© 2006 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents a technique to obtain electrical characteristics of analog and RF circuits, based on measuring temperature at the silicon surface close to the circuit under test. Experimental results validate the feasibility of the technique. Simulated results show how this technique can be used to measure the bandwidth and central frequency of a 2.4 GHz low noise amplifier (LNA) designed in a 0.35 microns standard CMOS technology.Peer ReviewedPostprint (published version

Aldrete Vidrio, Héctor

Altet Sanahujes, Josep

González Jiménez, José Luis

Mateo Peña, Diego

English

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Frequency Characterization of a 2.4 GHz CMOS LNA  by Thermal Measurements Diego Mateo, Josep Altet, Eduardo Aldrete-Vidrio and José Luis González Universitat Politècnica de Catalunya, Electronic Engineering Department, Barcelona, Spain   Abstract  —  This paper presents a new technique to obtain electrical characteristics of analog and RF circuits, based on measuring temperature at the silicon surface close to the circuit under test. Experimental results validate the feasibility of the technique. Simulated results show how this technique can be used to measure the bandwidth and central frequency of a 2.4 GHz low noise amplifier (LNA) designed in a 0.35 microns standard CMOS technology.  Index Terms  —  RF testing, RF characterization, thermal testing. I. INTRODUCTION The scaling down of CMOS technologies has enabled the possibility of integrating a whole system on a single silicon chip (System on Chip, SoC), with the benefits of low cost, high reliability and low power consumption. A drawback of SoC integration is the significant loss of observability it entails, since fewer nodes are accessible from the outside. As a consequence, the complexity and cost of the test, monitoring and characterization of the individual parts of the system increase, specifically in RF front-ends where the operating frequency is in the range of gigahertzs [1].  The inclusion of built-in testers together with the circuit under test (CUT) [2] is one of the solutions proposed to increase the observability of analogue and RF systems. Requirements for this on-chip monitoring circuitry are low area overhead and almost inappreciable loading effects on the CUT. This paper presents a novel procedure to characterize high frequency and RF analog circuits, consisting in measuring the temperature at the silicon surface, close to the circuit under test (CUT). As we present along this paper, the amplitude of some spectral components of the temperature near the CUT depends on the electrical characteristics of the circuit.  Measuring temperature to extract the electrical characteristics is an innovative and attractive solution as the CUT is not electrically loaded. The temperature measuring system gets the information thanks to the intrinsic thermal coupling provided by the silicon substrate. Thus, the electrical performances of the CUT are unaffected. Temperature can be sensed with embedded sensors, which would allow in-field test, as well as with external temperature sensors [3].  This paper is organized as follows: section 2 explains the principle of the procedure. Experimental measurements that validate its feasibility are in section 3, while section 4 shows an application of the technique based on simulated results: the bandwidth and central frequency of a 2.4 GHz LNA designed with a 0.35 µm CMOS technology are estimated. Finally, section 5 concludes the paper.  II. PRINCIPLE OF THE TECHNIQUE  The proposed technique is based on three circuital properties:  i) The existing relation between the power dissipated by a device/circuit and its electrical characteristics.  ii) The frequency shift that can be observed in the spectral components of the power dissipated by a device/circuit when compared with the spectral components of the electrical signals that drive it.  iii) The thermal coupling provided by the silicon die, which allows the observation of the dissipated power by measuring temperature.  