Accurate Absolute and Relative Power Measurements Using the Agilent N5531S Measuring Receiver System. Application Note

Transcription

1 Accrate Absolte and Relative ower easrements Using the Agilent N5531S easring Receiver System Application Note

2 Table of Contents Introdction... N5531S easring Receiver System...3 N553A/B sensor modle...3 Two-resistor power splitter db pad...3 ower sensor...4 Fnctional smmary...5 RF ower easrement...6 Example: Verifying the power-level accracy of a signal generator...6 easrement procedre...6 Applying the specification...7 Tned RF Level easrement...8 Specifications...8 Spporting information for specifications...9 Range-to-range cal factor correction...9 Absolte TRFL measrement...11 easrement procedre...11 Applying the specification...11 Relative TRFL measrement...11 easrement procedre...1 Applying the specification...1 Appendix A: Derivation of Absolte RF ower Accracy...13 easrement eqation...13 Uncertainty eqation...14 Appendix B: Derivation of Tned-RF-Level (TRFL) Amplitde Uncertainty... Detector linearity...4 Residal noise...7 Range-to-range cal factor...9 Combined ncertainty for TRFL measrement...30 Introdction The Agilent N5531S measring receiver system is the sccessor to the venerable (and now discontined) 890A measring receiver. The center piece of the N5531S is an optional firmware personality modle for the Agilent SA Series spectrm analyzers (Option 33). The N5531S measring receiver system matches or otperforms the 890A in every operating mode, while extending the fndamental operating freqency range from 1.3 GHz (890A) to as high as 50 GHz. Accrate power-level measrement was a key capability in the 890A that has been carried over to the N5531S. This capability is essential for the calibration of signal-generator otpt level and step-attenator accracy. Among the more important performance parameters for any signal generator are the absolte and relative accracies of its otpt power level. The highest-accracy measrement of the otpt level of a signal generator reqires a power meter and sensor. However, modern power sensors can measre only part of the otpt range of modern signal generators. Below 70 dbm, some other method mst be sed. The traditional approach has been to check the relative accracy of the generator s otpt level for power levels below the range of power sensors. The power meter is employed to establish a reference power level, and a sensitive, linear measring receiver is sed to verify level accracy relative to that reference down to 140 dbm. Appendix C: Two-Resistor Verss Three-Resistor ower Splitter Choice...33

3 N5531S easring Receiver System As shown in Figre 1, the N5531S measring receiver system consists of an E444xA SA Series high-performance spectrm analyzer (with measring receiver personality, Option 33), a -Series power meter (N1911A or N191A) or an E power meter (N1913A or N1914A), and an N553A/B sensor modle. Agilent -Series power meter RF inpt N553A/B sensor modle 3-dB pad Splitter ower sensor HWCI LAN cable HWCI3 Figre 1: N5531S measring receiver system N553A/B sensor modle The sensor modle incldes a low-freqency, mlti-signal cable between the power sensor otpt and the power meter, and a coaxial RF cable between the sensor modle and the spectrm analyzer inpt. Figre shows the internal block diagram of the N553A sensor modle. The newer N553B sensor modle is the drop-in replacement of the N553A, sing the N848X power sensor in lie of the 848X. Agilent SA Series spectrm analyzer HWCI 1 Two resistor splitter 3 db ad 848x power sensor Figre : N553A sensor modle (N553B has similar architectre bt ses an N848x power sensor instead) Two-resistor power splitter The details of the two-resistor power splitter, especially why it was chosen over a three-resistor power splitter, are covered in Appendix C. 3 db pad At the expense of 3 db of signal loss, this pad improves the match between the otpt of the power splitter and the inpt of the power sensor. It does this by attenating the reflected voltage waves moving in either direction (toward or away) from the power sensor. 3

4 ower sensor The N553A sensor modle contains an Agilent 848XA power sensor. The N553B sensor modle contains an Agilent N848XA power sensor. While the analyses in this application note are based on the 848X they apply to the N848X as well. Table 1. N553A/B Option map N553A/B Option Freqency range Sensor sed khz 4. GHz 848A/N848A Hz 18 GHz 8481A/N8481A Hz 6.5 GHz 8485A/N8485A Hz 50.0 GHz 8487A/N8487A The power measrement range of the 848XA sensor family is +0 dbm to 30 dbm. The (nominal) 7 db of loss provided by the power splitter and 3 db pad inside the N553A offsets the measrement range of the N553A to +30 dbm to 0 dbm. The 848XA power sensor family incorporates thermocople technology. Thermocople sensors have been the technology of choice for sensing RF and microwave power since their introdction in 1974 (The N848XA power sensor family was introdced in 008 as a direct replacement to the 848XA). This is primarily becase of their: 1. higher sensitivity, as compared to thermistor-based sensors. higher accracy, as compared to diode-based sensors 3. inherent sqare-law detector characteristic (inpt RF power is proportional to DC voltage ot) Since thermocoples convert RF energy into heat, they are tre averaging detectors. This allows them to accrately measre the power of all types of signals from continos wave (CW) to complex digital phase-modlated waveforms. In addition, they are more rgged than thermistors, measre power levels as low as 1.0 μw ( 30 dbm, fll scale), and they have lower reflection coefficients reslting in lower vales of mismatch loss. Althogh the conversion of RF-inpt power to DC-otpt voltage is highly linear over most of a thermocople s measrement range, the DC-otpt voltage varies nonlinearly with the average temperatre of the thermal element. At high power, the average thermocople temperatre increases, increasing the otpt voltage by a larger factor than predicted by linearly-extrapolating data from lower power levels. At a power level of 30 mw, the DC otpt is 3% higher than predicted by the low-level vale. At 100 mw, the otpt is abot 10% higher. Circitry inside the power meter compensates for this non-linear temperatre-driven power-level effect. Circitry inside the sensor itself compensates for changes in its ambient temperatre. The otstanding linearity of the 848XA sensors is reflected in their specifications. Table. 848XA ower sensor linearity Linearity for 30 dbm to +0 dbm Sensor model nmber ower range 8481A 848A 8485A 8487A 30 dbm < < +10 dbm ~0 ~0 ~0 ~0 +10 dbm < < +0 dbm ±3.0% ±3.0% ±3.0% ±3.0% The principles and application of thermocople power sensors are discssed in: Fndamentals of RF and icrowave ower easrements (art ): ower Sensors and Instrmentation, AN 1449-, literatre nmber EN. 4

