Tests and Measurements II: Distortion

Transcription

1 Tests and Measurements II: Distortion.1 Introduction A lot of changes have been made to the methodologies used for testg for distortion modern RF-contag SoC devices. Many excellent resources are available describg the types of distortion and how to test them. With the recent tegration of RF front ends to SoC transceivers, especially the area of wireless communications, some changes have been made to the fundamentals of distortion testg. In particular, the rise of homodyne, or ZIF, architectures has led to the importance of distortion mechanisms and products that have traditionally been ignored due to past architecture types. This chapter is aimed at enlighteng the SoC production test engeer to distortion testg techniques required as the levels of tegration contue to crease. However, it can also serve as an updated review of the fundamentals of distortion and distortion testg for all electronic devices general. This chapter takes concepts from traditional RF and traditional mixed-signal testg and unites them one discussion. With the tegration levels of today s SoC devices for wireless communications, it is necessary to have a full understandg of how these traditional analog measurements are performed, regardless of whether they are at RF frequencies or baseband frequencies. The concepts used performg RF frequency distortion measurements are the same as those used performg lower frequency distortion tests. Nonlear properties such as harmonic and termodulation distortion occur all real devices. The methods used to determe these properties, and other distortion properties, devices will be shown this chapter. Numerous papers have been written on various types of distortion tests rangg from audio frequencies to several gigahertz, but when one considers the 5

2 6 Advanced Production Testg of RF, SoC, and SiP Devices basic phenomenon of distortion, it all leads to the same result: degradation of desired signal.. Learity Distortion occurs due to the nonlear behavior of a device. All devices, whether RF or otherwise, exhibit nonlear behavior. At times it is part of proper operation, as the case of a high-efficiency power amplifier, mixer, or frequency doubler. At other times, nonlear behavior is undesired and a problem that deteriorates the tended performance of a DUT. Fundamentally, the learity of a system has two requirements [1]: 1. All frequencies the output of a system will be relative to the put by a proportionality, or weightg factor, dependent of power level.. No frequencies will appear the output, that were not present the put. However, because semiconductor devices are based on diodes and transistors, there is nonlear device behavior between the put and output signals. This is known as distortion.. Distortion SoC Devices When signals are sent through a device, the occurrence of distortion is evitable. The problem with distortion and it does not matter which type of distortion because it nets the same result is that distortion products take away from the tended, or fundamental, signal. For example, assume all of the desired power comg from a DUT was contaed a sgle tone at the fundamental frequency when the device was operatg at low power levels. When the device power level is creased and distortion occurs, the power begs to be seen at the distortion products (e.g., second and third harmonics), takg away from the power tended to be at the fundamental frequency. Distortion can occur any of the followg most common forms: harmonic distortion, termodulation distortion, or ga compression. Testg techniques for the presence of distortion consist of the application of sgle-tone (ga compression and harmonic distortion), two-tone (termodulation distortion), and multitone (cross modulation) stimuli to the DUT while analyzg the output spectrum.

3 Tests and Measurements II: Distortion 7.4 Transfer Function for Semiconductor Devices Because semiconductor devices are made of diode structures, a derivation of voltage behavior diode-based devices is presented here and will be used the subsequent harmonic and termodulation distortion explanations []. Most literature starts from the statement that the transfer function can be represented as a power series, but this discussion will beg with fundamentals. The defition of the current through a diode is αv ( ) I = I e 1 (.1) out S where I S is a constant (saturation) current of a diode, α is a constant dependent on temperature and the design of the diode structure, and V is the combed ac and dc voltage across the diode. If the total put voltage is generalized to conta both dc and ac components, then V = V0 v (.) ( V v ) S ( ) α I = I e 0 1 (.) out where V 0 is a dc voltage and v is a small signal ac voltage. Because v is small, a Taylor Series (or power series) expansion can be used to rewrite (.) as From (.), I I v di v d I out 1 out 0 = 0 K (.4) dv dv V 0 V0 di dv out V0 = αi e S αv0 (.5) and each successive derivative is just a constant, α, multiplyg the exponential, d N dv I out N V0 = α N I e S αv0 (.6)