To illustrate the first two properties, let’s consider a linear resistor R. When driven with a voltage sum of two tones of amplitude A and frequencies f1 and f2:   ( ) ( )1 2(2 ) (2 )inV t A cos f t cos f tπ π= ⋅ + , (1) its dissipated power is: ( ) ( )( )(( )( ) ( ) ( ))22 12 1 2 12 2 222 2 2 2 2 2AP t cos f f tRcos f f t cos f t cos f tππ π π= + − ++ + + +. (2)  As it can be seen, the electrical signals have only spectral content at frequencies f1 and f2, whereas the power dissipated has spectral components at f2-f1, f1+f2, 2f1 and 2f2. This effect can be called frequency mixing. In the case of having a resistor driven with (1) plus a DC bias, other spectral components of the power appear, for instance, at f1 and f2.  Authorized licensed use limited to: UNIVERSITAT POLITECNICA DE CATALUNYA. Downloaded on September 20,2022 at 07:00:22 UTC from IEEE Xplore.  Restrictions apply. On the other hand, the amplitudes of the spectral components of the dissipated power depend on the value of R, i.e., they carry information about electrical characteristics of the circuit considered. Then, by estimating the power dissipated we will obtain information about the circuit. The power will be estimated by measuring the temperature near the circuit, thanks to the thermal coupling of the silicon substrate.  Specifically, if we consider the power dissipated at f2-f1:   ( ) ( )( )2 122 12f fAP t cos f f tRπ− = − , (3) we observe the dependence of the power dissipation amplitude with R. Since in the example considered R is independent of the frequency, so it is the amplitude of Pf2-f1. But it must be remarked that by measuring the power dissipated at f2-f1 (which can be a low frequency if f1 and f2 are close to each other), the information that we obtain comes from high frequency, in this case f1, f2.  To show this, let us suppose that R depends on the frequency, R(f). In such a case, the amplitude of the power dissipated at f2-f1 becomes:   ( )( ) ( )( )( )2 122 11 21 122f fAP t cos f f tR f R fπ−  = + −  , (4) Assuming that f1 and f2 are close and inside the working bandwidth of R(f) (i.e., f2-f1 is much smaller than the bandwidth of R(f)), then the power dissipated at f2-f1 is:   ( )( )( )( )2 122 112f fAP t cos f f tR fπ− ≈ − , (5) From the last expression is obvious that the power dissipated at a low frequency as f2-f1 depends on a characteristic of the circuit at high frequency. Since the dissipated power will be estimated by thermal measurements, this down conversion is very useful, thus thermal coupling of the silicon substrate behaves as a low pas filter: some works have reported thermal measurements, corresponding to power dissipated, up to 100 kHz [3],[4].  If instead a so simple circuit as a resistor a more complex one is considered, for example an amplifier, is possible to find that the power dissipated at f2-f1 when two tones are applied depends also on the characteristics of the circuit, for example, the voltage gain of the amplifier.  From the analysis performed in this section, we propose a new technique for characterizing analog and RF circuits consisting in driving the circuit with the sum of two tones and, if the spectral component of the power dissipated at f2-f1 carries electrical information about the characteristics of the circuit at high frequencies, to derive these characteristics by thermal measurements at f2-f1.  III. FEASIBILITY OF THE TECHNIQUE  The goal of this section is to show the feasibility of the temperature measurements needed to track the spectral content of the power dissipated at f2-f1.    Fig. 1 Experimental set-up and sensor schematic.  Fig. 1 shows the layout of the IC used in the experimentation. It contains MOS devices in diode configuration (Fig. 2) which behave as dissipating devices and a differential temperature sensor embedded in the same silicon die. The output voltage of differential temperature sensors is proportional to the difference of temperature at two points of the silicon surface. In our case, the temperature at the sensing points is named T1(t) and T2(t) [3][5].   Fig. 2. Dissipative NMOS transistor in diode configuration.   