A COMPARISON BETWEEN VOLTAGE AND TRUE POWER BASED EMBEDDED MEASUREMENTS FOR RF TESTING

Pedro Mota, Jose Machado da Silva INESC Porto, Faculdade de Engenharia, Universidade do Porto

Rua Dr. Roberto Frias, Campus FEUP, 4200-465 Porto, Portugal

[dee05001, jms]@fe.up.pt

Abstract - Peak voltage sensors, namely diode based detectors, have been used for in-circuit testing of RF circuits. These detectors are simple to implement but provide a limited accuracy. On the other hand, the power inferred from these measurements assumes that impedance is known. This work presents a comparison between measurements obtained with peak voltage and true power detectors. The trade-off between observing one and the other are discussed, namely as far as information concerning the output load is concerned. Simulation results, acquired with the model of a prototype demonstration chip, show that more accurate information is obtained with power rather than voltage measurements in case load impedance variations occur. Experimental results obtained with a prototype chip are currently being obtained.

1 - INTRODUCTION

Today's RF products are expected to not only provide excellent performance characteristics, but also to maintain proper operation for several years of performance in the field, what adds a new degree of importance to embedded test and calibration circuits.

Power measurements are critical in RF and microwave systems in both cost and technical terms. This importance requires that measurements are accurate, repeatable, traceable, and convenient. Traditional RF testing relying on bench-top laboratory instruments provides accurate measures but is time consuming and expensive. On the other hand, accessing deeply embedded circuits requires delicate electronic probes [1-4].

There are, mainly, three types of average power detectors for RF and microwave frequencies. All of them provide indirect measurements: the thermistor, the thermocouple, and the diode detector.

Diode based voltage peak detectors have been used as a simple means for in-circuit observation of RF signals, namely as envelope detectors. By rectifying and averaging the RF output voltage, a measure of the power delivered by, e.g. a power amplifier (PA) can be obtained. The power of low amplitude signals can be obtained resorting to the square-law part characteristic of a biased diode [7]. Another type of RF power detector is that based on the translinear operation which, namely, make use of the exponential Ic-V BE relation of a bipolar transistor to provide a square of the input signal, i. e., v = e21n(vi,,) = v2 .

out m

978-1-4244-7793-711 0/$26.00 ©20 10 IEEE

However, observing voltage (or current) only represents power in an indirect way as power is estimated by assuming

that the load resistance is known (p = v';'�J. In case of

phase mismatch between voltage and current, the RF power measurement based on observing one or the other is not accurate.

Thermal sensors, namely thermistors and thermopiles, are also commonly used but their usefulness is limited due to their too long time constants in response to signal peak power changes.

On the other hand, the currently used complex modulations such as Wide-bandwidth Code-Division for Multiple Access (W-CDMA) which present high crest factors (CF), i.e., high instantaneous peak to carrier's rms voltage ratios, also require the observation of peak powers to prevent peaking or compression. A correct measurement of transmitted RF power allows avoiding interferences among RF systems. E. g., the GSM system requires that no excessive power is transmitted into adjacent frequency and time slots.

The work presented herein discusses the use of voltage detectors and true power detectors, in particular as far as load variations are concerned. Simulations results are presented which show that a correct detection of load variations required the use of the power detector. A prototype chip which incorporates both voltage and power detectors is being used to obtain experimental results.

The remaining of the paper presents in section 2 a comparison between observing output voltage and power for testing purposes. Section 3 describes the circuit being used as the true power detector which performs the cross­correlation between voltage and current signals. Section 4 presents the circuit being used as peak voltage detector.

Section 5 describes a demonstration prototype chip that has been used to obtain preliminary simulation results and is now being prepared to obtain experimental results. Section 0 highlights the main conclusions.

2-POWER VS. VOLTAGE MEASUREMENT

When observing an RF voltage signal care must be taken that asymmetries are detected in the waveform. When that is the case both positive and negative peaks have to be observed using both positive and negative peak detectors, in order to get a full and correct characterization (the average

of the positive and negative peak voltages have also been used).

