Instructor ： Po-Yu Kuo

教師：郭柏佑

Lecture4: Voltage References (1)

EL 6033類比濾波器 ( 一 )Analog Filter (I)

2

Outline

Introduction Performance Requirements Zener Diode Voltage Reference Bandgap Voltage References Bandgap Voltage References Implemented in

CMOS technologies

3

Introduction Here, we will learn to build a reference voltage to provide a stable and

accurate supply voltage. The voltage reference is an electronic circuit to provide an accurate and stable DC voltage that is very insensitive to the change in supply voltage and temperature

How accurate is a voltage reference? E.g. Weston cell is an electrochemical device which provides a reproducible voltage of 1.018636 V at 20°C with a small temperature coefficient of 40ppm/°C. For integrated circuit implementation, active solid-state devices can achieve a tempco of 1-4 ppm/°C if appropriate compensation technique is employed

Note To minimize error due to self-heating, voltage reference usually

operates with modest current (e.g. < 1mA) Tempco = temperature coefficient, usually expressed in ppm/°C (parts

per million/°C or 10-6/°C

4

Outline

Introduction Performance Requirements Zener Diode Voltage Reference Bandgap Voltage References Bandgap Voltage References Implemented in

CMOS technologies

5

Performance Parameters (1) The primary requirements of a voltage reference are accuracy and stability.

Some important parameters are:

Load Regulation = ΔVo/ΔIo (usually expressed in mV/mA or mV/A) or

Load Regulation = 100(ΔVo/ΔIo) (in %/mA or %/A)

Line Regulation = ΔVo/ΔVin (usually expressed in mV/V) or

Line Regulation = 100(ΔVo/ΔVin) (in %/V)

Power Supply Rejection Ratio (PSRR) is a measure of the ripple in the reference voltage due to the ripples in the supply voltage

)dBin(V

V20logPSRR

ro

ri10

6

Performance Parameters (2) Example of line regulation / supply-voltage dependence at VDD = 3.3, 4.15

and 5V (step size of 0.85V)

Line regulation at T 27°C is

VmVVVVVVV DDrefDDref

/7.143.35

176.1201.1

3.35

)3.3()5(

7

Performance Parameters (3)

The maximum (Vref(max)) and minimum (Vref(min)) reference voltages are1.1761V and 1.1731V, respectively. The reference voltage at

T = 27°C (Vref) is 1.1761V. The tempco in ppm/°C can be found by

CppmTTV

VV

ref

refref

/5.25)0100(

10

1761.1

1731.11761.1

)(

10 6

minmax

6(min)(max)

8

Outline

Introduction Performance Requirements Zener Diode Voltage Reference Bandgap Voltage References Bandgap Voltage References Implemented in

CMOS technologies

9

Review on Zener Diode Voltage Reference The Zener can be considered as a voltage reference. Since the breakdown

voltage due to Zener breakdown mechanism has a negative temperature coefficient, and the breakdown voltage due to the avalanche multiplication has a positive coefficient, the reference voltage is somewhat independent of the change of temperature

Lzs

zsZK

zs

sin

zs

zo I

rR

rRV

rR

RV

rR

rV

zs

zs

L

o

zs

z

in

o

rR

rR

I

V

rR

r

V

V

RegulationLoad

RegulationLine

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Improved Zener Diode Reference (1) In the case of Zener diode, the output voltage Vo heavily depends on the

load current IL, which in most cases are not good. It would be better if we could shield the Vz from the influence of the load. This can be done with the help of an op amp as shown below. This method refers to self regulation which shifts the burden of line and load regulations from the diode to the op amp.

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Improved Zener Diode Reference (2) By observation,

The output voltage is also adjustable via R2

The load current IL is supplied from the opamp such that the current flowing through the Zener diode is almost constant at

Since the diode current is independent of the load current, the diode voltage is insensitive to the load

R3 can be raised to avoid unnecessary power wastage and self-heating effects

VK

KV

R

RV

VRR

RV

zo

zo

102.6)39

241()1(

1

2

21

1

mAkR

VVI ZoZ 15.1

3.3

2.60.10

3

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Load Regulation (1) The load regulation is directly related to the output

impedance. To find Ro, we suppress the input source Vz and apply the test-voltage technique. By voltage divider formula:

Summing currents at the output node

Eliminating vN and solving for the Ro=v/I, we obtain

vRrR

rRv

in

inN

21

1

//

//

02

o

NN

r

vAv

R

vvi

21

1

2121

where

1)]//1/()//[(1

RR

Rb

Ab

r

rRRRrrRrA

rR o

ininoo

oo

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Load Regulation (2) Typically rin is in the MΩ range or greater, R1

and R2 are in kΩ range and ro is on the order of 102 Ω. The terms ro/R1, ro/rin, and R2/rin can thus be ignored to yield Ro≈ro/(1+Ab)

The load regulation Ro≈ro/(1+Ab) which is much smaller than the Zener diode voltage reference without opamp

Since ro and A are frequency dependent, so are the load regulation. In general, load regulation tends to degrade with frequency

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Thermal Stability (1) Thermal stability is one of the most demanding performance requirement of voltage references due to

the fact that semiconductor components are strongly influenced by temperature The forward-bias voltage VD and current ID of a silicon pn junction, which forms the basis of the diodes

and BJTs, are related as VD=VTln(ID/IS), where VT is the thermal voltage and IS is the saturation current. Their expressions are

where

k=1.381x10-23 is Boltzmann’s constant

q=1.602x10-23 C is the electron charge

T is the absolute temperature

B is a proportionality constant

VG0 = 1.205V is the bandgap voltage for silicon

)/exp(and/ 03

TGST VVBTIqkTV

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Thermal Stability (2) The temperature coefficient (TC) of the thermal voltage:

Assume VD=650mV at 25°C, we get TC(VD) ≈ -2.1mV/°C.