The aspect ratio of the dissipating device is 10/1.2 and it is placed at 47 microns from the temperature monitoring point T1(t). Fig. 3 shows the I/V DC characteristic of the dissipating device. This plot can be fitted to a third order polynomial, resorting to the following expression:   2 30 1 2 33 30 13 62 3( )0.14·10 0.25·100.56·10 49.74·10s in in in inI V m m V m V m Vm mm m− −− −= + ⋅ + ⋅ + ⋅= − = −= =−, (6) Fig. 4 (left) shows the experimental set-up: the dissipating device is activated with two tones of frequencies f1 and f2. The sensor’s output is connected to a spectrum analyzer. Fig. 4 (right) shows the spectrum of the sensors output when f1 = 1 kHz and f2 = 1.130 kHz. In this Authorized licensed use limited to: UNIVERSITAT POLITECNICA DE CATALUNYA. Downloaded on September 20,2022 at 07:00:22 UTC from IEEE Xplore.  Restrictions apply. figure the temperature frequency components at f2-f1, 2f1-f2, 2f2-f1, f1 and f2 are clearly observed. If we apply two tones plus a DC voltage for polarizing the diode, the power dissipated at frequency (f2-f1) is:   ( )2 12 2 2 2 41 2 3 33 6 3f f DC DCP A m A mV A mV A m− = + + +  (7)  Fig. 3. I/V DC characteristic of the dissipative transistor.   Fig. 4. Experimental set-up (left) and temperature sensor output spectrum (right).   Analyzing this expression we can see that the first term 21A m  corresponds to the linear behavior of the diode (similar to the case of the resistor), and the other three terms correspond to the non-linearity of the diode. To validate experimentally expression (7) we have replaced the spectrum analyzer of Fig. 4 by a Look-in Amplifier. Fig. 5 shows the amplitude of the spectral component at (f2-f1) of the sensor’s output voltage versus amplitude A. We have fixed (f2-f1) at 1 kHz for three different values of f1: 100 kHz, 1 MHz and 10 MHz, with VDC fixed to 2V.   Fig. 5. Amplitude measurements from the Look-in Amplifier (Vout sensor), and equation (7) multiplied by the sensitivity of the sensor (all values are at f2-f1).  Additionally, the estimated amplitude of sensor’s output is plotted in the same figure, which is obtained by multiplying analytical expression (7) by the sensitivity of the sensor (81.73 V/W [5]). In Fig. 7 the power amplitude at (f2-f1) estimated from analytical equation (7) is drawn.    Fig. 6. Power amplitude estimation at f2-f1 from analytical equation (7).   From these figures we observe:  i) By comparing Vout for the three values of f1, we see that the magnitude of the spectral component of the temperature at f2-f1 does not depend on the absolute value of f1. This means that the m’s coefficients in expression (13) do not depend on the frequency in the range considered.  ii) We also observe a good matching between the measured and the estimated output voltage Vout, that validates the analysis performed.  iii) We can also observe from Fig. 6 that power dissipation magnitudes lower than 1 µW can be detected with temperature sensors embedded with the CUT.  IV. APPLICATION OF THE TECHNIQUE In this section we consider a tuned amplifier, whose gain is frequency dependent. Since the amplitude of the power dissipated at f2 -f1 depends on the gain of the amplifier, if the value of f1 and f2 are swept (keeping constant the value f2 -f1), then it is possible to obtain the bandwidth and the central frequency of amplifiers by plotting the magnitude of the dissipated power as a function of f1.  The circuit considered is a fully differential 2.4 GHz Low Noise Amplifier (see Fig. 7), designed in a 0.35 µm CMOS technology. Its electrical performances are: 24 dB voltage gain (16 in linear), 15 dB input return loss, 5 dB NF, -10 dBm 1 dB compression point and 10 mA DC current consumption. We have applied to its input two tones of equal amplitude (-15 dBm) and frequencies f1 and f2=f1 + 1 kHz. By sweeping f1 from 2 GHz to 3 GHz (and keeping always 1 kHz between the two tones) we have obtained by means of simulation both the voltage gain Av Authorized licensed use limited to: UNIVERSITAT POLITECNICA DE CATALUNYA. Downloaded on September 20,2022 at 07:00:22 UTC from IEEE Xplore.  Restrictions apply. inside this frequency range, as well as the amplitude of the power dissipated by the MCn transistor at 1 kHz, 1MCnkHzP .   Fig. 7. LNA schematic.  