5 Calibrating (i.e., characterizing) the N553A/B sensor modle is almost as simple as calibrating an 848XA power sensor. By terminating the spectrm analyzer otpt of the modle with a precision, 50 Ω load, the modle becomes a one-port device, behaving essentially as an attenated power sensor. The path throgh the series connection of the power splitter/3 db pad/848xa sensor is calibrated as if it were a reglar power sensor. The reslting calibration data incldes: calibration factor calibration factor ncertainty reflection coefficient magnitde reflection coefficient-magnitde ncertainty reflection coefficient phase This data is provided on a floppy disc so that it can be stored in the SA memory as a correction file to be sed by the N5531S measring receiver personality. The calibration factor ncertainty is combined with the other power sensor and power meter ncertainties to determine the overall ncertainty of a specific power measrement. Fnctional smmary Table 3: N5531S measrement site easrement N5531S component Freqency conter SA spectrm analyzer, Option 33 A depth SA spectrm analyzer, Option 33 F deviation SA spectrm analyzer, Option 33 deviation SA spectrm analyzer, Option 33 A/F/ modlation rate A/F/ modlation distortion Tned-RF level absolte Tned-RF level relative Absolte-RF power Adio: Freqency, AC level, and distortion SA spectrm analyzer, Option 33 SA spectrm analyzer, Option 33 N553A/B pls SA spectrm analyzer, Option 33 and, -Series or E-Series power meter SA spectrm analyzer, Option 33 N553A/B pls SA spectrm analyzer, Option 33 and, -Series or E-Series power meter SA spectrm analyzer with Option 107 and Option 33 5

6 RF ower easrement In the RF power mode, the N5531S measres absolte power in the range 10 to +30 dbm via the N553A/B sensor modle and the -Series power meter. The accracy of this measrement mode is dependent on power level and freqency as indicated by the specification table below. lease refer to the easring Receiver ersonality chapter of the latest Specifications Gide for the Agilent SA Series spectrm analyzer for the complete and crrent specifications. Table 4: N5531S RF power measrement ower meter range ower level (dbm) Freqency range Absolte RF power accracy** 1 +0 to khz 4. GHz ±0.356 db to GHz ±0.400 db to GHz ±0.387 db to GHz ±0.40 db to khz 4. GHz ±0.190 db to GHz ±0.67 db to GHz ±0.380 db to GHz ±0.97 db 550 N553A/B option ** ismatch effects between the DUT and the N553A/B sensor are NOT inclded in the specifications given in this table, becase of the dependence on the DUT SWR. Other mismatches are nder control becase of the two-resistor splitter (see Appendix C), the effects of mismatch between the spectrm analyzer and the sensor modle case negligible changes in the relationship between the otpt voltage of the DUT and the power sensor measrement reslts. Ths, this effect is inclded in this absolte RF power accracy specification colmn. The mismatch presented by the spectrm analyzer does affect the impedance seen at the inpt of the sensor modle. This effect is inclded in the system Inpt SWR specification. Example: Verifying the power-level accracy of a signal generator E448C signal generator specification: For the power otpt range: +15 to 100 dbm, ower level accracy: ±0.5 db, for 50 khz < f.0 GHz ±0.6 db, for.0 GHz < f 3.0 GHz Becase the power range covered by the N5531S RF power level measrement is limited to a lower level of 10 dbm, the signal generator will be set to an otpt level of at least 10 dbm. easrement procedre 1. Connect and configre the measring system. Calibrate and zero the power meter 3. Select easring Receiver mode on the SA 4. Set the signal generator freqency to.0 GHz 5. Set the signal generator power level to 10 dbm 6. ress the RF ower soft key on the SA front panel 7. Wait for the N5531S to retrn a stable reading (e.g., 10 dbm) 6

7 Applying the specification A specification is a qantitative statement abot the range of vales, centered on the indicated vale, within which the tre vale of some performance parameter lies, with a stated level of statistical confidence (typically 95%). When applied to a measrement, a specification essentially becomes an ncertainty for that measrement. RF power level accracy is defined as: ACC RF [ db] ACTUAL IND This eqation applies both to the E448C signal generator and to the N5531S measring receiver. For the E448C (assming: 50 khz f.0 GHz), the specified accracy is: [ ] 0.5 db 0.5 db ACTUAL IND + ACTUAL IND the tre power available at the otpt of the signal generator the power level indicated by the signal generator For the N5531S with the N553A/B sensor modle option 504, the specified accracy is: SG [ ] db 0.19 db ACTUAL IND + ACTUAL IND R the tre power level present at the N553A/B inpt connector the power level indicated by the N5531S Alternatively: IND [ ] 0.19 db 0.19 db + ACTUAL R This says that the actal power present at the inpt to the N5531S lies within ±0.19 db of the power level indicated by the N5531S. To nderstand how this vale of ±0.19 db was derived, see Appendix A. Note that this specification does not inclde the effect of mismatch. Ignoring mismatch for the moment, and eqating the actal power ot of the signal generator to the power incident on the N553A/B sensor modle: [ ACTUAL] [ ACTUAL] SG R In terms of the eqations shown above, this leads to: Note that is the ncertainty of the measrement made by the N5531S Inserting the nmerical vales listed above: IND [ ACC ] [ ACC ] + [ ] RF SG [ ACC RF ] R, in db RF R IND R IND SG [ ACC ] [ ± ( )] RF SG 0, in db IND R IND SG 7

8 Tned RF Level easrement In the N5531S, Tned RF Level (TRFL) is measred by the SA spectrm analyzer. Specifications Absolte TRFL accracy is specified relative to an absolte power level reference established by the sensor modle and power meter components of the N5531S. The reslting measred vale depends on the specifications of the power sensor, power meter, and SA. Table 5. N5531S absolte TRFL measrement accracy ower level range re-amp OFF Absolte TRFL accracy [db] +0 dbm to maximm power ±(ower meter range 1 ncertainty db/10 db step) Residal noise threshold power to +0 dbm inimm power to residal noise threshold re-amp ON Residal noise threshold to +16 dbm inimm power to residal noise threshold Definition Residal noise threshold ±(ower meter range ncertainty db/10 db step) ±(Cmlative error Note Note3 (Inpt power residal noise threshold power) ) ±(ower meter range ncertainty db/10 db step) ±(Cmlative error Note Note3 (Inpt power residal noise threshold power) ) inimm power + 30 db Notes: 1. In absolte TRFL measrements, the cmlative error is the error incrred when stepping from a higher power level to the residal noise threshold power level. The formla to calclate the cmlative error is ±(0.190 db db/10 db step). For example, assme the higher level starting power is 0 dbm and the calclated residal noise threshold power is 99 dbm. The cmlative error wold be ±( [99/10] x db), or ±0.40 db. The mltiplier in brackets is converted to the smallest integer that is not less than the vale in brackets.. In absolte TRFL measrements, the cmlative error is the error incrred when stepping from a higher power level to the residal noise threshold power level. The formla to calclate the cmlative error is ±(0.356 db db/10 db step). For example, assme the higher level starting power is 0 dbm and the calclated residal noise threshold power is 99 dbm. The cmlative error wold be ±( [99/10] x db), or ±0.406 db. The mltiplier in brackets is converted to the smallest integer that is not less than the vale in brackets. 3. The nits of absolte TRFL accracy are decibels. The nits of inpt power and residal noise threshold power are both dbm. The nits of their difference is ths decibels. The nits of the sqare of their difference is ths decibels-sqared. Therefore, the nits of this constant are inverse decibels. 8