4 8 Advanced Production Testg of RF, SoC, and SiP Devices It is often easier to work terms of voltages rather than currents sce they are simpler to measure. If the current through a diode is measured as a voltage across some resistance R, then from Ohm s law, (.4) becomes v = a av av av K (.7) out 0 1 where a 0, a 1, a, a,, are constants that have absorbed R and the derivatives. The term a 0 is a dc term describg the dc parameters of a diode. An amplifier, when workg the lear region, is described by the lear term a 1. The higher order terms are used to describe either the proper operation of nonlear devices, or the undesirable, nonlear distortion found many SoC devices. Equation (.7) is the fundamental equation that has been used to describe all effects of distortion on devices rangg from audio frequencies to RF applications for many years. The two common distortion tests, for harmonic distortion and for the various forms of termodulation distortion, volve applyg a sgle-tone susoid and two combed susoids to the device and analyzg the response. Mathematically this is described by acquirg the solutions to (.7) for each case. These are discussed the followg sections..5 Harmonic Distortion Consider what happens if the put voltage waveform to a DUT is a sgle-tone frequency, Then (.7) becomes v = Acos( ω t) (.8) vout = a0 a1acos ωt aa cos ωt a A cos ωt K (.9) Considerg only the first three components and applyg trigonometric identities show that each higher-order term can be rewritten as a multiple of the fundamental frequency ω; for example, and cos ωt = ( cos ) 1 ωt (.10) 1

5 Tests and Measurements II: Distortion 9 cos ωt = ( cos cos ) 4 ωt ωt (.11) 1 Therefore, a A vout = a0 a1acos ωt ( 1 cos ωt ) a A ( cos ωt cosωt) 4 a A a A a A vout = a0 a1 A cos ωt cos ωt 4 a A 4 cosωt (.1a) (.1b) Harmonic distortion occurs when some of a DUT s tended power is transferred from a desired frequency to a higher order multiple of the fundamental frequency. These higher order terms are called harmonics and are classified by their order. The order is an teger and is taken to be m. All of the higher order terms can be written terms of the fundamental frequency and from that it is immediately noticed that each higher order term is really the fundamental frequency ω multiplied by the order (e.g., ω, ω, and so forth) of the term. Thus, for any v = cos(ωt), the output will consist of all harmonics, mω, where m is an teger gog from mus fity to fity. Figure.1 shows the first few harmonic distortion products for a fundamental signal havg frequency, f 1, where f = ω/π. Note that if the frequency axis could be extended fitely, the harmonic distortion components would contue defitely, equally spaced, but decreasg amplitude. Harmonic distortion typically occurs at higher power levels, but because no devices are perfect, harmonic distortion can even be generated at low power Amplitude DUT f 1 f 1 f 1 f 1 Frequency Figure.1 Harmonic distortion products due to a sgle-tone put, f 1, to a DUT.

6 40 Advanced Production Testg of RF, SoC, and SiP Devices levels. It has been rarely tested for traditional, pure-rf devices for wireless communications because RF frequencies are so high already and the second and third harmonics are far from the frequency band of terest. On receiver devices, the harmonics will be filtered due to the fite bandwidth of the receiver. However, on transmittg devices, there is a little more concern, because it is important to ensure that signal transmission is mimal at other frequencies that may be used for other purposes. Harmonic distortion is defed and tested by application of a sgle-tone (frequency) susoidal waveform, as the precedg derivation. Even-order harmonics result from α j with even j. In (.1b) it is important to note that the amplitude of the nth harmonic consists of a term proportional to A n..5.1 Measurg Harmonic Distortion The two primary ways to quantify the harmonic distortion content of a DUT are (1) total harmonic distortion and () signal, noise, and distortion, both of which are discussed the followg sections Total Harmonic Distortion A standardized measure of harmonic distortion is total harmonic distortion (THD). THD is the relative power contaed all harmonics of a signal expressed as a percent of the fundamental signal power. It is a measure of how well the device converts energy to the desired fundamental signal versus the undesired harmonic signals. Harmonic distortion is specified (and tested) at a specified output power of the DUT. It is defed as follows: P P P4 K THD( %) = 100% P fundamental (.1a) where P, P, P 4, are the power, watts, of the second, third, fourth, and so on harmonics, respectively. P fundamental is the power of the desired fundamental signal. Alternatively, units of volts, as when measurg a digitized analog baseband signal, ( ) ( ) ( ) V V V4 K THD( %) = 100% V fundamental (.1b) where V, V, V 4, are the voltage amplitudes of the second, third, fourth, and so on harmonics, respectively. V fundamental is the voltage amplitude of the desired

