Noty an137f Linear Technology

Application Note 137

May 2012

Accurate Temperature Sensing with an External P-N
Junction

Michael Jones

Introduction

Many Linear Technology devices use an external PNP
transistor to sense temperature. Common examples are
LTC3880, LTC3883 and LTC2974. Accurate temperature
sensing depends on proper PNP selection, layout, and
device configuration. This application note reviews the
theory of temperature sensing and gives practical advice
on implementation.

Why should you worry about implementing temperature
sensing? Can’t you just put the sensor near your inductor
and lay out your circuit any way you want? Unfortunately,
poor routing can sacrifice temperature measurement
performance and compensation. The purpose of this ap­plication note is to allow you the opportunity to get it right
the first time, so you don’t have to change the layout after
your board is fabricated.

Why Use Temperature Sensing?

Some Linear Technology devices measure internal and
external temperature. Internal temperature is used to
protect the device by shutting down operation or locking
out features. For example, the LTC3880 family will prevent
writing to the NVRAM when the internal temperature is
above 130°C.

External temperature compensation is used to compen­sate for temperature dependent characteristics of exter­nal components, typically the DCR of an inductor. The
LTC3880 uses inductor temperature to improve accuracy
of current measurements. The LTC3883 and LTC2974 also
compensate for thermal resistance between the sensor
and inductor, plus the thermal time constant.

This application note will focus on external temperature
sensing. Proper up front design and layout will prevent
performance problems.

Temperature Sensing Theory

Linear Technology devices use an external bipolar transis­tor p-n junction to measure temperature. The relationship
between forward voltage, current, and temperature is:

IC=ISe

V

⎛
⎜

(nVT)

⎜
⎝

kT

=

T

q

BE

–1

⎞
⎟
⎟

⎠

V

IC is the forward current

is the reverse bias saturation current

I

S

is the forward voltage

V

BE

is the thermal voltage

V

T

n is the ideality factor

k is Boltzmann’s constant

For V

>> VT the –1 can be ignored, and the approximate

BE

model of the forward voltage is:

⎛

VBE≈ n•

kT

q

In

⎞

I

C

⎜

⎟

I

⎝

⎠

S

The approximation eliminates the need for an iterative
solution to the forward voltage. This equation can be
rearranged to give the temperature

V

nk •In

BE

⎛

⎞

I

C

⎜

⎟

⎜

⎟

I

S

⎝

⎠

T =q•

L, LT, LTC, LTM, LTspice, Linear Technology and the Linear logo are registered trademarks of
Linear Technology Corporation. All other trademarks are the property of their respective owners.

an137f

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Application Note 137

Because n, k, and IS are constants, the simplest way to
measure temperature is to force current, measure volt­age, and calculate temperature. However, the accuracy
will depend on n and I

, the ideality factor and reverse

S

saturation current. These constants are process dependent
and vary from lot to lot.

The diode voltage can be rewritten in delta form:

ΔVBE= V

BE1–VBE2

=

nkT

q

In

⎛

⎞

I

C1

⎜

⎟

⎜

⎟

I

C2

⎝

⎠

Rewriting for temperature:

V

()

BE1–VBE2

T =

nk

q

In

⎛

⎞

I

C1

⎜

⎟

I

⎝

⎠

C2

If we set the currents such that:

= N • I

I

C2

C1

we now have:

V

()

BE1–VBE2

T =

nk

q

In

⎞

⎛

1

⎟

⎜

⎠

⎝

N

V1

C1

2N3906

10μF

Figure 1.

Q1

AN137 F01

500μA

I

1

The operating point at 500μA gives a DC impedance of

1.27kΩ. The small signal impedance can be plotted in
spice and is 52Ω out to 10MHz.(Solid line is magnitude
of impedance, and dashed line is phase of impedance).

4

AN137 F02

2
0
–2
–4
–6
–8
–10
–12
–14
–16
–18
–20
–22
–24
–26

(DEGREE)

(dB)

34.3

34.2

34.1

34.0

33.9

33.8

33.7

33.6

33.5

33.4

33.3

33.2

33.1

33.0

32.9
100k

10M 100M1M

(Hz)

Figure 2.

The small signal impedance can be calculated as follows:

Now the temperature measurement only depends on the
ideality factor n.

The ideality factor is relatively stable compared to the satu­ration current. Conceptually, the delta measurement is far
more accurate than the single measurement, because the
delta measurement cancels the saturation current and all
other non-ideal mechanisms not modeled by the equations.

For both cases, the accuracy of temperature measure­ment depends on the forcing current accuracy, the voltage
measurement accuracy, and relatively noise free signals.

Noise Sources

A typical diode temperature sensor is comprised of a
2N3906, 10μF capacitor, current source, and voltage
measurement.

⎛

⎞

kT

⎜

R

small–signal

⎟

q

⎝

=

26mV

⎠

=

I

C

I

C

26mV

=

500μA

= 52Ω

This implies that fast clock and PWM signals may inject
noise into the measurement if the driving impedance is
close to 52Ω.

