Improved Dynamic- RangeTesting Dynamic range is an important measure of transceiver performance. Learn to avoid the pitfalls of measuring it and reap a reward in accuracy. By Doug Smith, KF6DX D ynamic-range testing of trans- able signal to the largest tolerable sig- to get away from that term because it mitters and receivers is in- nal. That definition applies as well to implies something about individual creasingly important in view of transmitters as it does to receivers, perception. Many operators and auto- today’s crowded bands. That is evi- but I shall begin my discussion with mated systems can discern signals be- dently true for commercial services, the receivers, since they usually must ex- low the noise floor (SNR < 0 dB). military and Amateur Radio alike. Re- hibit larger dynamic ranges than must Either noise or distortion may deter- cently, I became more aware of certain transmitters. mine the upper limit of receiver factors in play during such testing that Noise should determine the lower dynamic range. When upper-limit mea- tend to significantly degrade the accu- limit of a receiver’s dynamic range. surements are noise-limited, it is often racy of the results. Let me explain what That lower limit may be defined by the because of so-called reciprocal mixing, I discovered and put forth some sugges- signal-to-noise ratio (SNR) of a desired wherein noise sidebands on a local os- tions for improvement. signal at its output. By the accepted cillator mix with out-of-band interfer- standard, the lower limit occurs when ence to produce in-band noise. When What is Dynamic Range? a desired signal, modulated by a single upper-limit measurements are distor- Dynamic range may be broadly sinusoid or tone, has SNR = 0 dB. Then, tion-limited, several interrelated defined as the ratio of the smallest us- signal power equals noise power. That mechanisms may be to blame. I leave power level is called the noise floor. It out any discussion of strong in-band has also been called minimum discern- signals here and focus on interference 225 Main St able signal (MDS),1 but we are trying outside the receiver’s passband. Newington, CT 06111 Second-order intermodulation dis- [email protected] 1Notes appear on page 52. tortion (IMD2) occurs when two un- 46 Jul/Aug 2002 desired signals combine nonlinearly to surable in-band IMD products and On Small-Signal Measurements produce their sum and difference fre- compares power levels. IMD dynamic and the Nature of Noise quencies. IMD2 happens when re- range (IMD DR) is the ratio of the level The chief enemy of small signals is ceiver components behave according of one of two equal-power, off-channel noise. Noise is generated in receivers to a square law. When the level of the signals producing some in-band by the random motion of atomic two undesired signals is increased si- power, P, equal to the noise floor, to particles inside circuit elements. A fa- multaneously by 1 dB, IMD2 increases that of a single, in-band signal produc- mous paper published in 1905 quanti- by 2 dB. Third-order IMD (IMD3) ing that same power, P. fies it.2 Physical law states that occurs when receiver components be- Sometimes, receiver IMD responses available noise power is directly pro- have according to a cube law. For ev- deviate significantly from the straight portional to the temperature (in ery 1 dB of increase in the two offend- lines that square-law or cube-law kelvins) of the thing generating the ing signals, IMD3 increases by 3 dB. It behavior predict. Nonetheless, one noise. Noise from a signal source (a might seem funny, but receivers can generally accepted way to calculate in- test generator) is also delivered to a exhibit both square-law and cube-law tercept points is to take the noise floor receiver and it may be significant. behavior at the same time. plus twice the IMD2 dynamic range for That is likely when receiver noise fig- One quantification of IMD is called IP2 and noise floor plus 1.5 times the ures are low—less than 6 dB or so. intercept point (IP): the power level at IMD3 dynamic range for IP3. In a re- Such noise must be distinguished from which IMD product strengths allegedly ceiver with a classic response, this receiver-added noise during testing. rise to match those of each interfering yields IPs precisely. A more generic A signal delivered from a source to a signal. See Fig 1. In modern receivers, formula can be used for any two points receiver has a certain SNR in the IPs may by quite high. It is not unusual along the two lines in Fig 1, without bandwidth of interest. A receiver’s job to see receivers with third-order inter- knowing where on the lines the points is to preserve that SNR as best it can. cept points (IP3s) of +30 dBm (1 W) and actually fall. For IP2, the equation is: All physical circuits add some noise, second-order intercept points (IP2s) of though. Under controlled conditions, +80 dBm (100 kW). IPs form an excel- IP2=2P −P (Eq 1) the