On Line Monitoring of RF Power Amplifiers with

Embedded Temperature Sensors

Josep Altet, Diego Mateo, Didac Gómez

Electronic Engineering Department

Universitat Politècnica de Catalunya

Barcelona, Spain

Josep.altet@upc.edu

Abstract—In the present paper we analyze that DC temperature

measurements of the silicon surface can be used to monitor the

high frequency status and performances of class A RF Power

Amplifiers. As a proof of concept, we present experimental results

obtained with a 65 nm CMOS IC that contains a 2GHz linear

class A Power Amplifier and a very simple differential

temperature sensor. Results show that the PA output power can

be tracked from DC temperature measurements.

Keywords; on line temperature monitoring, RF test, analog

test, thermal test, temperature sensors, power amplifiers test.

I. INTRODUCTION

Embedding sensors with a circuit under test (CUT) is a

strategy that has been used to monitor the on line status and

performances of analog and digital circuits. Focusing on

analog circuits, several examples are found in the literature,

e.g. [1-4].

In analogue circuits, as the working frequency increases,

sensor and CUT have to be co-designed to avoid significant

CUT performance degradation. This fact, on the one hand,

increases the cost of the sensor and, on the other hand, requires

designing ad-hoc sensors for each CUT.

CUT performance degradation can be avoided if the sensor

does not load any CUT node. One strategy that achieves this

requirement is the use of temperature sensors to monitor the

electrical behavior of circuits. This strategy takes advantage of

the inherent thermal coupling provided by the silicon

substrate: a temperature sensor embedded in the same silicon

die and placed in close proximity with the CUT can track its

dissipated power through temperature measurements, without

loading any CUT node.

The goal of this paper is to show that there is correlation

between the DC temperature variations sensed at the silicon

surface close to the CUT and the RF power delivered to the

external load, when this CUT is a class A RF power amplifier.

There are precedents in the literature that show the theoretical

basis and some examples that illustrate that some high

frequency characteristics of RF low noise amplifiers can be

extracted from DC or low frequency temperature

measurements [5-8]. In this paper, the CUT is a 2GHz Class A

Power Amplifier (PA) designed in a commercial 65nm CMOS

technology and the objective is to show that there is

correlation between DC temperature measurements and the

amount of RF power delivered by the PA to its external load.

This paper is structured as follows: the next section

reviews the principle of thermal testing of RF circuits and

presents a theoretical foundation of the proposed method. The

integrated circuit used in the experimentation is described in

section III. Section IV rapports the experimental

measurements. These results are only presented as a proof of

concept to show that DC temperature measurements can be

used to monitor the RF power delivered by a class A PA.

Section V discusses challenges that have to be addressed in

future research to make this technique feasible for commercial

applications of on-line test. Finally, section VI concludes the

paper.

II. ON LINE RF THERMAL TESTING: PRINCIPLES

A. Thermal coupling modelling.

Detailed theoretical analysis is already available in the

literature (e.g. [5,6,9,10]) but it is shortly included here to

make this paper self-contained.

Thermal coupling is defined as the temperature increase

that experiences the silicon surface due to the power dissipated

by running circuits placed on the same silicon die. Figure 1

shows a schematic representation of an integrated circuit that

contains a high frequency analogue CUT that dissipates power

due to its DC bias and to its high frequency operation together

with a temperature sensor placed next to it. On the bottom part

of the figure, there is a simple but valid model for the thermal

coupling modeling that links the electrical signals present

within the CUT devices and the working temperature of the

transducer device within the temperature sensor. It is a

multiphysics model, as it involves electrical variables (voltage

and current), energy (power consumption) and temperature.

Starting from the right part of the model, temperature and

power dissipation are related with a linear transfer function

behaving as a low pass filter, with a cut-off frequency around

10kHz-1MHz [9].

109978-1-4673-2085-6/12/$31.00 c©2012 IEEE

Figure 1. Integrated circuit containing a CUT and a temperature sensor (up).

Model of the thermal coupling between the CUT and the temperature sensor

(bottom).