9 Relative TRFL accracy is specified relative to an arbitrary power level selected by the spectrm analyzer. This accracy depends solely on the specifications of the SA. Table 6: N5531S relative TRFL measrement accracy ower level range Residal noise threshold to maximm power inimm power to residal noise threshold Range ncertainty Range 3 ncertainty Residal noise threshold power Relative TRFL accracy [db] ±( db/10 db step) ±(Cmlative error Note Note (Inpt power residal noise threshold power) ) ±0.031 db ±0.031 db inimm power + 30 db Notes: 1. In relative TRFL measrements, the cmlative error is the error incrred when stepping from a higher power level to the residal noise threshold power level. The formla to calclate the cmlative error is ±(0.015 db db/10 db step). For example, assme the higher level starting power is 0 dbm and the calclated residal noise threshold power is 99 dbm. The cmlative error wold be ±( [99/10] x db), or ±0.065 db. The mltiplier in brackets is converted to the smallest integer that is not less than the vale in brackets.. The nits of relative TRFL accracy are decibels. The nits of inpt power and residal noise threshold power are both dbm. The nits of their difference is ths decibels. The nits of the sqare of their difference is ths decibels-sqared. Therefore, the nits of this constant are inverse decibels. Spporting information for specifications In order to se the accracy specification, the minimm power and residal noise threshold information is needed. The relationship between these levels is given in both Table 5 and Table 6. A sbset of information from the specifications gide is given in Table 7. Table 7: inimm power Freqency range RBW Uninstalled reamplifier Installed GHz 10 Hz 136 dbm 140 dbm Range-to-range cal factor correction The SA measres the tned-rf-level in three distinct ranges, as shown in Figre 3 below. This approach allows the SA to maintain a favorable signal-to-noise ratio as the signal level decreases toward the noise floor of the SA. The actal range switching involves changing the setting of the internal attenator and either inclding or exclding the internal preamp of the SA. See Table 7. Table 8: N5531S TRFL measrement ranges Range SA atten (db) re-amp Switch point** (dbm) 1 30 OFF 0 10 OFF ON 78 ** Example vales. Actal switch point power level depends on the signal-to-noise ratio. CalFactor1 (see Figre 3) is simply the ratio of the power measred by the N5531S power meter to the power indicated by the SA in range 1. Sbseqent measrements made in range 1 are atomatically corrected by the SA to inclde CalFactor1. If a relative TRFL measrement is being made, then CalFactor1 is 0 db. CalFactor is the ratio of the power indicated by the SA in range 1 to the power indicated in range at the switch-point between range 1 and range. The power level is held constant while the range is switched and the measrements are made. Sbseqent measrements made in range are atomatically corrected by the SA to inclde CaFactor1 pls CalFactor. CalFactor3 is the ratio of the power indicated by the SA in range to the power indicated in range 3 at the switch-point between range and range 3. The power level is held constant while the range is switched and the measrements are made. Sbseqent measrements made in range 3 are atomatically corrected by the SA to inclde CalFactor1, CalFactor, and CalFactor 3. The ncertainty of the vales of the three range-to-range cal factors is derived in Appendix B. 9

10 Signal level step down SA readot First Cal point ower meter range reading: SA 1, CalFactor 1 SA 1 Range 1 the displayed TRFL SA 1 + CalFactor 1 Second Cal point Range switch level reading: SA 1, SA CalFactor SA 1 SA Range the displayed TRFL SA + CalFactor + CalFactor 1 Third Cal point Range 3 switch level reading: SA, SA 3 CalFactor 3 SA SA 3 Range 3 the displayed TRFL SA 3 + CalFactor 3 + CalFactor + CalFactor 1 Figre 3. N5531S TRFL measrement ranges 10

11 Absolte TRFL measrement aking an absolte power measrement sing TRFL mode reqires calibrating the SA with a known, absolte power level via the N553A/B sensor modle and -Series power meter. Then, the power level to be measred is presented to the SA. The SA will atomatically set itself to the correct measrement range and will calclate the appropriate range-to-range cal factors. Example: easring a low power level ( 100 dbm) from an Agilent E448C signal generator. easrement procedre 1. Set the signal generator to.0 GHz and 0 dbm. Select easring Receiver mode on the SA 3. Set the SA center freqency to.0 GHz 4. Select Tned-RF-Level mode on the SA 5, Wait for the SA to achieve a stable reading near 0.0 dbm 6. Decrease the signal generator otpt power level in 10 db steps ntil 100 dbm is reached 7. The SA will indicate a vale of approximately 100 dbm for the signal level. (This is the vale for the signal and noise.) Applying the specification Amplitde accracy in absolte TRFL mode is defined as: [ ACC TRFL] ACTUAL IND ACC + ACCTRFL ABS First, we ll have to look p the minimm power. Table 7 shows that, with the preamp installed and sing the 10 Hz resoltion bandwidth setting, it is 140 dbm ( 136 dbm withot the preamp). Next, note that the residal threshold power is defined to be 30 db higher, or 110 dbm ( 106 dbm withot the preamp). The power in this example, 100 dbm, exceeds the residal threshold power with or withot the preamp. In Table 5, we can choose either case, and the accracy expression is the same: ±(power meter range ncertainty db/10 db step) Looking at Table 4, we see, in power meter range, with the N553A/B Option 504, the accracy is ±0.190 db. The measrement procedre began with a calibration sing a 0 dbm reference. Or measrement is of a power level of 100 dbm, which is 100 db lower, or 10 steps of 10 db each. Therefore, the term db per 10 db step evalates to ±0.05 db. Adding this to the ±0.190 db discssed above, we find: [ ] ± 0.40 db ACC TRFL ABS Relative TRFL measrement Example: Accracy verification of an Agilent 8496G programmable step attenator where: ACTUAL IND ACC ACC TRFL the tre power present at the N553A/B sensor inpt in dbm the power indicated by the SA, in dbm accracy of the power reading taken by the N553A/B and power meter accracy of the SA in making the differential measrement between the reference power (established by the power meter) and the power level nder test Freqency range: Attenation range: 50 khz to 4.00 GHz 0 to 110 db The accracy of a step-attenator is sally established by comparison to a laboratory-standard attenator whose accracy is traceable to NIST. In the following test, the N5531S will be sed in place of the reference attenator as an attenation standard. For this example measrement, the N5531S will employ the relative TRFL fnction. For optimm signal-to-noise ratio, we ll not se the N553A/B. 11