7 Tests and Measurements II: Distortion 41 fundamental signal. In either case, an ideal device with no distortion would have 0% THD. If a measurement receiver, or digitizer, does not have adequate bandwidth, THD measurements are measured by makg several simple power measurements because the fundamental and harmonic frequencies are often far apart Signal, Noise, and Distortion Signal, noise, and distortion (SINAD) is a measure of the quality of a received signal and is really just another variation of THD. The defition of SINAD decibels is: [ ] SINAD db = 10 log 10 S N D N D (.14) where S is the signal power (watts), D is the distortion power (watts), and N is the noise power (watts). Ideally, the distortion and noise powers would be zero. For zero noise and zero distortion (or noise and distortion that approach zero), the SINAD equation would reduce to: SINAD[ db] 10 log 10 S 0 0 = 10 log 10 = small small ( VeryBigNumber) (.15) and the end result would be a large number that would dicate that the device converts energy very efficiently, has almost zero distortion, and adds almost zero noise. If the measured distortion value of one DUT versus another device is higher, then the overall SINAD result will be lower, dicatg that the first device is not as efficient. This happens because the distortion is both added to the numerator, but then divided by the denomator. The same thg happens for the noise. As an example, let S = 1 and consider that there is zero noise and that the distortion power is 1/10 of the signal power; then [ ] SINAD db = 10 log 10 log ( 11) = Now, doublg the distortion to 1/5 of S yields 10 S S = S (.16)

8 4 Advanced Production Testg of RF, SoC, and SiP Devices [ ] SINAD db = 10 log 10 log ( 6) = S 0 0. S = 0 0. S (.17) Equation (.17) yields a result that is smaller than (.16) by.6 db. This gives a good dication that the distortion plus noise power has creased by approximately two times or that the fundamental power has decreased by two times. In any case, the efficiency has been reduced terms of power by a factor of two []..6 Intermodulation Distortion The sgle-tone description of the previous section only yields harmonic distortion products and only reveals part of the distortion story for wireless communication systems and SoC devices. Modern wireless systems use multiple tones and multiple modulation formats to squeeze as much formation as possible to the channel bandwidth. In a communications system this means that signals one channel can cause terference with signals adjacent channels. As the spectrum becomes busier and the channels become more tightly spaced, mimizg termodulation distortion becomes more important [4]. Consider a more complicated put waveform placed to (.8), say, a two-tone signal: v ( t) = Acos ω1t Bcos ω t (.18) where ω 1 and ω are two arbitrary frequencies. Then (.9) becomes 0 1( cos ω1 cos ω ) ( cos ω cos ω ) ( Acosω t Bcosω t) vout = a a A t B t a A t B t a 1 K 1 (.19) The followg sections will expand the various terms (.19)..6.1 Second-Order Intermodulation Distortion In this case of a two-tone susoid, the a 0 and a 1 terms are straightforward. Because the expansion of the higher order terms of (.19) becomes quite lengthy, each of the components will be treated separately, then grouped by frequency and combed afterward. First, however, the followg additional

9 Tests and Measurements II: Distortion 4 trigonometric identity is needed to obta dividual sgle-frequency cose functions: 1 cos αcos β= cos α β cos α β [ ( ) ( )] (.0) The second-order term of (.19) is expanded as follows: ( ) = ( cos cos ) v t A ω t B ω t (.1a) 1 v ( t) = A cos ω t ABcos ω t cos ω t B cos ω t (.1b) 1 1 Usg trigonometric identities to restate the frequencies as multiples of ω 1, we obta v A = ( t) ( cos ω t) ABcos( ω ω ) t AB cos B 1 ( ω ω ) t ( co ω t ) 1 s (.1c) The result (.1c) describes both harmonic and termodulation distortion. When expanded, it contas sgle-frequency terms (harmonic distortion) and terms with multiple frequencies (termodulation distortion). Intermodulation distortion is the nonlear product caused by application of multiple put frequencies to a device teractg with each other. It has a more pronounced effect at elevated power levels. As with harmonic distortion, termodulation distortion occurs at different output frequencies than those put to the device. In communication systems the end result is that termodulation distortion from signals one channel can cause terference other channels. Characterizg termodulation distortion becomes more important as channels become more tightly spaced with the frequency spectrum. Note that with second-order termodulation distortion there are four distortion products, at the followg frequencies: ω 1,ω, ω 1 ω, ω 1 ω. The term second order comes from the fact that there are four combations of the coefficients of ω 1 and ω that, when added, give the value of two. Figure.(a) shows second-order distortion products resultg from the application of two tones to a device. Traditionally, second-order termodulation products have been of little concern for wireless communications