Despite that the value of this cut-off frequency is much

lower than the frequency of the RF electrical signals present in

the CUT, this does not impel to monitor high frequency CUT

figures of merit through low frequency temperature

measurements. This can happen thanks to the non-linear nature

of the Joule Effect which can be modeled as a mixer in the

model. Let’s assume that the CUT is linear. Then, when it is

driven by a RF signal of frequency f, all AC current and

voltage waveforms present in the CUT are at this frequency.

However, as power is obtained as the product of voltage per

current, the Joule effect “mixes” this AC voltage and current

and “produces” dissipated power located in the frequency

domain at two different frequencies: DC and 2f. The former

generates a DC temperature variation which superimposes the

DC temperature increase generated by the CUT DC biasing

and that depends on the high frequency CUT characteristics as

it depends on voltages and currents at high frequency. The

latter, as its frequency is much higher than the cut-off thermal

coupling, does not generate any temperature increase.

As a first conclusion, DC temperature variations depend on

the RF electrical signals present in the CUT. That implies that

if temperature is used as parametric test observable, it

simplifies the design requirements for the monitor circuit and

the electronics needed to process the information given by it,

as it operates at low frequency regardless the CUT working

frequency Second, the monitor circuit is a temperature sensor

and it does not load electrically any CUT node: there is no

need to perform a co-design of the CUT and the monitor.

B. Temperature sensors as on-line power monitors for class A

Power Amplifiers: electrothermal analysis.

Temperature depends on the power dissipated by the CUT. What is the information about the RF CUT performances that carries this dissipated power when the CUT is a Class A PA?

To answer this question, let’s analyze the circuit present inFig.2, that shows a simplified schematic of a linear class A PA.

Figure 2. Simplified schematic of a Class A RF Power Amplifier.

The big inductor L is used to provide a constant current to the MOS transistor and to block the RF signal. For simplicity, let’s assume that:

·cos(2 )inv A f t (1)

If we assume linearity, the RF current and RF output voltage can be written as:

·

· · (2 )

rf m in

o L RF

i g v

v R i B Cos ft(2)

Where gm is the transistor’s transconductance.

In this circuit, since the load RL is off-chip, the only device that dissipates power and can generate a change in the silicon surface thermal map is the MOS transistor. The time evolution of this dissipated power can be found by multiplying the functions of drain-to-source voltage and current, expressed both as a function of time:

·DS DSP V I (3)

Where:

0DS DDV V v (4)

DS DC rfI I i (5)

After these calculations, it appears that the dissipated power has spectral components at DC, at the frequency of the vin input signal f and at twice this frequency.

According to the model represented in Fig. 1, only the spectral components of the dissipated power whose frequency is lower than the cut-off frequency of the thermal coupling mechanism will produce a temperature variation of the silicon surface thermal map. As in RF applications the cut off frequency of the thermal coupling is much lower than f (and of course twice f), only the DC component of the power dissipated by the MOS transistor will provoke temperature increases at the silicon substrate. Combining all the equations presented so far, the DC power dissipated by the MOS transistor can be related to the output voltage delivered to the load as:

110 2012 IEEE 18th International On-Line Testing Symposium (IOLTS)

L

DCDDDCR

BIVP

2

2

(6)

Equation (6) shows that the DC temperature increases at

the silicon surface depend, on the one hand, on the DC CUT

bias (first term of (6)), and on the other hand, on the RF CUT

operation (second term of (6), which is equal to the electrical

power delivered to the load).

C. Temperature setling time.

To use the temperature variation at the silicon surface as

test observable, we need to built-in a temperature sensor with

the CUT. The design and placement of the temperature sensor

is crucial for the feasibility of the test strategy. One of the

design parameters is the distance that exists in the layout

between the device used as temperature transducer within the

temperature sensor and the CUT. This distance affects, on the

one hand, the attenuation of the thermal coupling. On the other

hand, the settling time of the thermal coupling. These issues

have been already studied in other works (e.g. [10]). Both

parameters (attenuation and settling time) can be analyzed if

the heat transfer equation within the IC structure is solved.

