TUNING AND COMPENSATION OF TEMPERATURE EFFECTS IN
ANALOG INTEGRATED FILTERS
Robert Hägglund and Lars Wanhammar
Department of Electrical Engineering, Linköping University
SE-581 83 Linköping, Sweden
roberth@isy.liu.se and larsw@isy.liu.se
ABSTRACT
In this paper several tuning strategies for integrated
active filters are discussed. Furthermore we compare
two compensation schemes to decrease the temperature
dependence of the transconductance value of a differential gain stage. The compensation circuitry consists of
on-chip temperature sensors and a level adjustment circuit all realized by standard CMOS transistor techniques. The temperature sensors requires small chip
area and consumes a small amounts of power.
The performance of the temperature compensation
schemes has been evaluated in a first-order transconductance-C filter application where the temperature dependence of the bandwidth and thereby the
transconductance value are measured. Simulations show
that the filters relative bandwidth variation due to temperature changes can be as low as 0.07% in the temperature interval of 0 – 100°C .
1. BACKGROUND
In an active filter implementation using discrete components it is important to adjust the time-constants of the
filter. For example in an active RC -filter the RC products must be adjusted to their nominal values. This is a
time consuming task, especially in higher order filters,
but it is a straightforward operation.
However it is more efficient to integrated filters in a
single circuit. For this type of integration it follows that
it is not possible to change the time-constants by just
exchanging a component. To be able to perform the
adjustment on-chip circuity must be implemented that
tunes the time-constants.
If we are looking at the adjustment procedure in a
broader perspective it is desirable to keep the shape of
the transfer function independent of the variations for
example due to process variations, temperature variations, power supply variations and ageing of the integrated circuit. It is unfortunately hard to design a single
feedback loop that maintains the transfer function independent of various parameter variations. It is favorable to
use several independent feedback loops where each loop
is minimizing or at least decreasing the impact of one or
several of the variations mentioned above.
To implement a high-performance integrated filter
one must use several feedback loop for tuning. These
loops can be divided into a hierarchy, where some of the
loops just tune an individual component whereas other
loops tries to tune the whole transfer function. An example of the hierarchy of the feedback loops are shown in
Fig. 1.
The control loop that tune the transfer function can
for example use a combination of Q-tuning algorithm,
frequency tuning, and tuning methods based on adaptive
Frequency
tuning
Input
signal
Building
block
Building
block
Qtuning
Building
block
Reference
clock
Reference
clock
Building
block
Qtuning
Output
signal
Reference
clock
Figure 1. An example of a hierarchy of compensation loops.
filtering.
One problem with the above tuning strategies is that
the tuning circuitry have to be designed so it can tune
large deviations in the transfer function. To alleviate the
large tuning range a local tuning scheme can be used for
a group of, or a single part of, the filter. For example a
local temperature compensation circuit can minimize the
temperature variation of all individual component in the
filter and thereby lower the temperature dependence of
the transfer function. This lowered sensitivity of temperature variations can relax the specification of the outer
control loops.
2. TUNING ALGORITHMS
There are several tuning strategies in continuous-time
filter applications. Three of the most common strategies
will be discussed below.
All of the tuning schemes discussed below can be
used either to compensate the whole filter or it can be
used to minimize the variations of an individual component.
The purpose of the Q-tuning is to keep the Q-factors
of each complex conjugated pole pair in the filter constant. This can often be done by tuning the phase of the
integrators of the filter. Usually this type of compensation is performed by inserting a tunable resistor in series
with the integrating capacitor. The control signal to the
tuning signal is then generated from for example a network like the one shown in Fig. 2.
External
reference
clock
Q-reference
circuit
Peak
detector
A
Peak
detector
Gain K
Low-pass
filter
Control
voltage
Figure 2. A block diagram of the Q-tuning principle.
Frequency tuning is used to minimize the variation of
either the cut-off frequency of the filter or the time-constant of a subblock of the filter. The main idea, illustrated
in Fig. 3, is to compare the output frequency of a block,
the whole filter or a part of it, with an accurate external
reference clock. The circuitry adjusts the time-constants
to match the frequency to the reference clock frequency.