10 44 Advanced Production Testg of RF, SoC, and SiP Devices Amplitude DUT f 1 f f f f f 1 1 f 1 f Frequency (a) f 1 f Amplitude f 1 f DUT f1 f f 1 f f1 f f 1 f1 f f1 f Frequency (b) f f 1 f Figure. Intermodulation distortion products due to a two-tone put, f 1 and f, to a DUT [5]: (a) second-order products and (b) third-order products. devices because of their architecture. The superheterodyne architecture (see Chapter 1) that has been used from the begng of wireless communications devices converts the frequencies that are put to lower frequencies, but far from dc, thereby never havg to worry about the second-order product terference. More recently, the homodyne, or ZIF, architecture has elimated the termediate frequency, convertg the received RF signals to near-dc frequencies. This means that closely spaced frequencies at RF will be closely spaced after they are converted via a homodyne receiver. This holds for second-order products, as well as any other higher, even-ordered termodulation products, although for most communications devices, orders higher than two are relatively significant..6. Third-Order Intermodulation Distortion The third-order term of (.19) is expanded as follows: ( ) = ( cos cos ) v t A ω t B ω t (.a) 1 ( ) = ( cos ω cos ω ) v t A 1t B t ( A cos ω1t ABcos ω1t cos ωt B cos ωt ) (.b)

11 Tests and Measurements II: Distortion 45 v A AB = cos ω t ( t) ( cos ω t cosω t) ( 1 cos ω t) 1 AB ( 1 cos ωt) cos ω1t B ( cos ωt cosωt) 4 (.c) v A = B [ t t] 4 cos ω cos ω AB 1 cos ωt cos( ω1 ω) t cos( ω1 ω) t AB 1 cos ω1t cos( ω ω1) t cos( ω ω1) t ( t) [ cos ω t cos ω t] ( ) ( ) (.d) v A AB ( t) = 4 AB B 4 AB cos 4 AB cos 4 ( ω ω ) t A cos ω1t cosω1t 4 B cos ωt cosωt 4 AB 1 cos( ω1 ω) t 4 AB ω ω1 t cos ω ω1 t 4 ( ) ( ) (.e) Figure.(b) graphically shows the distortion products of (.e) arisg from two fundamental signals beg put to a device. There are six third-order distortion products, as shown. A few of these products are far from the fundamental (desired) frequencies and it is common practice to design filterg to a device to remove these products. Two terms of (.e), ω 1 ω and ω ω 1, however, are very close to the fundamental put frequencies. It is these two terms that have traditionally ( heterodyne device architectures) been the most troublesome and therefore tested exhaustively for. Specifically, the third-order products occur at the followg frequencies: ω 1,ω,ω 1 ω,ω ω 1,ω 1 ω, and ω ω 1 (notice the six terms). Note that the two products that are only dependent on a sgle frequency (only

12 46 Advanced Production Testg of RF, SoC, and SiP Devices ω 1 or only ω ) are third-order harmonic distortion products. The first four terms are aga relatively far away from the fundamental frequencies ω 1 and ω, so they are often outside of the normal frequency response of the device or can easily be filtered..6. Higher-Order Intermodulation Distortion Products Second- and third-order termodulation distortion products have been discussed. These are the most prevalent types tested for communications front ends. Although the products may be small, there are an fite number of termodulation distortion products. Sometimes termodulation distortion products havg orders greater than three may be of terest. This is true maly for high-power applications such as baseband power transmitter devices. Another possibility for which higher order termodulation products may be of concern is that as device performance is moved to lower signal levels through lower device noise floors, the higher order termodulation distortion products may become visible and impact the low-level signals. As with the even products, the higher-order odd products follow the same behavior as third-order products, makg troublesome terference many device architectures. A term called spectral regrowth is sometimes used to describe termodulation distortion [6]..6.4 Example of Harmonic and Intermodulation Distortion Products From (.1c), it can be stated that for any two-tone put waveform, v (t) = A cos ω 1 t B cos ω t, the output can be written terms of all harmonics of the form mω 1 nω, where both m and n are positive and negative tegers. The order of the distortion products can then be defed by order = m n (.) To demonstrate the impact of harmonic and termodulation distortion, an example is provided which two test tones (fundamentals), f 1 = 100 MHz and f = 101 MHz are put to a DUT. (These are just two arbitrarily chosen, close-spaced frequencies, and could have been any frequency range, that is, 1 MHz, 1 GHz.) The same methodology follows for all frequencies. Table.1 summarizes all of the harmonic and termodulation distortion products that have been discussed. Table. shows the distortion products that arise due to the chosen test frequencies discussed earlier. Dependg on the type of architecture of the device, this table shows how the various types of distortion impact it.