ratio of a receiver’s output SNR to QRM OC lent basis for comparison of receiver its input SNR is called its noise factor. distortion performance. They usually where P is the level of one of the When expressed in decibels, the ratio QRM cannot be measured directly at those two off-channel signals causing the is called the noise figure. To make power levels but must be extrapolated IMD and P is the level of an on- noise-figure specifications complete, a OC from lower-level measurements. channel signal producing an identical temperature must be included. Usu- To do that, one makes the assump- output power from the receiver. For ally, “room temperature” (290 kelvins) tion that IMD products behave accord- IP3, the equation is: is assumed. ing to either a square law or a cube I mentioned that noise in signal (3P −P ) law. One injects interfering signals of IP3= QRM OC (Eq 2) sources propagates directly to a re- sufficient amplitudes to produce mea- 2 ceiver output. Since noise powers add, noise from signal generators may skew measurements when the noise figure of the thing being measured is low. So the effective source impedance of the noise source must be known during noise-floor measurements. In actual operation, though, low receiver noise figures are not always neces- sary. A strong, noisy signal on 80 meters, say, would not have its SNR degraded much by a receiver having a noise figure as high as even 20 dB. Noise may be defined as the output of a randomly driven process. It can be understood by taking a large-scale view of the world. Given the large number of very small particles in the universe and the variety of forces at work on them, it is perhaps no surprise that seemingly random events occur. Some say that given the starting con- ditions and the laws of basic forces, the state of the universe at any time may be determined from its past state. Oth- ers have shown that presumption to break down at very small scales. Such small-scale breakdowns have a way of making themselves evident at much larger scales. In many ways, we find now that the Fig 1—Showing where fundamental receiver response and IMD intercept. universe tends to go from a more-or- Jul/Aug 2002 47 derly state to a less-orderly state.3 cause it reveals a pitfall that often computed for any filter by integrating That situation seems inextricably arises when measuring sensitivities of its normalized response over fre- linked to the passage of time.4 So receivers. A common procedure is to quency: many pseudo-random events have oc- connect an ac voltmeter to a receiver curred since the start of time that the loudspeaker and, in the absence of BW =∫fmaxA(f)df (Eq 7) electrical noise we experience may be input signals, set the volume control eff 0 characterized as truly random. so that the meter reads 0 dB. A desired where A(f) is the filter’s amplitude re- In a receiver circuit, a noise voltage signal, usually a single tone, is then sponse at frequency f. For this compu- may take on almost any value. Over injected into the receiver until the tation, the largest value of A(f) found is relatively short time frames, though, meter rises by some amount, often defined as unity and all other values it has some peak amplitude, A, and a 3 dB or 10 dB, depending on the type are normalized to that passband peak. peak-to-peak amplitude of 2A. The of measurement. Normally, 3 dB Tones used to measure noise-floor average value of that noise voltage is would be used for a noise-floor mea- power must be at or near the passband zero because it is just as likely to be surement. peak. Noise figure may then be com- positive as negative. It is also equally If the ac voltmeter were a peak-read- puted by finding the difference between likely to be small as large. One may ing type calibrated as RMS, it would the theoretical noise floor of a perfect use these facts to compute the average indicate A/√2 when the noise alone receiver (NF = 0 dB) and the measured and RMS power of noise. were present. The real RMS value of noise floor. In a 500-Hz bandwidth, the Over short time frames, a small leap the noise is A/√3, so the error would be: theoretical limit is about –147 dBm at reveals that the average absolute value room temperature. Noise figure is the  A  of noise having peak amplitude A is   true measure of a receiver’s noise per-   A/2. We can prove that by integrating ε=20log 2 =20log 3≈1.76 dB formance as it provides bandwidth-in- the noise voltage over the range of pos-  A   2 dependent information. sible values and dividing by the range:  3  Alternatively, a calibrated broad- (Eq 5) band noise source may be considered instead of a single tone during noise- EAVG = 21A∫−AAede If the ac voltmeter were an average- floor testing. Theoretically, a receiver’s reading type, the error would be: frequency response is then irrelevant 1 e2A because the test signal has energy at all =   frequencies, but this method has its 2A 2 −A (Eq 3) ε=20log 3≈−1.25 dB (Eq 6) own pitfalls. It does not account for the   1 A2 A2  2  effects of poor opposite-sideband rejec- =  +  tion and spurious responses of a 2A 2 2  In the first case, the SNR looks receiver. A unit with poor opposite- A worse than it should, while in the sec- sideband rejection, for example, might = ond case, it looks better than it should. yield erroneous noise figures because 2 A true RMS-reading voltmeter must additional energy would appear in the The average power is therefore pro- be used to get accurate results using passband that was caused by energy portional to the square of that, or the voltmeter method. The presence of outside that passband. A2/4. The peak-to-average ratio of noise noise in a 10- or 12-dB SNR sine-wave On the other hand, one can readily is thus about 6 dB over the short haul. signal is not enough to produce a sig- measure a receiver having good levels To find the RMS value of noise—or nificant error in the reading when the of spurious rejection and opposite-side- any function—take the average (mean) voltmeter is calibrated as RMS. band suppression with this method. of the square of the function (its mean To compute a receiver’s noise figure When the effective source resistance of square), then take the square root of from its noise floor, bandwidth must be the noise source is accurately known, a that. For noise, this yields: precisely known. Noise-floor measure- receiver noise figure may be found by ments made with filters having unde- comparing its output power with and fined bandwidths and responses do not without the external noise source. Be- E = 1 ∫A e2de constitute a good basis for comparison. cause of its bandwidth independence, MS 2A −A One receiver’s 500-Hz filter might be many RF designers consider this 1 e3 e3A closer to 350 Hz and another closer to method the best way to go. =  +  700 Hz, producing up to a 3-dB differ- 2A 3 3−A (Eq 4) ence in noise-floor power even if their IMD Measurements A2 noise figures were the same. Passband Receiver IMD measurements in- = ripple and stop-band response (shape volving large, off-channel signals are 3 factor) may throw results off by several difficult to perform accurately. One E = A more decibels. My first suggestion, reason for that involves trouble in gen- RMS 3 therefore, is that noise figures form a erating a clean two-tone signal for more useful basis for comparison of application to the receiver under test. RMS noise power is one-third of its receiver sensitivities than measure- A typical test setup for receiver IMD peak power. Compare this with a sine ments of noise-floor power. is shown in Fig 2. Two signal genera- wave, whose RMS power is one-half of To find a particular receiver’s noise tors are combined in a hybrid com- its peak power, or with a square wave, figure, its effective bandwidth must be biner. The output of the combiner is whose RMS power is equal to its peak determined. Effective bandwidth is fed into the receiver via an attenuator. power. easy to find for filters having flat pass- Some isolation between the genera- The exercise above is important be- bands and low shape factors. It may be tors is achieved exclusive of the com- 48 Jul/Aug 2002 biner because typical laboratory gen- test IMD3 in receivers. Crystal filters clean, off-channel two-tone interfer- erators use internal attenuators to set have been used, but even crystal ing signal is applied. The levels of the their output levels. The external at- manufacturers have a tough time two tones are simultaneously in- tenuator is strictly necessary because characterizing the IMD response of creased until the same S-5 indication the combiner must be operated into its quartz, especially at signal powers is attained. IP and IMD DR are then designed load impedance to get addi- near 0 dBm. In addition, crystal filters computed and recorded. This proce- tional isolation. The hybrid combiner are good for only one set of frequencies. dure applies equally well to second- achieves a certain isolation level be- It is better to start with a combiner order and third-order tests.6 tween generators’ outputs when its having very high port isolation. The results of tests must produce load impedance is right. In typical I have recently discovered how to noise-floor, IMD DR and IP numbers combiners, that is no better than about build broadband combiners exhibiting that agree. In other words, IP2 must 35 dB. Some energy from each genera- isolation several orders of magnitude equal twice the IMD2 DR plus noise tor appears at the other and nonline- greater than that of ordinary combin- floor, and IP3 must equal 1.5 times the arity in generator output stages ers. That is, isolation is typically 65 dB IMD3 DR plus noise floor. Published generates IMD in the test signal. instead of 35 dB. I have measured iso- numbers should be accompanied by an When the combiner output is not cor- lation as high as 90 dB at 200 MHz. estimated margin of error. When the