Observing power directly does not provide information on asymmetries in positive and negative peak values of the voltage waveforms, as those are either hidden by the power detector or filtered out if the detector only evaluates the power of the fundamental component. Also, unless one operates in the linear region and with well known waveforms, it is not possible to infer accurately about the peak voltage amplitudes. The presence of an nth harmonic with amplitude A causes a fractional error in the output voltage measurement of, in the worst case, A (n odd) or

n2 A2 /2 (n even), and twice these values in the output

power measurement (4]. Figure 1 shows the iDS/VDS curves of the MOS transistor

of a generic RF P A (not taking into consideration channel length modulation) parameterized for different VCS values, superimposed with three different load lines.

Ids vs \Ids: Load lkles

01 81

f'� \ , ,A1

�------ -------' - - - - - - - - - - - - - - - - - - - - - - - - - - -\� - -� - - - - - ::'-A2

Vd.

� �

82 02

-

Figure 1 - Load lines different from the optimum one (line 01-02) rend smaller output powers due to smaller iDS and VDS excursions.

When designing a P A its load resistance is adapted in order to maximizing power transference (Jacobi's law). Considering a linear operation, the application of an input signal rends !1vds = -!1id . RL . In the iDS vs vDS curves shown

in figure 1, the maximum power transfer occurs when voltage and current show their maximum variations. This corresponds to the optimum load line plotted in solid, which also defines the iDS;vDS triangle with the largest area. The triangles defined by the dash-dot and dashed load lines correspond to, respectively, load impedances smaller and higher than the optimum.

Assume that an input signal is applied driving the optimum load line between points 01 and 02. If the same input signal is applied within the other load cases, one can see that:

- for the higher load impedance, the swing across VDS is similar to that obtained with the optimum load, but the iDS excursion is limited to smaller values, leading to a drop in the output power.

- for the smaller load impedance, the iDS swing is equivalent to that of the optimum load, but the VDS excursion is smaller. The voltage gain increases, but the output power decreases.

These two cases show also that observing only either voltage or current does not reflect the actual power delivered to the load.

r<o r>o +- ---+

Zoptimum

Figure 2 - Evolution of the power delivered to a varying load resistance.

VLoad

VOUTnOIl).. :'

to. ISO :40 no

ZOptimum ... no 400

RLoad Figure 3 - Positive peak voltage for varying load impedance.

- l . 5

,-----,----,---,----,----r---,----, VLoad

- 1 . 7s+----1\---+--+--t---t--+----1

-2.0+----1---'\---+--+--t---t--+----1

-2.2S+---+----'�J'

-2.7 S+-----1---+---j---tT-=l----+---+i

10.0 15.0 20.0 25.0

Zoptimum 30.0 35.0 40.0

RLoad Figure 4 - Negative peak voltage for varying load impedance.

Figure 2 shows the variation of the output power with the load impedance (Z/) obtained from the simulation of a class AB P A. The input signal was maintained constant and with the amplitude required to drive the PA into its maximum operating limits with the optimum load impedance. In these conditions, the load impedance was swept from half to the double of the optimum value and the corresponding load power and peak voltage were observed. A non zero

fl · ffi . . Z -ZYz I d re ectIOn coe IClent, I.e., [" "" s

Z _ Z ' ea s to a s I

decrease of the power delivered to the load.

Figure 3 and Figure 4 show, respectively, the variation of the positive and negative output voltage peaks with the load impedance. One can see that the two peaks' excursions are different - for the optimum load the response is symmetric but not for different load impedances.

3 - POWER DETECTOR

It was shown [9] that the cross-correlation between a circuit's voltage and current signals provides the active power when correlation time delay T is null, i. e.,

jRVi(T "" 0) "" �VI cos(8) == 2 1 T 1 P "" - f Vet) x I(t)dt "" -(V x I) x cos(8) To 2

( 1 )

The correlation output provides a DC voltage proportional to the active power. In case voltage and current present different tones, the measurement provided by the correlator also includes the power due to intermodulation tones lying in the correlator's bandwidth.