Thermal coupling attenuation can be compensated designing a

temperature sensor with suitable sensitivity. The settling time

has a key impact in the test time. Results reported in [10] show

a settling time in the order of 10μs - 100μs when the distance

is about 10 microns.

III. CIRCUIT DESCRIPTION

Fig. 3 shows the schematic of the PA used as CUT, which

is designed for a 2GHz transmitter for coax-cable

communications. It is a wide-band, class-A PA with a

differential structure where each branch is a common-source

cascode stage. It has been implemented using a CMOS 65nm

process. The cascode transistor is a 1.8V thick oxide transistor

used to increase the drain voltage swing. The inductors L1 and

L2 as well as the CDC capacitors are off-chip components,

which are used to center the PA in one of four possible sub-

bands (2-2.5GHz). The characteristics measured from the PA

are: Gain @2.3GHz = 17.8 dB, PDC@VDD=1.1V = 96mW,

OCP1dB = 10.5 dBm.

Fig. 4 shows the schematic of the differential temperature

sensor embedded with the power amplifier. This sensor is

based on the structure published in [10]. The name differential

comes from the fact that the output voltage is proportional to

the difference of the working temperature of two transducers

placed at the surface of the silicon surface. Similarly to

differential amplifiers, the goal of this design is to achieve

high sensitivity to temperature gradients that appear in the

silicon surface due to the power dissipated by the CUT, and

ideally null sensitivity to common temperature variations that

affect both transducers, such as ambient temperature changes.

In this design, the two temperature transducers are the bipolar

transistors Q1 and Q2, whose temperature are T1 and T2

respectively. The temperature transducers are vertical NPN

bipolar transistors built using the deep-nwell/pwell/

n+diffussion structure available in this CMOS process. The

differential pair is unbalanced due to the difference of

temperatures between both transducers. The current mirrors

and the high impedance of the output stage convert this

temperature imbalance into changes of the output voltage

VOUT. This sensor was designed with a nominal differential

sensitivity of 0.19V/°C. Its power consumption is PDC@1.2V =

800 μW.

Figure 3. Schematic of the 2GHz Power Amplifier used as CUT.

Figure 4. Differential temperature sensor schematic used as monitor circuit.

Fig. 5 shows the placement of the temperature sensor and

the PA devices in the IC layout. The temperature transducer Q2

is placed close to the power amplifier (at 25 microns from the

cascode MOS transistor). The temperature transducer Q1 is

placed at 240 microns from Q2, together with the other devices

that form the temperature sensor. The goal of this placement is

to make the temperature imbalance between both temperature

transducers proportional to the power dissipated by the PA. As

thermal coupling will affect more Q2 than Q1, the former is

called hot transistor, whereas we named the latter cold

2012 IEEE 18th International On-Line Testing Symposium (IOLTS) 111

transistor. Although the CUT used in this example is more

complex that the one presented in section 2, the presence of

the cascade transistor does not alter the principle of the

technique. The power dissipated by each device is going to be

a portion of the power described by equation (6). In this

layout, the hot transistor is placed closer to the cascode MOS

transistor than the Input MOS as the first will experience

higher amplitude in the RF drain to source voltage, thus,

having a DC power dissipation with stronger correlation to the

RF PA behavior [5]. The sensor is differential and has

symmetrical behavior: if T1 is bigger than T2, Vout increases,

whereas if T1 is lower than T2, Vout decreases.

Figure 5. Detail of the placement of the PA devices and the differential

temperature sensor transducers.

IV. EXPERIMENTAL RESULTS

The goal of this section is to prove that with a simple

temperature sensor we can track variations in the RF power

delivered to the external load. To this end, we have swept the

input power of the PA (for VDD=1.2V, Vbias=0.7V and

f=2GHz) and then measure both the output power of the PA

and the DC output voltage of the thermal sensor. Fig 6. shows

the result of the measurements. In the left vertical axis, there is

the DC sensor output voltage, whereas on the right vertical

axis, there is the RF output power. Focusing on the RF output

power, it is clear that the PA enters in saturation. Focusing on

the DC sensor output voltage, results show that the thermal

imbalance between the hot temperature transducers and the

cold temperature transducer decreases as the RF input power

increases. This was predicted by equation (6). Remember from

the previous section, that as this sensor is differential, a

decrease of the temperature of the hot temperature transducer

manifests as an increase of the sensor output voltage.