12 easrement procedre 1. Set the signal generator to the freqency reqired for the attenator verification measrement. Insert a 3 db pad at the inpt and otpt of the step attenator nder test. (This will minimize the amplitde variation de to changes in mismatch as the attenator is switched from setting to setting.) 3. Set the signal generator power level to 0 dbm 4. Select easring Receiver mode on the SA 5. Select FREQ mode on the SA and manally set the SA center freqency to the signal generator freqency 6. Select TRFL mode on the SA 7. Wait for the SA to achieve a stable reading 8. ress the Set Ref key to perform a relative TRFL measrement 9. Step the attenator throgh its range and record the vale indicated by the SA at each step. The SA atomatically determines the appropriate range change cal factors as the power level passes throgh the range and range 3 threshold vales Applying the specification Let s start by assming a test freqency of 1 GHz. As in the previos example, we ll first look p the minimm power. We ll be sing the preamp, so the minimm power is 140 dbm. The residal threshold power is again 30 db higher at 110 dbm. The N553A/B is not in-circit bt the two 3 db pads on or attenator-nder-test affect the signal level. It varies from 6 dbm with the attenator set to its reference 0 db setting to 116 dbm. The final attenator setting (110 db) is measred at a power level below the residal threshold power; all other settings are measred at power levels higher than that. From Table 8, we see that the ranges switch at 58 and 78 dbm at the inpt of the SA, which corresponds to attenations of 5 and 7 db. Therefore, attenations of 10, 0, 30, 40 and 50 db are measred in Range 1, 60 and 70 db are measred in Range, and 80, 90, 100 and 110 db are in Range 3. The relative accracy for attenations of 10 throgh 50 db are given by the first row of Table 6. It is ±( db/10 db step). The nmber of 10 db steps is, of corse, 1 throgh 5 respectively. Therefore, the accracy is: Attenation Accracy 10 db ±0.00 db 0 ± ± ± ±0.040 The relative accracy for attenations of 60 and 70 db inclde the Range ncertainty. Table 6 shows this is ±0.031 db. This adds to the accracy in the first row of that table (with 6 and 7 10 db steps) to give: Attenation Accracy 60 db ±0.076 db 70 ±0.081 For attenations of 80 throgh 100 db, we experience the sm of Range and Range 3 ncertainties, at ±0.031 db each, giving: Attenation Accracy 80 db ±0.117 db 90 ± ±0.17 Finally, for the 110 db setting, we have to se the second row of Table 6. We find the cmlative error as we did in the last attenation: ±0.015 db, pls 11 steps of ±0.005 db each for ±0.055 db, pls Range ncertainty of ±0.031 db, pls Range 3 ncertainty, another ±0.031 db, for a sbtotal of ±0.13 db. To this we add the other term. The inpt power is 116 dbm; the residal threshold power is 110 dbm. We find the difference (6 db), sqare it (36 db ), and mltiply it by db -1, for another ±0.043 db error de to noisiness. The total: Attenation Accracy 110 db ±0.175 db Note that all these accracy figres are based on worstcase addition of error sorces; root-sm-sqare additions will give lower ncertainty estimates. 1

13 Appendix A: Derivation of Absolte RF ower Accracy easrement eqation An RF power measrement with the N5531S is made with the N553A/B sensor modle and a -Series power meter. The measrement path consists of one path throgh the power splitter, the 3 db pad, the power sensor, and the -Series power meter. This connection is shown in Figre, on page 3. Z N D is the power offset de to zero error of the power meter is the power de to noise in the sensor and power meter is the drift of the power meter after it is zeroed and calibrated The measrement made by jst a power sensor and power meter is described by: where: gz 0 m S IKLm gz 0 S Z N, in Watts D SCC m K C CAL C mc ZC NC is the power that wold be delivered to a Z 0 (matched) load is the mismatch factor at the power sensor to 3 db pad interface CAL K L m I is the calibrator power level is the power sensor calibration factor is the linearity of the power sensor/power meter combination is the gain factor that forces the power meter to indicate the calibrator power when the sensor is connected to the power meter s calibration port represents changes in the average vale of after calibration. m For a detailed derivation of this eqation and corresponding ncertainty eqation for a standard power meter measrement, follow the ISO Gide to Uncertainty in easrement, in the Fndamentals of RF and icrowave ower easrements, Application Note , literatre nmber EN. SC m is the mismatch factor at the calibrator otpt-to-sensor interface is the power indicated (reported) by the power meter 13

14 Adding a 3 db pad and a power splitter to the power sensor/power meter combination gives the fll path throgh the N553A/B sensor modle. The measrement eqation becomes: SS S IK Lm S IN 0 0 where: IN SS S S K 0 m 0 is the power at the inpt connector of the N553A/B sensor modle is the mismatch factor at the inpt of the power splitter is the mismatch factor at the power splitter to 3 db pad interface is the mismatch factor at the 3 db pad to power sensor interface is the composite calibration factor of the splitter+pad+power sensor is the composite gain factor that forces the power meter to indicate the calibrator power when the N553A/B modle is connected to the -series power meter s calibrator port. m 0 SS C K 0 C S C CAL S C C where: K C CAL is the composite calibration factor at 50 Hz (the calibrator freqency) is the -Series power meter s calibrator power level (0 dbm) 14

15 Uncertainty eqation ( ) ( ) + ( ) + ( ) ( I) ( K ) ( L) ( ) ( ) IN IN + m + ( ) ( ) ( ) ( ) ( ) + ( ) ( K ) ( ) mc S S N C + NC D SS C SS C + + K I + 0 C 0 C + K S C S C CAL CAL + + L S C S C ( 1 + C + SS SS 1 ) + ( ) Z S S Determining standard ncertainties ( ) m power meter resoltion: For this measrement, the power meter s measrement resoltion is set to 0.01 db. This means that the actal power level will fall somewhere within a 0.01 db range. The actal vale can be anywhere within this window and prodce the same reading (to within 0.01 db) on the power meter. Therefore, all vales that fall within the 0.01 db window are eqally likely to prodce the qantized readot vale. This sitation is best represented by a niform distribtion with a total range m 0.01 db. For a niform distribtion, the standard deviation is given by: σ RES m db db 1 Since this vale is in db, it has the form U ( m ) m σ R E S ± db Since >> + m, n+ Z d m Converting to a linear power ratio: ( ) U ( m ) U m 10 [ 10 1 m ] ± or ± 0.07% 15

16 ( ) mc ower meter resoltion dring calibration: C If the resoltion is set to 0.01 db, as in the case of : σ RES CAL Converting to a linear power ratio: U 0.01 db U ( mc) db 1 mc db ) ( 10 1) or 0.07% ( mc 0 mc m ( ) N ncertainty de to power sensor noise (in watts): For the 848XA power sensor copled to the N191XA power meter, the measrement noise (free-rn) is specified as 50 nw when averaging over a one-minte interval with averaging set to 1. See the specifications chapter (pages 1-1) in the N1911A/N191A Service Gide, Agilent docment nmber: N Assming that the specification of 50 nw represents 95% (σ) of a Gassian distribtion: ( D ) ncertainty de to power meter drift: For the 848XA power sensor copled to the N191XApower meter, drift is specified as ±10 nw at GHz. Example: For this test, the nominal power meter reading is -10 dbm (0.1 mw). Assming a niform distribtion for the power meter drift ncertainty: σ DRIFT ( ) 6 D 10 nw 3 1 mw ( ) N ( ) N ( ) NC NC C σ N 50 nw 5 nw 5 nw % 0.1 mw ncertainty de to power sensor noise (watts) dring meter calibration is identical to. ( ) NC NC N 5 nw % 1.0 mw 16

17 ( 1 1 C ) ( ) Z ncertainty de to power meter zero set (in watts): For the 848xA, power sensor zero set is specified as ±50 nw. Assming a Gassian distribtion for this parameter and assming that the specified vale represents 95% (σ) of the poplation of zero set vales: σ Z ( ) Z 50 nw 5 nw For this test, the nominal power meter reading is 10 dbm (0.1 mw). ( 1 ( C 1 ( ) 1 Z ) 1 mw 0.1 mw) 1 9 ( 5 nw) ( 9000) ( 5 10 ) % where: m Z N D 0.1 mw- 50 nw-110 nw-10 nw 0.1 mw C mc Z NC 1.0 mw - 50 nw-110 nw 1.0 mw ( I) I ncertainty of the power meter instrmentation gain: The ncertainty of the instrmentation gain is specified as ± 0.5%. Assming a Gassian distribtion for this parameter and assming that the specified vale represents 95% (σ) of the poplation of vales: Then: ( I) I 0.5% 0.5% 17