Consider that amplifier's output voltage and current can be represented by polynomials (2) and (3), respectively,

V(x)""a3 ·x3

+a2 ·x2

+al·x

I(x) "" b3 . x3

+ b2 . x2

+ bl . X

(2) (3)

If a two tone stimulus x 0= A . cos( 11J1) + A . cos( 11J2) is

applied to the amplifier, multiples of the fundamental frequencies, as well as intermodulation products, are generated due to the non-linear behavior of the transfer characteristic. The output voltage and current are then given by

V(W) = kl . (cos(wd + cos«(02 »)+ k2 . (cos(2. (01) + cos(2· W2 »)+

···k3 ·(cOS(3·(OI)+cos(3·(02»)+ + k4 . (COS«(OI - (02) + COS«(OI + (02 »)+ ... (COS(2 . WI - (02) + cos(2· WI + (02) + cos(2· w2 - (01) +) ···+ks·

+ cos(2 . (02 + (01)

(4)

1«(0) "" ml . (COS(WI) + cos(w2 »)+ m2 . (cos(2· (01) + cos(2· w2 »)+

. ··m3 . (cos(3. (01) + cos(3· w2 »)+

+ m4 . (COS(WI - (2) + cos(wl + (02 »)+ ... (COS(2 . (01 - (02) + cos(2· (01 + (02) + cos(2· (02 - (01») ···+ms·

+ cos(2· W2 + (01)

(5)

where coefficients kj and mj depend of amplitude A and

coefficients Gj and hj' respectively.

After the multiplication of voltage and current signals, the DC terms, i. e., average power, returns also the contribution of the power of other tone components besides the fundamentals, as

The circuit shown in figure 5.a) provides the cross­correlation between output current and voltage and operates thus as a true power detector. The two signals are filtered in order that only the respective fundamental components,

Voutl and iddl , are observed.

VDD "T"---"""-":"'""--""T"-iJ

Optimum load

--I

a)

b)

I Corre- V Power vd • lator

Figure 5 - a) Correlator circuit; b) Power detector.

The correlator's input differential voltage Vd (which is proportional to the PA's output current) is obtained from the impedance of the network used to filter the dynamic signal current idd. This current is a scaled image of that flowing into the load provided by a coreless transformer.

Equation (7) shows that is (figure 5.a) is proportional to the product between Vd (proportional to idd (figure 5.b) and

Valli and thus provides a measure of the PA's output power. The cross-correlator output voltage is achieved after a last gain stage which provides an output voltage given by, before filtering,

Vcorr=f [2. K.g"! . rOeq' �-�]. gno' r06 Product Linear

(7)

Figure 6 shows that a good linearity is obtained for the power detector transfer characteristic.

•. s,---..----r---,----,----,---,---,---,----,----,

'.4

'.2

a • � 11 .. � O.S u

� � O.S

0.4

0.2

PotnIW)

Figure 6 - Power detector transfer characteristic.

4 - VOLTAGE DETECTOR

Diode based voltage peak detectors have long been used despite the necessity for relatively large input voltages and limited accuracy. In order to implement a more accurate and linear voltage detector the scheme proposed in [6] was adopted.

Jrpu'

a)

.:1' .

b)

B ;:!

l�-ot + ___ T

Figure 7 - Diagram of the voltage detector; b) Peak detectors.

This detector (figure 7.a) provides a low error measurement obtained after the use of two rectifYing units (figure 7.b). The detector output voltage is obtained from the sum of one of them with a scaled value of the difference between the two (Va = Vol + N(Vo2 - Vol )) .

The voltage detectors were calibrated in order to provide a linear response to the output peak voltage for the nominal load response. The transfer characteristic of the voltage detector (figure 8) shows that good measurement linearity is ensured.

2. 4,----,-----...,.---,----,---.----,--.---,-----...,.----,

2.2

1.8 -..S

O,S

O,S

0'8 .':-. --;0C:;.2--0;;';.3;---;;'0.4-;----;;07.5--;0;';:.S--,;'0.7;-----;;:0.�S --;0"".9-----;----;'1 . 1 VOU( detector

Figure 8 - Peak voltage detector transfer characteristic.