13 Tests and Measurements II: Distortion 47 Table.1 Two-Tone Harmonic and Intermodulation Distortion Products and Their Locations Number of Distortion Products Distortion Product Frequencies (Relative to Fundamental Two-Tone Input, f 1 and f ) Order Total Harmonic Intermodulation Harmonic Intermodulation 4 f 1, f f 1 f, f f f 1, f f 1 ± f, f ± f f 1, 4f f 1 ± f, f f 1, f 1 ± f, f ± f f 1, 5f f 1 ± f, f ± f 1, 4f 1 ± f, 4f ± f f 1, 6f f 1 ± f, f f 1, 5f 1 ± f, 5f ± f 1, 4f 1 ± f, 4f ± f f 1, 7f 4f 1 ± f, 4f ± f 1, 5f 1 ± f, 5f ± f 1, 6f 1 ± f, 6f ± f 1 N N N Nf 1, Nf Table. Location of Distortion Products for Input Tones of 100 and 101 MHz Frequency of Distortion Product (MHz) Order Harmonic Intermodulation 00, 0 1, 01 00, 0 99, 10, 01, , 404, 199, 0, 401, 40, , , 10, 99, 04, 501, 50, 50, , 606, 198, 04, 99, 400, 405, 601, 60, 604, , , 104, 98, 05, 499, 506, 701, 70, 70, 704, 705, 706 Harmonic distortion products are found at much higher frequencies and, as discussed earlier, are mostly only of concern to neighborg channels or frequency bands. If necessary, filterg can remove their presence. Intermodulation distortion products affect devices quite differently. In the case of heterodyne transceiver architectures, the odd-order termodulation products are of concern. In the case of more recent usage of homodyne (ZIF) architectures, the even-order products are of more concern because they arise the baseband signals (near dc) where filterg is not often possible for the tended signal would be filtered out.

14 48 Advanced Production Testg of RF, SoC, and SiP Devices.6.5 Intermodulation Distortion Products of a ZIF Receiver Consider a two-tone test signal applied to the put of an RF-to-baseband front-end ZIF receiver. In this DUT, the put RF signal is downconverted directly to a baseband analog signal. In the case of second-order termodulation distortion, Table.1 can be used to show that a second-order product exists at f 1MD = f tone1 f tone (.4) For the calculations showg the impact of third-order termodulation distortion products, it is now necessary to consider the LO frequency used downconvertg the signals. As an example, one of the third-order products falls at f = f f f (.5) 1MD tone tone1 LO This tone falls the baseband region and could possibly cause terference with the desired operation a multichannel environment, if not adequately characterized..7 Measurg Intermodulation Distortion A figure of merit known as the tercept pot has been established to describe and quantify termodulation distortion. It is the pot at which the termodulation distortion product power level equals (tercepts) that of the fundamental. Almost always, the tercept pot is beyond the lear operation of the device and, therefore, the tercept pot is a fictitious pot. The various tercept pots are each related to the order of distortion beg discussed. For example, the third-order tercept pot quantifies third-order termodulation distortion. The tercept pot of a device cannot be measured directly, because it is typically at a very large power level. Instead, the measurement is performed at lower, typical operational power levels and extrapolated to determe the tercept pot. The tercept pot is always referenced to either the put or output power. This is discussed Section The Intercept Pot, Graphically Figure. is a plot of the output power from a DUT versus the put power applied to it. The small-signal ga, second-order tercept pot (IP), and third-order tercept pot (IP) are shown on the graph. 1 It is of fundamental 1. Traditional RF measurement theory often refers to the third-order tercept pot with the abbreviation TOI.