18 ( ) K K 0 0 ncertainty of the calibration factor of the composite N553A/B sensor/splitter/ 3 db pad (%): There are two parts to this ncertainty factor: 1. The ncertainty of the vale of the calibration factor, as spplied by the calibration facility.. The ncertainty de to the fact that the N553A/B sensor modle is calibrated with a precision 50 Ω load attached to the SA otpt port, bt is sed with the actal SA attached to that port. The difference in reflection coefficient between the two conditions cases an ncertainty in the actal power emerging from the power splitter and impinging on the 3 db pad. [ K 0 ] CAL 1. Specified vale (from cal. Lab) ±1.5% For the N553A/B, assming a Gassian distribtion for this parameter, and assming that the specified vale represents 95% (σ) of the poplation of vales: σ KCAL ([ K0] ) CAL [ K ] [ K 0 ] SA 0 CAL ([ K0] ) CAL [ K ] 0 CAl 1.5% 1.5% 0.75%. A signal flow graph analysis verified with experimental data, has shown that the ncertainty cased by the reflection of power from the SA inpt back throgh the power splitter and throgh the 3 db pad into the power sensor is approximately ±3.0%. Assming a Gassian distribtion for this parameter, and assming that the specified vale represents 95% (σ) of the poplation of vales: σ K SA ([ K0] ) SA [ K ] 0 SA ([ K0] ) SA [ K ] 0 SA 3.0% 3.0% 1.5% ncertainty of the calibration factor of the composite N553A/B sensor/splitter/ 3 db pad (%) at the calibrator freqency (50 Hz): ncertainty de to power sensor linearity: The linearity of a power sensor depends on the power level being measred. ower sensor linearity 848xA with N119XA meter Spec. nc. Std. nc. < +10 dbm (negligible) (negligible) +10 dbm +0 dbm +%, 4% +1%, % For this measrement, 10 dbm. Therefore, ( K ) K σ 0 C 0 C KCAL ( K ) K 0 C 0 C ( L) L K U ( L) 0 L ( ) SG SS SS SLITTER ( ) SS SS ( K ) 0 C 0 C 1.5% 1.5% 0.75% ncertainty de to mismatch between the signal sorce and the N553A/B inpt (assming a sorce of 1.5:1) SG SG SG SG SL SL S S % 18

19 ( ) S S ncertainty de to mismatch between the power splitter and the 3 db pad ( ) SS C SS C ncertainty de to mismatch between the calibrator sorce and the inpt of the N553A/B dring power meter calibration. SLITTER SL SL CAL SOURCE CS CS AD S S SLITTER SL SL ( ) S S SL 1 SL AD AD % ( ) SS C SS C SL 1 SL CS CS % ( ) S S ncertainty de to mismatch between the 3 db pad and the 848XA power sensor SENSOR SEN SEN AD S S ( ) S S SEN 1 SEN AD AD % 19

20 ( ) S C S C ncertainty de to mismatch between the power splitter and the 3 db pad dring power meter calibration. ( ) CAL CAL ncertainty of the calibrator otpt power (nominally 1 mw) Specification: ±0.4 % SLITTER AD S S SL SL Assming a Gassian distribtion for this parameter: ( ) CAL CAL σ CAL 0.4% 0.% ( ) S C S C SL 1 SL AD AD % ( ) S C S C ncertainty de to mismatch between the 3 db pad and the power sensor dring the power meter calibration. SENSOR SEN SEN AD S S ( ) S C S C SEN 1 SEN AD AD % 0

21 Combined ncertainty The combined ncertainty for the reference power sensor reading is: [ ( 0.07) + ( 0.07) + ( ) + ( 0.05) + ( 0.005) U ( gz0) + ( 0.03) + ( 0.5) + ( 0.75) + ( 1.5) + ( 0.75) + ( 0.0) gz UC ( ) gz 0 gz 0.0% ( ) ( ) ( ) ( ) ( ) ( ) ( 0.) ] 4.0 % Converting to db: UC ( ) gz 0 gz log( ) db Expanded ncertainty Assming a Gassian distribtion of combined ncertainty vales and assming a 99% confidence interval, the coverage factor is.57. U EX ( ) gz 0 gz 0 (.57) ( db) 0. db 1

22 AENDIX B: Derivation of Tned-RF-Level (TRFL) Amplitde Uncertainty easrements made in TRFL mode tilize the SA spectrm analyzer easrements made in TRFL mode tilize the SA spectrm analyzer. Inpt signal RF inpt attenator re-selector or Low-ass filter ixer Gain Local oscillator Analog IF Crystal filters Digital IF Dither generator 14 bit ADC DS Display CU The critical blocks that determine the relative-amplitde (e.g., TRFL) accracy of the SA are the Analog IF and the Digital IF. The most important performance characteristic of the SA for amplitde measrement is detector linearity. The detector in the SA is a 14-bit, analog-to-digital converter (ADC) copled to a digital signal processing (DS) chip. This detection method is far more accrate than the traditional method employing analog logarithmic amplifiers and analog detectors. Detector linearity applies throghot the entire TRFL amplitde measrement range. When the signal level drops below abot 70 dbm, residal noise and range changing in the SA become the dominant contribtors to the ncertainty of the TRFL measrement. Absolte power measrement by the N5531S below the range covered by the power meter (below 10 dbm) reqires the TRFL measrement mode tilizing the SA. The SA s absolte power reference is established by the power meter. Conseqently, in TRFL mode, there are two contribtors to the vale of the absolte RF power accracy specification: The absolte reference measrement made by the power sensor/power meter combination; The relative TRFL measrement made by the SA. The combined ncertainty of these two separate contribting measrements becomes the specified performance limit (i.e., the specification) for absolte TRFL power accracy. ( ) ( ) + ( ) ABS TRFL REF TRFL

23 When operating as a measring receiver in the TRFL mode, the SA amplitde accracy (ncertainty) is dominated either by the SA linearity or by the residal noise level, as shown in Figre B-1. These two regions are separated by the line labeled Residal Noise Threshold, which marks the power level below which the signal-to-noise ratio (SNR) becomes the dominant contribtor to the accracy of the TRFL measrement. In the easring Receiver ersonality chapter of the SA Specifications Gide (hereinafter called the N5531S data sheet ): Residal noise threshold minimm power + 30 db inimm ower is specified in the N5531S data sheet for varios freqency bands, resoltion-bandwidth settings and pre-amp settings. Throghot the power ranges shown in Figre B-1, the power indicated by the SA, TRFL, is sbject to the following sorces of measrement ncertainty: ( LIN TRFL) ( SNR TRFL) ( RANGE TRFL) Uncertainty de to the detector linearity Uncertainty de to the residal noise Uncertainty of the range-to-range cal factor easred ncertainty vs. inpt power relationship easrement ncertainty Uncertainty dominated by lineaity Range ncert. Range 3 ncert. Uncertainty dominated by noise Range 1 Range Range 3 aximm power Inpt power Residal noise threshold inimm power Figre B-1: Tned RF level measrement ncertainty 3