5 - DEMONSTRATION PROTOTYPE

A prototype demonstration chip was designed in a CMOS 0.35 11m technology and is currently being assembled to obtain experimental results. It implements an 863 -870MHz class AB power amplifier, a pre-amplifier, a cross­correlator, as well as peak voltage detectors (figure 9). The pre-amplifier is a digitally controlled variable gain amplifier usually employed to control PA's output power, but that for testing purposes is also used to generate different amplitude testing stimuli.

Figure 9.b) shows the layout of the prototype chip correlator. The area reserved for the cross-correlator occupies an area of 80 x 80 11m2 (red circle in figure 9.b) mostly composed by the capacitors and bias resistors. Nevertheless, this area is less than 10 % the PA total area (inductors included) representing thus a small area overhead.

This chip is now being assembled in order to obtain experimental results of the measurements provided by the voltage and power detectors and to compare their accuracy in case load deviations occur. A preliminary comparison was obtained after simulations carried-out with the circuit model.

a)

b)

Figure 9 - Block diagram of prototype chip and, b) layout.

Using values given by the voltage and power detectors, the power transfer characteristics for different load resistances were obtained.

[ � 0 0..

CAPACITIVE 0.1 .............................. , . . . . . . . . . . . . . . .. ... . . . . .. ... . . .

,-'---'------'---'-, r- -----

-" __ Correlator : ' . . . \

-)t -Expected I '. • I 0.08 ..... --"Detectors I . . . . . '\ .:

• I I

0.06

0.04

0.02

Nominal I ' I : \: I I : I

. . . . . : . . .. . . . . . . . . : I I I I I I I I I I : : I

... • . . . '1'. .. ... ; .... J.

r�'-------\: [ /� [

I �� \ . . ... .. . . : f\· · � .•. ·« , ... ·······ri \�----j I: ••.•. � •. \x\.· :1

1:.... • ;/

o :J��¥�)

-0.02 L-----'--_-'---------'-_-'---------'-_--'----------'L--_ 10 15 20 50 70 80 90

IZI(QI

0.035

0.03

� 0.025 o 0..

0.02

0.015

0.01

0.005

Figure 10 shows the PA's Pout vs. Pin' transfer characteristics obtained with both detectors, together with the expected one. It can be seen that a good agreement among the three is obtained.

22

20

18

16

12

10

�:�2--f��-��--7� - �.2-�-� --+-�-� �(d8m)

Figure 10 - Pout vs Pin' transfer characteristics obtained with the voltage and power detectors.

However, if load impedance changes (figure 11), the power measured with the peak voltage detectors is different as their response has been calibrated for the nominal

optimum load resistance, i. e., power ( P = vj�L ) is

computed using the expected load resistance value and not the actual one.

INDUCTIVE

[ !

RESISTIVE 0.07

=correlator

.. .

.. • . . . . . . . .

•.

.. . . . . . • . . . .

.. . .

0.06 ...... �:��:r::t�r� (CCf""-''''':T''\

0.05

0.04

--Nominal: .... ." : I / I I /' I ... 1. . . 1 . .

• . • [

• • [

0.. 0.03

i. • • i .. • ..• . .• 0.02

0.01

I · . : I: 'j'" · 1 · · · · · · . , . . . . . . . .. . . . . . . ; . .

I I' I /, I :

: / :. : . / . : . ' r / ' . .. . . . :

\..!�- ______ I :

10 15 20 50 70 80 90 IZI(QI

Figure 11 - Output power values obtained with the two detectors for different load impedances.

The measures provided by the power detector are more accurate. In figure 11 the dot corresponding to the nominal case shows that the same values are obtained with the two sensors when the load is the expected optimum. When load varies, the values provided by the true power detector remain close to the expected ones. Only for low capacitive impedances the detector provides a better accuracy.

In all the cases, the measures provided by the power detector differ also slightly from the expected ones but provide, anyway, a better estimation than those given by the peak voltage detector. This difference is due to the correlator (Vd and VallI inputs, Figure 5) being now operated in the edge of the linear dynamic range.