15 Tests and Measurements II: Distortion 49 IP IP Ouput power (dbm) Lear (slope = 1) nd order (slope =) rd order (slope =) Input power (dbm) Figure. Output power versus put power, demonstratg the concept of tercept pots. importance is to observe that, Figure., the slope of the small-signal ga is 1. The slope of the second-order termodulation distortion product power level is, and that of the third-order product is. This means that with a 1-dB reduction of the put power, the fundamental tone will reduce by 1 db, whereas the third-order product power will reduce by db. (The converse is also true.) Notice that it is physically impossible to measure either of the tercept pots directly. As the put power is creased toward either fictitious tercept pot, the DUT becomes nonlear. The output signal starts clippg, and the extra energy is diverted to the higher order harmonics. The lear portion of the small-signal ga le must be extended to fd the crossg pot of the second- and third-order products. Notice that the IP pot tercepts the lear curve before the IP pot. The graph highlights that a high IP number is desired. The higher the IP number, the less distortion the device exhibits under normal operatg power levels..7. The General Intercept Pot Calculation In a general sense, for any order of termodulation distortion product, the tercept pot (dbm) is calculated by measurg the power levels of the output of a DUT resultg from the application of a two-tone signal. There are many variations of the calculation, but they are all terrelated, as described next section. One such calculation is

16 50 Advanced Production Testg of RF, SoC, and SiP Devices IPN = P Fundamental,Output ( PFundamental,Output PIMDN) N 1 (.6) where P Fundamental,Output is the power (dbm) of either of the two put tones, N is the order of the distortion product, and P IMDN is the power level (dbm) of the distortion product as measured at the respective frequency at the output of the DUT. Sometimes the value parentheses (.6) is represented as a sgle variable. Whichever way it is represented, it is simply a difference power, havg units of dbc (db below carrier ). Assumg that the frequency response of the device is flat across the frequency spacg of the two tones, the output power of either of the two tones could be used as the value for P Fundamental,Output. Extendg (.6), the equation for calculatg the second-order tercept pot is ( ) IP = Fundamental,Output Fundamental,Output IMD and for the third-order tercept pot is P P P (.7) IP = P Fundamental,Output ( PFundamental,Output PIMD) (.8) Keep md that the title of this section uses the term calculation. This is done because the tercept pot is an direct measurement where the termodulation distortion product power level is what is measured, then the tercept pot is calculated from that value. Note that P Fundamental,Output is the power level of one of the output tones. This assumes that the two tones have power levels equal to each other at the output of the DUT. Often this is not the case. To handle this situation of uneven output power levels of the two tones, the average power between the two tones at the output can be used. Alternatively, both can be used to arrive at two different values of IP and then the lower, or worse, value of IP is reported..7. Input- and Output-Referencg of Intercept Pots Equations (.6) to (.8) used the output power levels of the device as the reference pot of their calculation. This is the common approach to this calculation. When done this fashion, the termodulation products are termed output-referenced. For completeness, these equations can be rewritten as

17 Tests and Measurements II: Distortion 51 ( ) OIP = Fundamental,Output Fundamental,Output IMD P P P (.9) and OIP = P Fundamental,Output ( PFundamental,Output PIMD) (.0) The only difference between these two sets of equations is the name on the left-hand side of the equations. The standard convention (which is almost always the one that is used) is that the tercept pot (regardless of order) for any termodulation distortion measurements on the transmitter/upconversion cha of a DUT (such as a power amplifier) is output referenced, and for any receiver/downconversion cha of a DUT (such as an LNA) measurements, it is put referenced. The terestg thg is that for a given tercept pot measurement, the only difference between put referencg and output referencg is the small-signal ga of the DUT. In practice, the ga can simply be measured, or the equations can be rearranged. In this case ga is represented as G = PFundamental,Output PFundamental, Input (.1) where G is the ga of the DUT (db) and P Fundamental,Output is, aga, the power (dbm) of either of the two put tones, but now it is the power that is applied to the DUT. Thus, ( ) IIP = PFundamental, Output PFundamental,Output PIMD G (.) or and or ( ) IIP = Fundamental, Input Fundamental,Output IMD P P P (.) IIP = P Fundamental, Output ( PFundamental,Output PIMD ) G (.4)

