EL 6033
類比濾波器 (一)
Analog Filter (I)
Lecture4: Voltage References (1)
Instructor：Po-Yu Kuo
教師：郭柏佑
Outline





Introduction
Performance Requirements
Zener Diode Voltage Reference
Bandgap Voltage References
Bandgap Voltage References Implemented in
CMOS technologies
2
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
3
Outline





Introduction
Performance Requirements
Zener Diode Voltage Reference
Bandgap Voltage References
Bandgap Voltage References Implemented in
CMOS technologies
4
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
Vri
P SRR  20log10
Vro
(in dB)
5
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
Vref (VDD  5V )  Vref (VDD  3.3V )
5  3.3

1.2011.176
 14.7mV / V
5  3.3
6
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
Vref (max)  Vref (min)
Vref
106
1.1761 1.1731
106



 25.5 ppm/ C
(Tmax  Tmin )
1.1761
(100 0)
7
Outline





Introduction
Performance Requirements
Zener Diode Voltage Reference
Bandgap Voltage References
Bandgap Voltage References Implemented in
CMOS technologies
8
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
Vo 
Rs
Rr
rz
Vin 
VZK  s z I L
Rs  rz
Rs  rz
Rs  rz
Line Regulation
Vo
rz

Vin Rs  rz
Load Regulation
Vo
Rr
 s z
I L
Rs  rz
9
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.
10
Improved Zener Diode Reference (2)

By observation,
R1
Vo 
 Vz
R1  R2
 Vo  (1 


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
IZ 


R2
24K
)Vz  (1 
)6.2  10V
R1
39K
Vo  VZ 10.0  6.2

 1.15mA
R3
3.3k
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
11
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:
vN 

Summing currents at the output node
i

R1 // rin
v
R1 // rin  R2
v N  v  AvN  v

0
R2
ro
Eliminating vN and solving for the Ro=v/I, we obtain
Ro 
ro
r
 o
1  [( A  ro / R1  ro / rin ) /(1  R2 / R1  R2 / rin )] 1  Ab
where b 
R1
R1  R2
12
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
13
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
VT  kT / q
and
I S  BT 3 exp(VG0 / VT )
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
14
Thermal Stability (2)

The temperature coefficient (TC) of the thermal voltage:
TC (VT ) 
VT k
  0.0862mV/ C
T
q
I
 ln D
IS
VT  I D 



TC (VD ) 
ln
 VT
T  I S 
T


  VD  V
T
T

V
 3 ln T  G 0
VT

T


   VG 0  VD  3k 

T
q 

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
15
Thermally Compensated Zener Diode Reference

Idea of thermally compensated Zener diode is to connect a forwardbiased 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.
16
Outline





Introduction
Performance Requirements
Zener Diode Voltage Reference
Bandgap Voltage References
Bandgap Voltage References Implemented in
CMOS technologies
17
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
18
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
19
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):
VBG  VBE  KVT
i.e. TC (VBG ) 300 K TC (VBE )  K  TC (VT )  0
K 

 TC (VBE )
2.1

 24.4
TC (VT )
0.086
If for a particular transistor with certain bias current such that
VBE =650mV, then
VBG  VBE  KVT  0.65  24.4  (0.0259)  1.28V

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
20
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
I /I 
IR3  VBE 2  VBE1  VT ln C 2 S 2   VT ln(n)
 I C1 / I S1 
Combine two equations give
2R V
R
K  4 T ln(n)  2 4 ln(n)
VT R3
R3
 R

 VBG  VBE 2  KVT  VBE 2   2 4 ln(n) VT
 R3

21
Bandgap Voltage Reference Circuit (2)

From the previous discussion, for a zero
tempco voltage reference VBG, K≈24,
with n = 4, then
R4
K
24.4


 8 .8
R3 2 ln(n) 2 ln 4

Note that I = VTln(n)/R3  VT, I is a PTAT
current
22
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
23
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),
NegativeLoop Gain 

For the positive loop (the inner loop),
P ostiveLoop Gain 

R2  1 / g m1
A( s )
R1  R2  1 / g m1
1 / g m1
A( s )
R1  1 / g m1
For stability, we must have a negative
loop gain magnitude > positive loop
gain magnitude.
24
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
25
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
26