Although the detection of load variations has been mainly addressed, defects occurring either in the P A or in the load can also be detected. In both cases a matching failure between the PA output impedance and the load occurs. New developments have been carried-out in order to improve the detectability of PA's defects. Figure 12 shows the variation of the power sensor's voltage for deviations of ±30 % and ± 15 % of the P A's transistor width. The golden response is given by the central continuous line. rt can be seen that different responses are obtained in all cases but for the sake of better detectability it is recommendable to use moderate power test stimuli to avoid an eventual saturation of the sensor's output in the case of positive deviations.

1.5,--------------------.."

1.25

1.0

.5

. '

....... - =::��:�� .---­

_ ... __ .... _ .. _-_._-

-30.0 -27.5 -25.0 -22.5 -20

Figure 12 - Power detector response in case of ±30% and ±I5 % of the PA's transistor width deviations.

6 - CONCLUSIONS

The development of built-in self-test solutions for radio­frequency circuits has not yet reached the maturity required to allow replacing comprehensive, but time-consuming characterization testing operations, for tests capable of screening malfunctioning circuits due to processing defects and process variations.

It is shown here that load impedance variations are not detected equally when observing either the output voltage or the actual power. On the other hand, peak voltage

measurements are required to detect deviations within current high crest factor modulations.

Simulation results obtained with a true power detector based in a cross-correlator circuit and a peak voltage detector are presented which show that more reliable measurements are obtained with true power detectors.

Eventually voltage and actual power detectors could be used together. Relying on actual power measurements one can implement regulation loops for automatic level control (ALC) namely to improve linearity, and correct the PA operation for process, voltage and temperature variations.

ACKNOWLEDGEMENTS - This work has been supported by the Portuguese government, Funda9ao para a Ciencia e a Tecnologia, under the framework of grant SFRHlBD/2565212005, project EDAM - SenseCardioHealth MIT-Pt/EDAM-EMD/0007/2008, and project TOETS­CT0302-CATRENE; http://www.lirmm.fr/�w3mic/TOETS/.

References [I] lee-Youl Ryu, Bruce C. Kim, and Iboun Sylla, "A New

Low-Cost RF Built-In Self-Test Measurement for System-on-Chip Transceivers", IEEE Transactions on Instrumentation and Measurement, Vol. 55, No. 2, pp. 381 - 388, April 2006.

[2] Voorakaranam, R.; Akbay, S. S.; Bhattacharya, S.; Cherubal, S.; Chatterjee, A., "Signature Testing of Analog and RF Circuits: Algorithms and Methodology", IEEE Transactions on Circuits and Systems I, Vol. 54, No. 5, pp. 1018 - 1031, May 2007.

[3] Farah Guillot, Patrice Garcia, Mireille Mouis, Didier Belot, "Analysis of the Intermodulation Distortion and Nonlinearity of Common-base SiGeC HBTs". 13th IEEE International Conference Electronics, Circuits and Systems, ICECS '06, pp. 664 - 667, 10-13 Dec. 2006.

[4] J.C. Cowles, "The Evolution of Integrated RF Power Measurement and Control", IEEE MELECON 2004, Dubrovnik, Croatia, May 12-15, 2004.

[5] Nathan O. Sokal, A. D. Sokal, "Accurate Measurement of RF Power Amplifier Efficiency and Power Output Without and RF Power Meter", IEEE lournal of Solid­State Circuits, Vol. SC-12, No. 5, October 1977.

[6] C. Presti, F. Carrara, A. Scuderi, and G. Palmisano, "Fast peak detector with improved accuracy and linearity for high-frequency waveform processing," IEEE International Symposium on Circuits and Systems, ISCAS 2007, pp. 3884-3887, May 2007.

[7] Agilent Fundamentals of RF and Microwave Power Measurements, Application Note 64-1 C.

[8] Ricardo Veiga, Jose Machado da Silva, Pedro Mota, "Estimation of RF PAs' Nonlinearities after Cross­Correlating Power Supply Current and Output Voltage", IEEE 15th International Mixed-Signals, Sensors and Systems Test Workshop (IMS3TW) Scottsdale, Arizona, June 10-12, 2009.