18 5 Advanced Production Testg of RF, SoC, and SiP Devices IIP = P Fundamental, Input ( PFundamental,Output PIMD) (.5) where IIP dicates put referencg. It must be emphasized that the ga value used (.) and (.4) has to be the small-signal ga (measured durg lear mode of operation of the DUT). If this ga is measured when the device is compression and used the calculation of the tercept pot, then the tercept pots will mistakenly be reported to be worse than their actual values..7.4 Example: Calculatg the IP of an RF LNA Consider an RF low-noise amplifier that has had its ga measured as 0 db. The first step the distortion measurement is to apply a two-tone signal to the put of the DUT. Consider the two tones to be, and,140.0 MHz, with both havg a power level of 0 dbm. Usg the equations for determg the frequencies of second-order termodulation distortion products Table.1, these put tones will generate a product at 400 khz that is very far away from the operational capability of this device, so there is no need to measure IP. Aga, usg Table.1, a third-order termodulation distortion product falls at MHz, which is the operational bandwidth of the LNA and must be measured. The next step is to measure the power of the third-order termodulation product, P IMD. In this example, accept that it was measured to be 84 dbm. Because this is an LNA, it would be most appropriate to represent the result as put referenced. Usg (.5), the result is ( 10 ( 84) ) IIP= 0 = 7 dbm (.6).8 Source Intermodulation Distortion The residual termodulation distortion that is due to the hardware volved sourcg the two-tone signal (sources, tone comber circuitry, and so forth) is called source termodulation distortion (SIMD). Most often, any SIMD contribution comes from poor isolation between the two sources that supply the put tones. It is important to be aware of the amount of this contributed distortion from the measurement setup. To measure the SIMD, simply remove the DUT and connect the two-tone source directly to the measurement equipment and

19 Tests and Measurements II: Distortion 5 measure the power at the frequencies where the termodulation distortion products are expected [7]. One would thk that this is only of concern LNA and PA testg where the output of the device is the same frequency range as the put signals. However, keep md that for a frequency-translatg device like a front-end receiver, any SIMD will also be downconverted. In many termodulation distortion measurement setups where multiple power levels need to be applied to the DUT (as characterizg power-out versus power- to establish the nonlear characteristics), attenuators are often used between the two-tone output and the DUT. The reason for this is so that the sources can stay at a constant power level and, hence, a constant value of SIMD. The power levels can be adjusted simply by adjustg the attenuators. This elimates changes the source settgs and elimates the possibility of the SIMD changg. The contribution of error due to SIMD can be calculated from the followg formula [7]: SIMD MIMD 0 ( ) error = 0 log 1± 10 (.7) 10 where SIMD and MIMD are the relative (dbc) values of termodulation distortion products at the expected product frequencies for the source and measurement (DUT), respectively. Usg this equation, and an error of ± db leads to the rule of thumb that the SIMD should be at least 0 db below that of the expected DUT IMD. In practice, SIMD of >40 db below that to be measured is better..9 Cross Modulation Cross modulation, sometimes called XMOD, is a type of distortion caused by the termodulation/teraction between more than two tones the same operational bandwidth. Historically, this measurement was not too common except cable television devices, such as le amplifiers where up to hundreds of simultaneous signals are transmitted across the same wide bandwidth of operation (which can be greater than 1 GHz). Recent multicarrier digital modulation formats, such as orthogonal frequency division multiplexg (OFDM) for WiMAX or WLAN, use multiple carriers with the same bandwidth. This makes them susceptible to the effects of cross-modulation distortion products. Reference [8] provides an -depth analysis of how cross modulation impacts the performance of CDMA receivers based on transmitter leakage through duplexers to the LNA front end.

20 54 Advanced Production Testg of RF, SoC, and SiP Devices The measurement of cross modulation is performed by turng on all tones/carriers except one, and then measurg the power at the frequency of the carrier that is not turned on. Any power at this frequency is due to cross modulation between all other carriers..10 Ga Compression The a 1 term of (.9) is a lear term correspondg to the ga of a DUT. Under lower power level (i.e., small-signal) conditions, the output of the DUT is related to the put by the proportionality factor, or ga a 1. As the power level is creased, a distortion mechanism termed ga compression can come to play where the output begs to saturate, no longer followg the lear ga. If only the a 1 (lear) term of (.9) is considered and it is converted to logarithmic scale and plotted as Figure.4, the slope of the trace is unity. This plot, however, is that of a real device, which does not follow (.9) at higher put power levels. At some pot, the output power deviates from the unity sloped curve, movg to a saturation region (the dashed le shows the extrapolation of the lear trace). The measure of saturation, which is sometimes called first-order distortion, is ga compression and it is described by the standardized Output power (dbm) =1dB 1 db compression pot Lear (slope = 1) Ideal lear output Actual device output Input power (dbm) Figure.4 Output power versus put power, demonstratg the concept of ga compression.