A simulation of a capacitive coupled source shows that
the filter capacitor is quite effective.

R1

1Ω

V1

I

1

500μA

Figure 3. Pulse (0 3.30 10ps 10ps 100ns 2.5μs 10000)

C1
10μF

C2
10nF

2N3906

Q1

+
–

AN137 F03

V1

an137f

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Application Note 137

672

665

658

651

644

637

(mV)

630

623

616

609

602

0

(ms)

2024681012141618

AN137 F04

Figure 4.

The simulation uses a 10ps 3.3V signal (V1) injected into
the p-n junction (V1) via a 10nF capacitor (C1). Even a
10nF coupled noise source with very fast 10ps edges can
only generate 30mV spikes shown in the simulation plot.

Another source of error comes from ground impedances.

V1

C1

I

1

500μA

REMOTE

GND

Figure 5. Pulse (0 2A 0 10n 10n 100ns 2.5μs 10000)

658

656

654

652

650

648

(mV)

646

644

642

640

638

636

33

2N3906

10μF

Figure 6.

(μs)

Q1

R2

0.01Ω

I

2

AN137 F05

4834 35 36 37 38 39 40 41 42 43 44 45 46 47

AN137 F06

A 2A current and 10mΩ trace results in a 20mV error. A
typical delta V

ΔVBE=

nkT

q

is

D

⎞

⎛

1

⎜
⎝

10

≈ 60mV

⎟
⎠

In

For a 10% duty cycle, this might result in a 2mV DC shift.

A third source of error is a magnetic field and loop. Magnetic
coupling can be modeled as a coupling between inductors.

V1

K L2 L1 0.01

t

L1

10nH

I

1

500μA

C1
10μF

2N3906

Q1

I

2

t

L2
10nH

AN137 F07

Figure 7. Pulse (0.2A 0 10n 10n 1.25μs 2.5μs 10000)

660

655

650

645

640

635

(mV)

630

625

620

615

610

464

(μs)

478466 468 470 472 474 476

AN137 F08

Figure 8.

A 3cm PCB trace over a ground plane can have about
10nH of inductance. If 2A is injected into a parallel trace
and the coupling is 1.0%, 30mV of noise can be gener­ated, possibly causing a DC shift of 3mV.

HOW NOISE AFFECTS MEASUREMENTS

Linear Technology devices typically implement a lowpass
filter, which filters spikes and noise. However, in some
cases filtering results in a significant DC shift.

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AN137-3

Application Note 137

Figure 9.

The example shown in Figure 9, from an LTC3880, shows
an asymmetrical waveform on the TSENSE pin (channel

1) caused by injecting some of the switch node signal into
the TSENSE pin. When this is filtered, it results in a DC
shift. If temperature is calculated using a ΔV
and the DC shift is the same for both V
the effect will be cancelled out. This means that if the
error mechanism is consistent between current measure­ments, ΔV

is robust. If the single VBE measurement is

BE

used, the DC shift from the filtering will be a source of
measurement error. (LTC3880 does not support single

measurements)

ΔV

BE

calculation,

BE

measurements,

BE

Figure 10.

An Example Coupling Problem

The example shown in Figure 10 comes from an LTC3880.
Signal 1 is the TSENSE signal. When the LTC3880 is ap­plying 32μA, you get the higher signal level, and when it
is applying 2μA, you get the lower signal level. The last
high and low portions of the waveform are where the
two measurements are taken. Signal 2 is the V

OUT

of the

LTC3880, which is coupling into the 32μA measurement.

If the magnitude of noise is very large with respect to ΔV

BE

,
and the noise is asymmetrical (as in the scope shot) and
different between current measurements, ΔV

cannot

BE

cancel out the noise. In this case a single measurement
can produce a more accurate temperature measurement.
For example, suppose noise causes an error of 50mV. A
typical ΔV
single V

Therefore, in systems with systematic noise, the ΔV

is 70mV. The error can be as high as 70%. If a

BE

is used, the error is about 50mV/600mV, or 8%.

D

BE

measurement produces the highest accuracy by eliminating

as a source of error. (See ΔVBE equation). In systems

I

S

with large non-systematic noise, the V

measurement

BE

produces the highest accuracy.

Overall, the best accuracy comes from a good layout that
ensures near zero noise that is systematic, and uses a

calculation.

ΔV

BE

Non-systematic noise sources require good layout because
the ΔV

approach cannot reject them.

BE

Figure 11.

The same coupling can occur in the 2μA measurement as
shown in Figure 11. The asymmetry comes from the fact
that the coupling affects only one of two measurements, so
it is not cancelled by the ΔV

calculation. Furthermore, the

BE

error will appear random because the output turn-on event
and the current forcing mechanism are not synchronized.
The only defense against this error is prevention of the
coupling by proper layout, or widening the fault limits.

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