24 Detector linearity For the SA, there are no factory or field adjstments for detector linearity. Its vale depends directly on the accracy of the analog-to-digital converter (ADC) in the SA. The ncertainty de to the detector nonlinearity arises from five distinct mechanisms in the SA: a. Single-tone compression in the conversion chain The nonlinear behavior of the front-end of the spectrm analyzer can be characterized as compression. Compression begins when the plot of otpt level vs. inpt level begins to deviate from a linear relationship. As the inpt power level increases, the otpt level begins to flatten ot and it takes larger and larger increases in inpt level to prodce steady increments in otpt level. Compression in the SA is cased primarily by the conversion chain (mixers and amplifiers). If the power level at the first mixer is limited to 8 dbm, the ncertainty cased by compression has been determined to be less than 0.00 db. COR 0.00 db The N5531S measrement algorithm adjsts the amont of SA inpt attenation to maintain inpt mixer level at or below 8 dbm. b. Crystal filter hysteresis The SA tilizes a single-pole crystal filter in the final analog IF stage. Crystal filters sffer from a hysteresis effect, wherein their loss depends on their signal-level exposre history. This problem is well known and designers take precations to keep the drive level to the crystal filter low enogh to minimize this effect. This hysteresis effect decreases as the bandwidth of the crystal filter is increased. In the worst case, a crystal filter can have hysteresis as large as 0.04 db. This level is assred by factory and field-calibration testing of the scale fidelity. The effect of hysteresis can be modeled as ΔESR with drive, the change in the crystal filter s eqivalent series resistance with drive level. When the bandwidth of the analyzer is increased from the narrowest settings, the effect of the ΔESR decreases proportionately. The linearity of the SA is tested with the narrowest crystal-filter bandwidths. In the SA, the crystal-filter bandwidth is a fnction of resoltion-bandwidth setting when in swept mode, or of the FFT freqency span in FFT mode. The crystal-filter bandwidth is never less than 5 khz. All SAs are tested in prodction to ensre that the nonlinearities in the minimm bandwidth case never exceed 0.04 db. For bandwidths of 50 khz or greater, the hysteresis effect will, therefore, never exceed db. Crystal bandwidths are set to.5 times the RBW for swept operation or 1.5 times the FFT-width for FFT operation. The N5531S system ses zero-span mode for TRFL measrements. The hardware in the analyzer is cstom-controlled to apply the 50 khz crystal filter to the measrement. The reslting ncertainty de to that filter is db. HYST db 4

25 c. rocessing resoltion Trace processing in the SA generates an error de to qantization that can be as large as db. TRACE db d. ADC-range gain alignment The ADC ato-ranges its gain from nominally zero to as mch as +18 db, based on the inpt signal level. This ranging is sbject to alignment errors that have never been seen to exceed 0.01 db. However, if the power level at the first mixer of the SA is 8 dbm, then the ADC-range gain is always set to maximm. Conseqently, for an N5531S TRFL measrement, there will be no error de to switching the gain in front of the ADC. e. ADC linearity The ADC is garanteed by its manfactrer to have an integral linearity error of less than one part in 14. The SA employs a dithering signal techniqe to enhance the ADC linearity. The dither signal is a sine wave with psedo-random freqency modlation at 0% of fll-scale level. The effect of this dither signal can be modeled as a transfer fnction that is the convoltion of the ADC transfer fnction with the probability density fnction of the dither signal. In the worst case, the ADC transfer fnction has a maximm linearity error of one polarity for a positive signal jst above zero and an opposite linearity error for a signal jst below zero. Even with this nonlinearity, the slope variation of the effective transfer fnction does not exceed 0.00 db. See figres below. ADC LIN 0.00 db ADC GAIN db ADC transfer fnction N ADC Ideal Effective average transfer fnction N ADC Ideal Worst case Worst Case V i aximm slope aximm Slope V i robability density fnction (DF) of the dither amplitde DF(V ) i V i 5

26 f. Combined ncertainty for detector linearity As a conservative estimate of the total ncertainty de to the detector linearity, the worst case linear sm of the contribtors listed above is: LIN ( TRFL) COR+ HYST + TRACE + ADC GAIN ADC LIN + ( ) 0.00 db db db db db db LIN TRFL When the ncertainty is compted, as shown, instead of demonstrated, there is always the risk that additional error contribtors exist bt have not been discovered or inclded in the sm. To minimize that risk, many analyzers were tested against calibrated reference attenators. These reference attenators had errors of their own that increased with the amont of attenation. This verification techniqe still allowed risk that nknown errors might exist in the SA that are not inclded in this analysis. To cover that risk, the SA is specified to have another component of error. That component is ±0.003 db/10 db. To match cstomer needs to replace the H 890, and to be extra conservative in specifications, the specification is widened to: ( ) db ± db/10 db LIN TRFL 6

27 Residal noise The indicated TRFL power is de to the sm of the signal power at the freqency of interest and the noise power within the selected resoltion bandwidth. For high vales of signal-to-noise ratio ( 40 db), the noise has a negligible effect on the displayed amplitde of the signal. When the signal-to-noise ratio (SNR) drops below abot 0 db, the noise becomes a significant component of the indicated vale of the signal. At low SNR, the instantaneos, indicated vale of a steady CW signal is continally changing de to the additive/sbtractive effect of the noise. The SA actally indicates the combined power of the signal pls noise: S + N. In order to make a precise estimate of jst the signal power, S, we need to eliminate the mean error de to noise and minimize the flctation de to the noise. The SA acts to minimize the flctation de to the residal noise by averaging the combined S + N and to eliminate the mean error de to the noise by performing a sbtraction: where: S S + N S + N N N [ db] is the power in the signal pls noise is the power in the residal noise alone After the mean error is sbtracted, the flctations remain. The mean error sbtraction process has errors de to imperfect estimation of the noise, bt these errors are mch smaller than the errors de to noise flctations even with large amonts of averaging. Therefore, the rest of this section will deal with the noise flctations only. The analyzer is set p in varying ways according to the signal-to-noise ratio. Or interest here is in the most difficlt, low signal-to-noise ratio cases. In these cases, the measrement is made by averaging a zero span sweep with a sweep time compted as 10/RBW, and with the maximm nmber of sch traces averaged atomatically selected by the software (to keep the measrement time from growing withot bond), which is 900. The signal-to-noise ratio can be sed to compte the standard deviation of the averaged traces. First, we mst compte the standard deviation of each individal trace. To compte that, let s start with the standard deviation of the instantaneos measrement of a CW signal with noise. The noise added to a CW signal is random. Being random, its phase relative to the CW component is random. We can describe this noise in more than one way. One way wold be in terms of its magnitde and phase distribtion. Another way wold be in terms of its real and imaginary components. The most sefl way is a rotated version of its real and imaginary components: we can decompose it into two random components one component is in-phase with the CW signal, and one is in qadratre. Each of these components has the same average power. Therefore, each one has 3 db less power than the total noise. When the signal-to-noise ratio is large, the qadratre component adds negligibly to the variation in measred level. So the relevant noise is the in-phase component with half the total noise power. 7

