOS devices

introduce error in Vout.

nVRRVV TBEREF ln

1

23 +=


Constant-Gm biasing

Supply-independent bias

It is often desirable to bias the transistors such that their transconductance does not

depend on the temperature, process, or supply voltage.

Supply-independent bias circuit:

The transconductance of M1 equals ,

independent of the supply voltage and MOS device parameters.

In reality, the value of RS does vary with temperature and process.

( )

2

2111

/2

=

KRLWCI

SNoxnout

=

=

KRI

LWCg

SD

Noxnm

1122 11


Constant-Gm biasing (contd)Constant-Gm biasing by means of a switched-capacitor resistor.

Switched-capacitor resistor

Since the absolute value of capacitors is typically more tightly controlled and since the

TC of capacitors is much smaller than that of resistors, this technique provides a higher

reproducibility in the bias current

and transconductance.

CKSS fC

R 1=

Voltage-to-current conversion by means of a switched-capacitor resistor.


Speed issueEffect of circuit transients on reference voltages and currents

For fast changes in VN, the op amp cannot maintain VPconstant and the bias currents of M5 and M6 experience

large transient changes. Also, the duration of the transient at

node P may be quite long if the op amp suffers from a slow

response. For this reason, many applications may require a

high-speed op amp in the reference generator.

The critical node P can be bypassed to ground by means of

a large capacitor (CB) so as to suppress the effect of

external disturbances.

This approach involves two issues:

The stability of op amp must not degrade with the addition of CB, requiring the op amp

to be of one-stage nature.

Since CB generally slow down the transient response of the op amp, its value must be

much greater than the capacitance that couples the disturbance to node P.


Speed issue (contd)

Effect of increasing bypass capacitor on the response of a reference generator

Setup for testing the transient response of a reference generator


iD1 = iD2 = gmPVP = Vn,out /(R1 + gmN1) VP = gmP1Vn,out /(R1 + gmN1)

and VP = A0Vin,op

Node A:

Since typically gmPA0 >> gmN >> R11, we have |Vn,out| Vn,op.

The noise of the op amp directly appears at the output.

Even the addition of a large capacitor from the output

to ground may not suppress low-frequency 1/f noise

components ,a serious difficulty in low-noise application.

Noise issueA/D converter using a reference generator

Circuit for calculation of noise in a reference generator

outnopnopinmNmN

outn VVVggR

V,,,1

1

, 1 +=++

If a high-precision A/D converter employs a bandgap

voltage as the reference with which the analog input

signal is compared, then the noise in the reference is

directly added to the input.


Simplified core of a bandgap circuit

(a) Addition of cascode devices to improve supply rejection

(b) Use of self-biased cascode to eliminate Vb1 and Vb2


Generation of a floating reference voltage

nVRRV

RRV TBEout ln2

1

54

6

4 +=


Regulation of supply voltage to improve supply rejection

Documents

Bandgap References - 國立中興大學cc.ee.nchu.edu.tw/~aiclab/teaching/AIC/lect11.pdf · Bandgap References 類比電路設計 ... reference generators in CMOS technology, focusing