0.48

0.49

0.5

0.51

0.52

0.53

0.54

0.55

0.56

0.57

-11 -9 -7 -5 -3 -1

RF Input Power(2G@Hz), dBm

DC

Sen

sor

Vo

ut,

V

7

7.5

8

8.5

9

9.5

10

10.5

11

11.5

12

RF

Ou

tpu

t

Po

wer

(@2

GH

z), d

Bm

Sensor Vout

RF Output Power

Figure 6. RF PA output power (right) and DC temperature sensor Vout (left)

as a function of the RF input power. VDD = 1.2V, Vbias = 0.7V, f= 2GHz

In Fig. 7 we relate the RF output power as a function of the

DC sensor output voltage. As it can be seen, it is possible to

track the power at the output of the PA by just reading the DC

output of the thermal sensor: tracking the RF output power is

possible with a DC contact-less method.

7

8

9

10

11

12

13

0.48 0.5 0.52 0.54 0.56

DC Sensor output voltage, V

RF

Ou

tpu

t

po

wer

(@2

GH

z), d

Bm

Figure 7. PA output power vs sensor output voltage. VDD = 1.2V,

Vbias = 0.7V, f= 2GHz.

V. ON THE USE OF TEMPERATURE MEASUREMENTS FOR ON

LINE TESTING

In this section we discuss two points that require further

research and possible solutions are pointed out.

First, it is clear that the design of the sensor should be

improved. The sensor used in this work has the advantage that

is very simple and can be used easily as proof of concept.

However, as it is based on an open-loop transconductance

operational amplifier, therefore its sensitivity and output

resistance is affected by process variations. Other differential

tempeature sensor topologies, such the one presented in [6]

does not present this drawback as sensitivity to process

variations is reduced with feedback electrical loops and the

sensor temperature sensitivity is made controllable as it

depends on the ratio between resistance values. The drawback

of that sensor is that it is more complex than the one

implemented in this work, occupping a bigger area overhead.

Another solution to make the sensor independent to process

112 2012 IEEE 18th International On-Line Testing Symposium (IOLTS)

variation consist in implementing a de-embedding calibration

of the sensor prior to the test. An example of such procedure is

described in [8]. Any of these solutions ensures a callibration

of the sensor sensitivity, which is important to relate the DC

sensor output voltage with the real RF electrical power

delivered to the load.

Another point to address is to analyze the “on-line” nature of

the measurement. Both the theoretical analysis and

experimental results have been based on the assumption that a

sinusoidal input signal is applied to the PA input. This may not

be the case in an “on-line” situation. Two considerations

regarding this point. First, sinusoidal characterization can be

done “in-field” during CUT idle times. Second, from the DC

sensor output voltage we can know the average value delivered

to the load.

VI. CONCLUSIONS

In this paper we have shown that the output powers in RF frequency of a class A power amplifier can be inferred from DC temperature measurements performed on-line with a built-in thermal sensor.

Using temperature sensors as built-in monitors for RF circuit has two major advantages: measurements are performed at DC although input and output signals are in the RF range, and regardless the frequency operation of the CUT. This simplifies the design of the monitor circuit, which can be re-used for different CUT working at different frequency bands.

As temperature is a contact-less measure, the performances of the CUT are unaltered, and no need of codesign is required when designing both the CUT and the sensor.

ACKNOWLEDGMENT

The Authors would like to thank Dr. José Luis González and Mr. Cédric Dufis for the design of the PA sample. This

work has been partially supported by the project MICINN TEC2008-01856.

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2012 IEEE 18th International On-Line Testing Symposium (IOLTS) 113