21 Tests and Measurements II: Distortion 55 measure called the 1-dB compression pot, or P 1dB. While mixers exhibit compression, the measurement was traditionally most often made on amplifiers; hence, the term ga compression. Wireless devices must operate over a wide dynamic range. The upper bound of the dynamic range is often specified with the 1-dB compression pot. P 1dB can be referenced to the put power level or the output power level (the projections onto the put or output axes of Figure.4). These are termed put referred and output referred, respectively. The P 1dB of receivers are usually put referred, and the P 1dB of transmitters are usually output referred. The equation describg the ga, db, at the 1-dB compression pot is G = db G (.8) where G 0 is small-signal ga. The output power can be rewritten terms of the compression as follows: P P = G = G (.9) ( ) ( ) ( ) db output db put db Given (.9), the 1-dB compression pot can be found by measurg the difference the output power mus the put power. When that difference is 1 db less than the small-signal ga, the 1-dB compression pot has been determed. For production testg, test time must be considered. The 1-dB compression pot can be found usg a brute-force approach whereby the put power starts at a low level and is learly swept upward small steps, until the 1-dB compression pot is found. A much more efficient method is the one which, first, the ga is measured at a power level where the DUT is known to be lear. Then, a bary search route is used to vary the put power to fd the 1-dB compression pot with some stated resolution. A variation on ga compression that is often used production testg of wireless SoC devices is to operate the DUT at the P 1dB pot and then to perform another type of measurement. An example, usg a Bluetooth device, is to overdrive the receiver to the 1-dB compression pot and perform a bit error rate (BER) test under this condition to ensure tegrity. To show that the put-referred and output-referred compression pots are related, consider a DUT with nomal small-signal ga of 8 db that has had the put-referred P 1dB pot determed to be 19 dbm. Rearrangg (.9), P = P G = = 8 (.40) 1 db( output ) 1dB( put ) 1dB dbm

22 56 Advanced Production Testg of RF, SoC, and SiP Devices.10.1 Conversion Compression Frequency-Translatg Devices A mixer, although considered a nonlear device, has the same compression behavior. The only difference is that the put and output of the mixer, taken to be RF and IF, respectively (for example), are at different frequencies. The same algorithms apply, usg power measurements at the RF and IF ports of the DUT. As RF put power is creased, IF output power creases. However, at some power level, the IF output power begs to crease at a lesser rate than the RF put power, and eventually the IF power level deviates from its learly expected value by 1 db. This pot is the conversion compression pot..11 Mimizg the Number of Averages Distortion Measurements Many distortion measurements volve measurg low-level signals and comparg them to a high-level (e.g., carrier) signal. A common mistake production measurements is to set up the entire measurement hardware for the needs of the low-level signal acquisition. Consider that a low-level distortion signal such as the third-order product can, at times, be very near to the measurg equipment s noise floor. Often, the clation is to set up the entire measurement to accurately acquire the low-level signal. This can require multiple averages and oversamplg. If N is taken to be the number of averages, then the test time can be creased, learly, up to N times the sgle acquisition test time. For the low-level signal, it could be necessary to do this. However, dog this for the acquisition of the high-level signal, which is significantly above the measurement noise floor, leads to wasted test time and, ultimately, creased cost. References [1] Oliver, B., Distortion and Intermodulation, Hewlett Packard Application Note 15. [] Pozar, D. M., Microwave Engeerg, Readg, MA: Addison-Wesley, [] Schaub, K., and J. Kelly, Production Testg of RF and System-on-a Chip Devices for Wireless Communications, Norwood, MA: Artech House, 004. [4] Theory of Intermodulation Distortion Measurement (IMD), Maury Microwave Application Note 5C-04, [5] Texas Instruments, Understandg and Enhancg Sensitivity Receivers for Wireless Applications, Technical Brief SWRA00, [6] Ba, D., RF Distortion: Reducg IM Distortion CDMA Cellular Telephones, RF Design, December 1996, pp

23 Tests and Measurements II: Distortion 57 [7] Barkley, K., Two-Tone IMD Measurement Techniques, RF Design, June 001, pp [8] Ko, B., et al., A Nightmare for CDMA RF Receiver: The Cross Modulation, Proc. First IEEE Asia Pacific Conf. on ASICs, August 5, 1999, pp