External
reference
clock
Phase
detector
Control
voltage
Low-pass
filter
Figure 3. The principle of frequency tuning.
A third method to perform tuning in continuous-time filters is to use adaptive algorithms. The adaption is nearly
always done in the digital domain. For this type of
implementation both an analog-to-digital converter,
ADC, as well as a digital-to-analog converter, DAC, are
needed. There are some interesting algorithms that can
be used in the digital domain, but the input capacitance
of the ADC will load the analog filter and this must be
considered in the design of the tuning scheme. An example of an adaptive tuning scheme is shown in Fig. 4.
16-level
DAC
Reference
signal
Tunable
filter
Gradient
signals
Coefficient
signals
(1)
where µ ( T nom ) is the mobility at the T nom = 300 K .
The temperature dependence of the threshold voltage
is [2]
K T 1l
T
V T = V T ( T nom ) + K T 1 + ----------+ K T 2 V bseff  ------------ – 1 (2)
 T nom 
L eff
Voltagecontrolled
oscillator
4-bit PN
squence
plus DAC
T – 1.35
µ ( T ) = µ ( T nom )  -------------
 T nom
Error
signal
Adaptive
tuning
circuitry
Figure 4. One way to perform adaptive tuning of continuous-time filters.
3. TEMPERATURE DEPENDENCE OF MOS
TRANSISTORS
In an implementation of a high-performance integrated
filter one must take care of the temperature effects for
the transistors in the design. An increase in the temperature will cause the CMOS transistors to conduct a larger
current. This means that neither the transconductance
value nor the drain-source resistance will have a constant
value and thereby the gain, bandwidth and phase
response will vary with the temperature. These variations will then affect the transfer function.
The two parameters that have the largest impact on
the drain current due to temperature variations are the
mobility of charge carriers, µ , and the threshold voltage,
VT .
The mobility of charge carriers decreases as the temperature increases, especially for temperatures around
300 K [1]. In the AMS 0.35 process the temperature
dependence of the mobility µ of a PMOS transistor can
be expressed as
where the process parameters K T 1l = 0 .
4. TEMPERATURE MEASUREMENTS
There are several ways to perform temperature compensation. There have been some work on how to implement
a temperature sensor. The usual way of implementing
the sensor is to use bipolar transistor techniques, but it is
also possible to design a CMOS only temperature sensor.
The advantage of using the bipolar approach is that
the temperature can be easily extracted by measuring the
base-emitter voltage of a transistor. The base-emitter
voltage varies as [3]
r
kT
kT
V be ( T ) = V g ( 0 ) + ------  ln I c – ln ---------
(3)
q
η 
The base-emitter voltage decreases by approximately
2 mV/K as the temperature increases.
Another way of implementing the sensor for temperature measurement is to measure the difference of the
base-emitter voltage from two matched bipolar transistors carrying different current or having different
sizes [4] - [7]. The difference in voltage can then be
expressed as
kT I c1
∆V be = V be1 – V be2 = ------ ln ------(4)
q I c2
The advantage of this implementation is that the difference of the output voltage is proportional to the absolute
temperature, PTAT, i.e. it does not depend on material or
transistor parameters.
In a CMOS process it is possible to implement bipolar transistors as lateral devices which makes it possible
to use the two approaches described above. There are
also ways to implement temperature sensors using only
CMOS transistors.
There are three parameters that changes with the
temperature in the CMOS circuit. First, the polysilicon
resistance has a positive temperature coefficient which is
approximately linear although it displays some secondorder effects. The second parameter is the decrease in
mobility with respect to temperature. The third in the
fact that the threshold voltage decreases with the temperature.
The two last temperature effects are used in the
design of a temperature sensor [8]. Another sensor with
fewer transistors uses only the temperature dependence
of the threshold voltage [9], the design of this sensor is
shown to the left of Fig. 5.
The temperature sensing devices are often used
inside a bias network [6], [10], [11]. The temperature
compensation circuits are commonly realized as a bandgap reference. This type of reference uses two different
temperature dependent sensors, one with positive temperature coefficient and the other with a negative one.
