# Accurate temperature sensing with an external P-N junction

**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:

I_{C} is the forward current

I_{S} is the reverse bias saturation current

V_{BE} is the forward voltage

V_{T} is the thermal voltage

n is the ideality factor

k is Boltzmann’s constant

For V_{BE} >> V_{T} the –1 can be ignored, and the approximate model of the forward voltage is:

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

Because n, k, and I_{S} 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_{S}, the ideality factor and reverse saturation current. These constants are process dependent and vary from lot to lot.

The diode voltage can be rewritten in delta form:

Rewriting for temperature:

If we set the currents such that:

I_{C2} = N • I_{C1}

we now have:

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.

**Figure 1: A typical diode temperature sensor is shown**

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).

**Figure 2: This graph shows the small signal impedance plotted in SPICE**

The small signal impedance can be calculated as follows:

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.

**Figure 3: The simulation shown uses a 10ps 3.3V signal (V1) injected into the p-n junction (V1) via a 10nF capacitor (C2)**

**Figure 4: Even a 10nF coupled noise source with very fast 10ps edges can only generate 30mV spikes shown in the simulation plot.**

The simulation uses a 10ps 3.3V signal (V1) injected into the p-n junction (V1) via a 10nF capacitor (C2). 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.

**Figure 5: A simulation showing a 2A current and 10mΩ trace is shown here**

**Figure 6: Shown in this graph is the 20 mV error from the 2A current pulse**

A 2A current and 10mΩ trace results in a 20mV error. A typical delta V_{D} is

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.

**Figure 7: A simulation showing that a 3cm PCB trace over a ground plane can have about 10nH of inductance. **

**Figure 8: The figure shows 30 mV of noise generated by injecting 2A into a parallel trace**

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.

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