28 The standard deviation of the envelope voltage of the in-phase component is eqal to the voltage compted from its total power. With this information, the standard deviation of the instantaneos envelope voltage can be compted. Let s start with a noise voltage sinsoid, of level v, that is expressed in decibels relative to the signal power, that may either add to or sbtract from the carrier power. The error associated with v is: Error _ db 0 log (1 ± 10 For small vales of v, the error is linearly related to v. We can do a Taylor-series expansion on the error eqation: This works ot to: v/0 Error _ db v d (0 log10( dv The latter term, 0log(e), is 8.69 db, also known as 1 neper. Sbstitting in the voltage error (from the signal-to-noise ratio) for v, we can compte the standard deviation of or measrement: This expression is actally slightly conservative compared to a fll statistical treatment sing Rician distribtions, so it is sefl for or prposes. This standard deviation is redced by filtering. The filtering comes from averaging the reslt for a dration of 10/RBW. How mch filtering does that give s? The distribtion of the noise of the detected signal can be described as having a noise bandwidth of half of the predetected signal. The noise bandwidth of the predetected signal is times the RBW for or very close to Gassian RBW filters. The noise bandwidth of the averaging process is 1/( t INT ), where t INT is the integration time. 10 Error db v 0 log10(e) σ CW (8.69 db) 10 SNRatio ) v/0 )) The standard deviation of the filtered envelope will be redced by the sqare root of the ratio of the noise bandwidth of the signal to the noise bandwidth of the averaging process. Therefore: σ TRACE Given that t INT 10/RBW, and that NBW RBW RBW, we get: σ TRACE When we average this 900 times, the standard deviation improves by the sqare root of 900, which is a factor of 30, giving: σ AVG We can express the total error in this format instead: SNRatio 30 db is the same as inpt power mins residal noise threshold power. For SNRatio vales in the 0 to 30 db range, the 3σ reslt is either well nder 0.01 db, or the Error expression is conservative relative to three standard deviations. Here is a table that demonstrates the nmerical relationship: Signal-to-noise ratio 8.69 db t NBW INT.67 db db 10 RBW 3 x standard deviation 10 SNRatio SNRatio db db 0 db SNRatio Error ( SNRatio 30) Error expression The Error expression is sed as a component of both the absolte and relative TRFL accracy expressions shown in Table 5 and Table 6. 8

29 Range-to-range cal factor TRFL measrement with the SA spans three amplitde ranges. This section will discss the errors in each of those three ranges. Here is how those ranges are arranged: Signal level step down SA readot First Cal point ower meter range reading: SA 1, CalFactor 1 SA 1 Range 1 the displayed TRFL SA 1 + CalFactor 1 Second Cal point Range switch level reading: SA 1, SA CalFactor SA 1 SA Range the displayed TRFL SA + CalFactor + CalFactor 1 Third Cal point Range 3 switch level reading: SA, SA 3 CalFactor 3 SA SA 3 Range 3 the displayed TRFL SA 3 + CalFactor 3 + CalFactor + CalFactor 1 Figre B-: Tned RF level neasrement ranges To avoid error de to signal compression, the power level at the first mixer of the SA is maintained at 8 dbm by maniplating the inpt attenator of the SA and internal preamplifier settings. Example: If the signal power level at the inpt of the N553A/B sensor modle is 0 dbm, then the nominal power level at the SA inpt will be 7 dbm (de to the power splitter loss). The internal attenator of the SA mst be set to 1 db or more to ensre that the power level never exceeds 8 dbm at the mixer. By maintaining this attenator setting, the SA mixer always identifies a level that is 8 db lower than the level at the sensor modle inpt. 9

30 Range-to-range cal factor ncertainty Cal factor 1 Cal factor 1 applies in Range 1, Range, and Range 3. It acconts for the difference in reading between the power meter and the SA for a fixed power level measred in Range 1. Cal factor 1 is determined as follows: 1. The power level of the signal is measred in Range 1 by the N553A/B sensor modle and the -Series or E Series power meter. The vale is stored as 1 (in dbm);. The SA is set to Range 1 (the internal attenator is set to 30 db) and the same power level is measred by the SA, via the N553A/B connection. The vale is stored as SA1. 3. The ncertainty of Cal factor 1 is: where C1 and C are sensitivity coefficients given by: Therefore: CalFactor1 C The ncertainty vale and is db. and 1 SA1 [ db] ( CF ) C ( ) + C ( ) SA 1 ( CF) C ( CF) 1 1 SA 1 1 ( CF ) ( ) ( ) SA 1 ( ) 1 is derived in Appendix A From the SA data sheet: (KR) db, with averaging ON. Becase this parameter is specified in db, we will assme that it was determined from data taken in db. The marker readot vale is a qantized vale that is assigned to the power level within a distinct vertical-scale bcket. Any vale that falls within the bondaries of this bcket will be assigned the same amplitde vale. Conversely, the probability of any vale within the bcket bondaries having cased the reading is the same. This sitation is best described by a niform probability distribtion (i.e., every vale in the bcket interval is eqally likely and will be assigned the same vale by the SA). For a niform distribtion, the standard deviation is σ UNIFOR w 1, where w is the width of the niform distribtion. So, the standard ncertainty of a tre vale that falls within a particlar amplitde bcket is eqal to: db 1 ( KR) σ db KR The ncertainty of the Range 1 Cal factor is then: ( CF ) ( KR) ( ) U C ( CF1 ) ( db) + ( ) db ( ) db CF U C The ncertainty vale SA1 is dependent only on the marker readot resoltion. All other SA ncertainties are eliminated by the comparison of the power meter reading to the SA reading. So, ( ) db 1 ( SA1 ) ( ) can be expressed as: ( ) ( KR) SA 1 30

31 Cal factor Cal factor applies in Range, and then contribtes in Range 3 as well. It acconts for the change from Range 1 to Range. Cal factor is determined as follows: 1. The power level of the signal is measred in Range 1 and the vale is stored as R1 (in dbm);. The SA is switched to Range : a. The preamp (if present) remains OFF. b. The internal attenator is changed from 30 db to 10 db. 3. The power level of the signal (nchanged) is measred again, now in Range, and is stored as R (in dbm); CalFactor R1 R [ db] The ncertainty in Cal factor is de entirely to the noisiness of the pair of measrements that compare Range and Range 1. The transition between ranges is constrained to occr at a signal-to-noise ratio of db or more, therefore, db is the worst case. The comptation of ncertainty de to this noise will be brief becase the comptation process has been more thoroghly explained in the Residal Noise section of this appendix. With db signal-to-noise ratio, the in-phase noise is 5 db below the CW signal, giving a standard deviation error of: This standard deviation is redced by the sqare root of the nmber of averages (900) to give a standard deviation of db. The signal is measred again in Range, bt the signal-to-noise ratio is 100 times better, so when the standard deviation of that measrement is combined with the standard deviation of this measrement, the effect is negligible. To compte the 95% confidence interval de to this noise, we mltiply the standard deviation by 1.96 and get an interval of ±0.031 db. Therefore, ±0.031 db can be said to be the 95% confidence reslt for the worst case signalto-noise ratio. The signal-to-noise ratio is likely to be any vale between and 3 db. When we compte the probability of the noise casing an error otside the range of ±0.031 db, we find the reslt is within this error 99.3% of the time. Unlike other specifications for this prodct which are worst-case specifications, this one is 99.3% confidence specification. This seems sitable becase this specification is never sed by itself, only in combination with other terms which are themselves pretty large, so that statistical combining leaves very little risk of failing to meet specifications. σ 5 0 single 8.69 db 10 31