TC(VT) have a positive tempco and TC(VD) have a negative tempco. Hence, these two equations form the basis of two common approaches to thermal stabilization, namely, thermal compensated Zener diode references and bandgap references

CmV/0862.0)(

q

k

T

VVTC TT

q

k

T

VV

T

V

VT

VT

V

T

I

I

VI

I

T

VVTC DGT

G

TDS

D

TS

DTD

3ln3ln

ln)( 0

0

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Thermally Compensated Zener Diode Reference Idea of thermally compensated Zener diode is to connect a forward-biased

diode in series with a Zener diode having an equal but opposing tempco as shown below

Since TC(Vz) is a function of Vz and Iz. We can fine tune Iz to drive the tempco of the composite device to zero. In this case, a 7.5mA is used to give a reference voltage of Vz = 5.5+0.7 = 6.2V.

17

Outline

Introduction Performance Requirements Zener Diode Voltage Reference Bandgap Voltage References Bandgap Voltage References Implemented in

CMOS technologies

18

Bandgap Voltage Reference (1)

Since the best breakdown voltages of the Zener diode references range from 6 to 7V, they usually require supply voltages on the order of 10V to operate. This can be a drawback in systems powered from lower power supplies, such as 5V. This limitation is overcome by bandgap voltage references, so called because their output is determined primarily by the bandgap voltage of silicon VG0 = 1.205V

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Bandgap Voltage Reference (2)

Addition of the voltage drop VBE of a base-emitter junction, which has a negative tempco, to a voltage proportional to the thermal voltage VT, which has a positive tempco, to generate a reference voltage, which is independent of temperature

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Basic Concept

As TC(VBE) ≈ -2.1mV/°C and TC(VT) = 0.086mV/°C, then zero tempco is achieved at a particular temperature (e.g. T=300K):

If for a particular transistor with certain bias current such that

VBE =650mV, then

Note that VT = kT/q T, i.e. VT is proportional to absolute temperature. We call VT a Proportional To Absolute Temperature voltage, or in short, PTAT voltage

4.24086.0

1.2

)(

)(

0)()()(i.e. 300

T

BE

TBEKBG

TBEBG

VTC

VTCK

VTCKVTCVTC

KVVV

V28.1)0259.0(4.2465.0 TBEBG KVVV

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Bandgap Voltage Reference Circuit (1)

From the circuit shown in the right hand side, the emitter area of Q1 is n times as large as the emitter area of Q2, hence Is1/Is2 = n

By op amp action with identical collector resistances, the collector currents are also identical, i.e. IC1 = IC2. Ignore the base currents, we have

KVT=R4(IC1+IC2)=2R4I

Combine two equations give

)ln(/

/ln

11

22123 nV

II

IIVVVIR T

SC

SCTBEBE

TBETBEBG

T

T

VnR

RVKVVV

nR

Rn

R

V

V

RK

)ln(2

)ln(2)ln(2

3

422

3

4

3

4

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Bandgap Voltage Reference Circuit (2)

From the previous discussion, for a zero tempco voltage reference VBG, K≈24, with n = 4, then

Note that I = VTln(n)/R3 VT, I is a PTAT current

8.84ln2

4.24

)ln(23

4 n

K

R

R

23

Brokaw Cell

Brokaw cell is commonly used bandgap-cell realization circuit and is shown in the figure

The function of op amp is replaced by Q3,Q4 and Q5. Q3 and Q4 form a current mirror to enforce the collector currents of Q1 and Q2 are identical

The emitter follower Q5 raises the reference voltage to Vref = (1+R1/R2)VBG

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Stability of a Bandgap Reference

In a bandgap reference, there exists 2 feedback loops, 1 positive loop and 1negative loop

For the negative loop (the outer loop),

For the positive loop (the inner loop),

For stability, we must have a negative loop gain magnitude > positive loop gain magnitude.

)(/1

/1GainLoopNegative

121

12 sAgRR

gR

m

m

)(/1

/1GainLoopPostive

11

1 sAgR

g

m

m

25

Stability of Simple Brokaw Cell (1)

If we neglect R3, then clearly Q1 and Q2 form a differential pair with positive and negative terminals tied together

Above is the way to break the loop for measuring loop gain. The circuit should have a DC closed loop and AC open loop. The DC closed loop is for biasing and the AC loop is to measure loop gain

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Stability of Simple Brokaw Cell (2)

With the presence of R3, the positive loop looks like an amplifier with degenerated emitter => the gain is smaller than that with R3.Therefore, negative loop gain magnitude > positive loop gain magnitude, i.e. stability requirement is satisfied

Cc is the compensation capacitor. Here, dominant pole compensation is employed