rectly terminated, some energy from Insertion loss is about 6 dB instead of numbers do not correlate within the the combined output signal is reflected the normal 3 dB, but the net gain in margin of error, something is wrong. back toward both generators. The at- isolation is still quite worthwhile. The Take that with a grain of salt, be- tenuator in Fig 2 must therefore pro- ARRL Lab is currently evaluating one cause quite often receivers that are vide a good termination, equal to the of my prototypes. supposed to behave according to per- characteristic impedance of the sys- During receiver IMD testing, a refer- fect square or cube laws act differently tem—usually 50 Ω. For example, were ence power level is chosen. That may be in the presence of signals at various the termination impedance at the com- at the noise floor or it may be much levels. Were one to inject signals equal biner output 60 + j0 Ω, the SWR would higher than that. It should not matter: to the calculated IP3 of a receiver, for be 1.2:1 and the reflection coefficient, The idea is to find a point on the line example, one might find that the real ρ, would be about 0.10. The isolation representing the square- or cube-law IP3 is much different—or one might between signal generators would be response of the receiver in the presence “toast” the receiver! degraded to a value equal to twice the of two, equal-level interfering tones. A My second suggestion is that as many combiner 3-dB insertion loss minus 20 reference power level much higher than reference power levels be used in IMD log(0.10) or roughly 6 + 20 = 26 dB. the noise floor is good because it avoids DR testing as are necessary to deter- Sometimes, 35 or even 50 dB of iso- difficulties in measuring noise powers. mine the slope of the IMD line. ARRL lation is insufficient to prevent IMD in Noise is constantly changing and as the Lab Supervisor Ed Hare, W1RFI, dem- generator output stages. Some labora- ARRL Handbook rightly points out,5 onstrates the need for that nicely in his tory generators do fine at lesser isola- picking a reference level well above the sidebar “What is the ‘Real’ Intercept tions, but any doubt may be easily noise floor makes life easier. Point?” From the receivers he has mea- overcome during IMD2 testing be- Having selected a reference power sured, note that the calculated IPs cause the frequencies of the two gen- level, a single, on-channel signal is strongly depend on the reference levels erators are so far apart. For example, applied and some measure of receiver used. Errors of 10 dB or more are easy two signals at 6 and 8 MHz may be response is noted. That can be an indi- to get when taking only one set of points combined to test for IMD2 at the sum cation on the S meter, such as S-5, or on the response curves. That has unfor- frequency of 14 MHz. It is reasonably an another absolute measure of the tunately engendered considerable simple to employ a low-pass filter at receiver’s output power. (A measure- doubt about accuracy in many in- the 6-MHz generator and a high-pass ment that distinguishes the level of stances. While receivers don’t always at the 8-MHz generator to increase the IMD product from the noise is pre- follow square or cube laws exactly, the isolation. Such filtering is generally ferred over a broadband measure- assumption must be made that they do impractical, though, when two signals ment. More on this below.) Then the when finding IPs and some fit to a 20 or even 5 kHz apart must be used to on-channel signal is removed and a straight-line response must be sought. Fig 2—A typical receiver IMD test setup. Jul/Aug 2002 49 What is the “Real” Intercept Point? Fig 1 shows how the relationship between a receiver’s two points at the same receiver output level. One would on-channel response and third-order intermodulation re- get the same IP3 using measurements made at S9 as sponse can be summarized into a single number—the one would with measurements made at the noise floor. third-order intercept point (IP3). As seen on the graph, Unfortunately, for test and design engineers, real-world this is the point where the first-order and third-order re- receivers do not know that they must follow this theo- sponse lines intersect. The intercept point can be a good retical response. In many cases, receivers perform just a way to easily compare one receiver with another. If the little bit differently than expected. This can make the real response of a receiver perfectly matches the curves intercept point of a receiver subject to the judgement of shown, the intercept point can be calculated using any the person looking at the real response curves and trying Fig A—The Yaesu FT-1000MP Mark V Field measured in the Lab for this sidebar shows a response that is pretty close to theoretical. Fig B—The third-order response of the Icom IC-746PRO measured in the ARRL Lab shows less than 3:1 output-vs- input ratio. 