32 Cal factor 3 Cal factor 3 applies in Range 3 only and acconts for the change from Range to Range 3. Cal factor 3 is determined as follows: 1. The power level of the signal is measred in Range and the vale is stored as R (in dbm);. The SA is switched to Range 3: 3. The preamp (if present) is trned ON; 4. The internal attenator is changed from 10 db to 4 db. 5. The power level of the signal (nchanged) is measred again, now in Range 3, and is stored as R3 (in dbm); 6. CalFactor 3 R R3 [ db] The derivation of Cal factor 3 is the same as that of Cal factor. The only difference is that the noisiness of the measrement in Range 3 is nominally 40 times lower than the noisiness of Range, compared with a factor of 100 in the former derivation. Both these noise ratios give negligible contribtion to the ncertainty. A measrement made in Range 3 will involve CF1, CF and CF3. The ncertainty of these combined cal factors will be: ( ) ( CF1) + ( CF ) ( CF3) RANGE TRFL + easrements made in Range or Range 1 will have smaller vales of overall range-to-range ncertainty. Combined ncertainty for TRFL measrement Since the effects of linearity, range offset, and signal-tonoise ratio are independent of one another, the combined ncertainty can be expressed as: C ( ) ( ) + ( ) + ( ) TRFL LIN TRFL SNR From this eqation, it is clear that the overall ncertainty of an indicated TRFL measrement made by the N5531S is dominated by the SA linearity and range offsets ntil the signal level nears the level of the noise. TRFL RANGE TRFL 3

33 Appendix C: Two-Resistor Verss Three-Resistor ower Splitter Choice The N553A sensor modle figre is repeated here: Two resistor splitter 3 db ad 848x power sensor Figre : N553A sensor modle (N553B has similar architectre bt ses an N848x power sensor instead) Inside the N553A, a two-resistor power splitter spplies eqal signals to the spectrm analyzer otpt port and to the 3 db pad/power sensor combination. A two-resistor power splitter is constrcted with 50 Ω resistors from the inpt port to each otpt port. The nominal power loss throgh the splitter to each otpt port is 7 db (6 db, ideally). The N553B has similar architectre as the N553A bt ses the N848X power sensor in lie of 848X. Why not se a three-resistor power divider instead? A three-resistor power splitter is constrcted with 16.7 Ω resistors from each of the three inpt ports to a central node. At first glance, this seems preferable for this application. If an ideal three-resistor power divider is terminated at each of its ports by the characteristic impedance of the transmission line (50 ohms), then each port of the power divider presents a 50 Ω inpt impedance. This insres that optimizing the match presented by the spectrm analyzer will also optimize the match seen by the signal generator and power meter. The same concept applies to all three ports, however, power reflected from the spectrm analyzer inpt wold be attenated by approximately 6 db before appearing at the inpt to the 3 db pad. This ndesired reflection from the spectrm analyzer wold change the total power seen by the sensor, casing an error in the power indicated by the external power meter. The effect of reflections with a two-resistor power splitter is qalitatively similar, thogh the reflection attenation is abot 14 db instead of abot 6 db. Bt let s look at it another way. Both the two- and three-resistor power splitters show ideally 50 Ω inpt impedance when the spectrm analyzer and the power sensor are both 50 Ω inpt impedance. The two-resistor splitter has the advantage, with its larger resistor vales, the inpt port match depends less on the matches at the splitter otpts. Ths, the optimm match goal is best served by the two-resistor choice. Regarding the optimize the accracy goal is where the two-resistor choice is most valable. Both of the measring devices are optimized and calibrated for accracy when driven from a 50 Ω impedance. Regardless of the impedances of the other instrments in the circit, both are configred to be reporting one-half of the voltage (the sitation is easier to nderstand from a voltage perspective than from a power perspective) at the node between the two 50 Ω resistors. This sitation is eqivalent to the sitation nder which they are calibrated. Ths, they are both, simltaneosly, optimally accrate as configred with a two-resistor splitter. This is why two-resistor splitters are known to be the most accrate devices for leveling and ratio measrements. Another discssion of this topic is available in the Agilent Application Note Differences in Application Between ower Dividers and ower Splitters, literatre nmber EN. It is tre that the instantaneos impedance seen by the two measring devices is 83.3 Ω ( of 1.67:1) in the two-resistor case, while being 50 Ω in the three-resistor case. Bt it is not the instantaneos impedance that determines the accracy, so the two-resistor splitter is the better choice. Or goals in designing the sensor modle are these: We want the optimm match at the inpt port. We want to optimize the accracy of both the spectrm analyzer and the power sensor. 33

34 Related Literatre Fndamentals of RF and icrowave ower easrements (art ) : ower Sensors and Instrmentation, AN 1449-, literatre nmber EN. ISO Gide to Uncertainty in easrement, in the Fndamentals of RF and icrowave ower easrements, Application Note , literatre nmber EN. N1911A/N191A Service Gide, Agilent docment nmber: N N1913A/N1914A Service Gide, Agilent docment nmber: N myagilent myagilent A personalized view into the information most relevant to yo. LAN extensions for Instrments pts the power of Ethernet and the Web inside yor test systems. Agilent is a fonding member of the LXI consortim. Agilent Channel artners Get the best of both worlds: Agilent s measrement expertise and prodct breadth, combined with channel partner convenience. Agilent Advantage Services is committed to yor sccess throghot yor eqipment s lifetime. To keep yo competitive, we continally invest in tools and processes that speed p calibration and repair and redce yor cost of ownership. Yo can also se Infoline Web Services to manage eqipment and services more effectively. By sharing or measrement and service expertise, we help yo create the prodcts that change or world For more information on Agilent Technologies prodcts, applications or services, please contact yor local Agilent office. The complete list is available at: Americas Canada (877) Brazil (11) exico United States (800) Asia acific Astralia China Hong Kong India Japan 010 (41) 345 Korea alaysia Singapore Taiwan Other A Contries (65) Erope & iddle East Belgim 3 (0) Denmark Finland 358 (0) France * *0.15 /minte Germany 49 (0) Ireland Israel /544 Italy Netherlands 31 (0) Spain 34 (91) Sweden United Kingdom 44 (0) For other nlisted contries: Revised: Janary 6, 01 rodct specifications and descriptions in this docment sbject to change withot notice. Agilent Technologies, Inc. 01 blished in USA, December 4, EN