The output of the band-gap reference is a linear combination of the temperature sensors [12].
Vdd
Vdd
M2
Vx
M1
2.1
2.09
2.08
2.07
2.06
2.05
2.04
Vdd
Vout
2.11
Output voltage (V)
5. TEMPERATURE SENSORS
A sensor is needed to measure the temperature of the
substrate in order to make the temperature compensation
possible. In this section two different types of temperature sensors have been investigated. These two temperature sensing devices are shown in Fig. 5.
Thermometer output voltage
2.12
M3
M2
2.03
0
20
40
60
Temperature in degrees Celsius
80
100
Figure 6. The output voltage from the voltage sensor as a
function of the temperature
Iout
Thermometer output current
73
M1
72
The sensor that has an output voltage that is temperature
dependent will be called the voltage sensor and the other
will be named the current sensor.
The voltage sensor designed with NMOS transistors
is presented in [9]. Here PMOS transistors are used since
they generate less flicker noise [10] which is a problem
at low frequencies. Another advantage of using PMOS in
the sensor is that it is possible to make a direct connection between the source and bulk. This is not possible in
the NMOS implementation in a standard p-substrate process that is not a twin-well process. The connection
between source and bulk will increase the linearity of the
sensor since the threshold voltage will not vary with the
DC operation point of the transistor.
The current sensor converts the output voltage of the
node V x to a current I out . In the implementation shown
in Fig. 5 all the transistors are of PMOS type to generate
less noise and make a direct connection of the source to
the bulk possible, and thereby increase the linearity as
stated above.
A common property for both temperature sensors is
that the temperature dependence of the output can be
increased or decreased by changing the ratio of the sizes
of the diode connected transistors, M1 and M2.
The temperature dependence of the two temperature
sensors are shown in Fig. 6 and Fig. 7.
Both of these figures shows that the output quantity
of the sensors are temperature dependent. The output
variations can also be approximated by a straight line,
especially for the voltage sensor.
In these simulation results no mismatch between the
transistors has been considered. If a transistor mismatch
of 0.1 percent is introduced, then a deviation from the
ideal temperature dependence will arise. For worst case
mismatch scenario for the voltage sensor the
Output current (µA)
71
Figure 5. The two temperature sensors. The voltage sensor
(left) and the current sensor (right).
70
69
68
67
66
0
20
40
60
Temperature in degrees Celsius
80
100
Figure 7. Temperature dependence of the output current
of the current sensor.
DC-value is changed by less then 0.1% whereas the
slope variation is smaller then 0.4%. On the other hand
the same variations in the current sensor are about 3.5%
and 1%, respectively.
6. DIFFERENTIAL GAIN STAGE
The performance of the temperature compensation is to
be tested in a simple filter where amplifiers are used as
integrators. The differential gain stage has been chosen
as the amplifier since it is a commonly used subcircuit in
analog circuit, for example in operational amplifiers.
The transconductance value of the differential gain
stage is dependent of the bias current through the amplifier. As the current increases the transconductance value
increases as well. Controlling the bias current in a proper
way will decrease the temperature variations.
The connection between the voltage sensor and the
bias voltage of the differential gain stage is made
through a level shifter used to set the correct working
bias voltage.
In the case where the current sensor is used the temperature dependent output current are copied to the differential gain stage trough a simple current mirror.
7. FILTER
The evaluation of the performance of the temperature
compensation scheme has been evaluated by checking
the bandwidth of a first-order transconductor-C filter
shown in Fig. 8.
gm2
Vinp
Iout
gm1
CL
Vinn
Figure 8. The first-order transconductance-C filter
The output of the temperature compensated filters using
the voltage- and current approach are compared with the
traditional way of biasing the circuit using a current mirror which is feed with a constant current. The outcome
of the comparison is shown if Fig. 9.
2
Voltage compensated
Current compensated
Current mirror
1.95
Bandwidth (MHz)
1.9
1.85
1.8
1.75
1.7
1.65
1.6
0
20
40
60
80
Temperature in degrees Celsius
100
Figure 9. The bandwidth of the filter as a function of the
die temperature.