2.2 2.4 2.6 2.82.0 3.01002003004005000600501001502002500294f1 [GHz]Power dissip. by MCn @ 1KHz [uW]Av*AvAv*AvPower MCn Fig. 8. LNA voltage gain squared (right axis) and power dissipated at 1 kHz by the MCn transistor, 1MCnkHzP  (left axis).   In Fig. 8 we show 1MCnkHzP  and Av squared (note that the power dissipated at f2-f1 by an active device depends on the voltage gain squared). The two curves shown in the figure agree well in the band of interest. From the 1MCnkHzP  curve (solid line, left axis) it is possible to estimate that the LNA -3 dB bandwidth is BW=402 MHz and that its central working frequency is f0=2.398 GHz. If we use directly the Av×Av curve (dashed line, right axis), the values obtained are BW=414 MHz and f0 =2.400 GHz. The error between the original BW and f0 characteristics and their values obtained from the low-frequency dissipated power is 3 % and 0.1 %, respectively. This demonstrates that some electrical characteristics of the LNA at 2.4 GHz can be effectively estimated by monitoring the power dissipated by one of its devices at 1 kHz (power that, as has been shown in the previous section, can be obtained by thermal measurements).  V. CONCLUSION In this paper we have presented a novel strategy to observe electrical characteristics of analog/RF circuits. It is based on measuring the amplitude of some spectral components of the temperature when sensed at the silicon surface, close to the circuit under test.  This test and characterization strategy presents the following advantages:  i) The circuit under test is not electrically loaded, and then its electrical performances are unaffected.  ii) There is no need to have direct access to electrical nodes of the CUT to measure electrical signals.  iii) Temperature sensors can be embedded with the CUT, allowing in-field test and characterization.  iv) The information is read at f2-f1, independently of the absolute values of f1 and f2. Thus, temperature sensors and filters of the testing/characterizing system are designed for this low frequency, independently of the specific spectral band at which f1 and f2 are placed. The experimental results presented have shown that it is possible to measure power amplitudes lower than 1 µW using differential temperature sensors embedded with the CUT. Simulated results have shown an application of the technique by estimating the BW and central frequency of a 2.4 GHz LNA designed in a 0.35 µm CMOS technology.  ACKNOWLEDGEMENT This work has been partially supported by project TEC03289 of the Spanish MEC and FEDER funds.  REFERENCES [1] S.S. Akbay, A. Chatterjee, “Feature extraction based built-in alternate test of RF components using a noise reference,” in Proc. 22nd. VLSI Test Symp., pp. 273 – 278, April 2004.  [2] M. G. Mendez-Rivera, A. Valdes-Garcia, J. Silva-Martinez and E. Sanchez-Sinencio, “An On-Chip Spectrum Analyzer for Analog Built-In Testing,” Journal of Electronic Testing: Theory and Applications, Vol. 21, 2005, pp. 205-219.   [3] J. Altet, S. Dilhaire, S. Volz, J. M. Rampnoux, A. Rubio, S. Grauby, L.D. Patino, W. Claeys, and J.B. Saulnier, “Four different approaches for the measurement of IC surface temperature: application to thermal testing,” Microelectronics Journal, Vol. 33, 2002, pp. 689-696.   [4] N. Nenadovic, S. Mijalkovic, L.K. Nanver, L. K. J. Vandamme, V. d’Alessandro, H. Schellevis, J. W. Slotboom, “Extraction and Modeling of Self-Heating and Mutual Thermal Coupling Impedance of Bipolar Transistors”, IEEE Journal of Solid-State Circuits, Vol. 39 No. 10, Oct. 2004, pp. 1764-1772.   [5] J. Altet, A. Rubio, E. Schaub, S. Dilhaire, W. Claeys, “Thermal coupling in integrated circuits: application to thermal testing,” IEEE Journal of Solid State Circuits, Vol. 36, No. 1, Jan. 2001, pp. 81-91.    Authorized licensed use limited to: UNIVERSITAT POLITECNICA DE CATALUNYA. Downloaded on September 20,2022 at 07:00:22 UTC from IEEE Xplore.  Restrictions apply. 

Frequency characterization of a 2.4 GHz CMOS LNA by Thermal Measurements

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Frequency characterization of a 2.4 GHz CMOS LNA by Thermal Measurements

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