From Fig. 9 it is obvious that the temperature compensation circuits are much more efficient, in the sense of
maintaining a constant bandwidth with respect to temperature variations, than the usual way of biasing the circuit.
The relative bandwidth variation due to temperature
changes in the interval 0 to 100 °C is defined as
y max – y min
∆BW
BWrel = ------------- = ----------------------------------------(5)
(
y
BW
max + y min ) ⁄ 2
The BWrel for the current mirror approach is 14.8%
whereas it is 0.072% and 0.78% for the voltage- and current sensor compensation scheme, respectively. The voltage sensor compensation scheme is then improving the
temperature insensitivity by approximately 200 times,
whereas an improvement of about 20 times is achieved
for the current sensor.
In a real chip implementation of the temperature
compensation scheme the transistors suffers from mismatch due to process variations. Simulations show that a
mismatch in the transistors size of the temperature compensation circuits increases the temperature dependency
of the filter. These simulations shows also that the cur-
rent sensor compensation scheme is more sensitive to
mismatch then the voltage sensor approach.
Another advantage of the voltage sensor approach is
that it can be designed to consume less power than the
current sensor. On the other hand, the chip area is
smaller using the current sensor approach.
A drawback of the temperature compensation
scheme is that the control is performed in an open loop
configuration. This means that all the nonlinearities must
be known to get a fully temperature independent circuit,
which of course is not possible. One may think that this
open loop regulation is not usable due to process variations and mismatch, but these compensation methods are
to be used as just one of several control loops in the filter. If the above compensation techniques just reduces
the temperature dependence of the filter then the design
of the outer control loops will be facilitated.
8. CONCLUSION
In this paper we described tuning schemes usable for
high-performance integrated active filters. To tune the
filter transfer function several control loops must be
applied where each loop decreases variations in the filter.
Two different temperature compensation circuits has
been proposed. The first one generates a temperature
dependent voltage whereas the other one generates a
temperature dependent current. The performance of the
compensation circuits has been evaluated in a first-order
transconductance-C filter. The variation of the bandwidth of the filter due to temperature variation is lowered
by a factor of about 200 and 20 for the two compensation
circuits.
A test chip has been fabricated in the AMS 0.35 µm
CMOS process.
9. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
B. G. Streetman, Solid State Elecronic Devices, Prentice Hall,
1995.
W. Liu, et. al., BSIM3V3.2.2 MOSFET Model Users’ Manual,
1999.
P. R. Gray and R. G. Meyer, Analysis and Design of Analog
Integreted Circuits, 3rd ed., John Wiley & Sons, 1993.
M. Ismail and T. Fiez, Analog VLSI Signal and Information
Processing, McGraw-Hill, 1994.
W. M. Sansen, F. P. Eynde and M. Steyaert, “A CMOS Temperature-Compensated Current Reference,” IEEE J. Solid-state
Circuits, Vol. 23 No.3, pp. 821-824, June 1988.
K. Koli and K. Halonen, “A 2.5V temperature compensated
CMOS logarithmic amplifier,” IEEE Custom Integrated Circuits Conf., pp. 79-82, 1997.
O. Salminen and K. Halonen, “The higher order temperature
compnesation of bandgap references,” IEEE Interna. Symp. on
Circuits and Systems, ISCAS ’92, Vol. 3, pp. 1388-1391, 1992.
V. Székely, M. Rencz and B. Courtois, “Integrating On-chip
Temperature Sensors in DfT Schemes and BIST Architectures,” 15th IEEE VLSI Test Symp., pp. 440-445, 1997.
M. A. Rybicki, R. L. Geiger, “A Temperature stable and process compensated mos active filter,” 1984 IEEE Interna. Symp.
Circuits ans Systems, ISCAS ‘84, pp. 940-943, 1984.
D.A. Johns, K. Martin, Analog Integrated Circuit Design, John
Wiley & Sons, 1997.
G.M Glasford, Analog Electronic Circuits, Prentice-Hall, 1986.
B. Razavi, Design of Analog CMOS Integrated Circuits,
McGraw-Hill, 2001.