50 Jul/Aug 2002 Fig C—What is the “real” intercept point of this Icom IC-765? to decide just what the IP3 of a receiver really is. sponse of the IC-765 we borrowed from W1INF, the The ARRL Lab grabbed a few radios from W1AW and ARRL HQ club station. Its third-order response shows a did some IP3 testing. (How many hams would love to be little “burble” within a few decibels of where receiver AGC able do that?) The results are shown in Figs A, B and C. would become active. In this case, the calculated IP3 is One of the radios behaved pretty close to the theoretical much higher for stronger input levels than it is for mea- response, but the other two don’t really seem to know that surements made at the noise floor. their responses are supposed to be straight lines. As an important aside, none of these deviations from Fig A shows the measured response of a Yaesu FT- theoretical indicates a receiver problem. They are just 1000MP Mark V Field. In this case, the receiver response artifacts of how very strong signals sometimes behave is pretty close to what theory predicts. The first-order re- inside of complex receivers. sponse (on-channel) increases by 1 dB for every 1 dB of In the case of the receivers shown above, what is the increase in signal, at least up until receiver AGC levels “true” intercept point of each receiver? There really is no the receiver output. The third-order intermodulation re- true number, but one could rightfully argue that one made sponse appears at much higher levels of off-channel by using a “best fit” of the theoretical lines against the signals, and once it appears, the receiver output in- actual curves best represents the receiver’s true IP3. creases 3 dB for every 1 dB of input level. If one makes That sounds good in principle, but in practice, doing the measurements of the input levels at any point, one gets tests for these sidebars took considerable time. QST approximately the same IP3. Because these are all readers want to see Product Reviews as soon as pos- relative measurements, the receiver S-meter can be sible, and the ARRL Lab can’t take the time to do much used as an indicator of relative receiver output. The inset extra testing for radios being reviewed. Measurements box in the graph shows the IP3 calculated using various made at the noise floor are difficult to make, and the in- S-meter readings. At S9, the deviation from theoretical fluence of the measured noise on an IP3 calculation has pushed the IP3 up quite a bit. The receiver AGC may made from receiver responses at the noise floor is not a be responding to the very strong off-channel signals very accurate way to make measurements. Even more 20 kHz away. important, in almost all “real-world” use, the ambient Fig B shows a less-classic receiver response—that of noise level when an antenna is connected to receiver is the IC-746PRO. In this case, the on-channel response is probably 10 or 20 dB higher than the receiver input noise. classic, but the third-order response increases by less In addition, if an intermodulation product is only a few than 3 dB for every 1 dB of receiver input. In this case, if decibels above the noise, it is not going to have as much one calculates IP3 using measurements made at the impact on listening as would one at a higher level. For noise floor, one will get a lower number than that obtained that reason, the ARRL Lab has used an S5 receiver out- by using IMD measurements made at stronger signal lev- put level as the point at which IP3 calculations are made els. I speculate that the two signals, spaced at 20 kHz since the mid 1990s. This probably represents a reason- and 40 kHz from the desired signal, may not be at the able strong signal that is apt to be encountered in the real same level inside the receiver at the point where the world. Although this is not quite as accurate as a best-fit intermodulation is occurring. calculation, as can be seen from the graphs, an S5 cal- The differences in receiver responses have little to do culated IP3 is reasonably close to the “real” IP3 of the with today’s technology. Fig C shows the measured re- radios tested.—Ed Hare, W1RFI, ARRL Lab Supervisor Jul/Aug 2002 51 Effects of Phase Noise Transmitters have perform improved dynamic-range In the May/June 2002 QEX,7 Peter Dynamic Range, Too testing. Careful methods, good in- Chadwick, G3RZP, took on the task of The concept of intercept point ap- strumentation and a little persistence deciding how much dynamic range HF plies equally well to transmitters. The lead to accurate and repeatable receivers need. He made some mea- chief difference from receivers is that results. surements of actual received signal for transmitters, output IP is specified Many heartfelt thanks to Leif Åsbrink, SM5BSZ, for getting me go- strengths and based his conclusions instead of input IP. If an SSB trans- on those. He found that quite often, mitter had IMD3 levels 30 dB below ing on this topic and for discussing it phase noise causes reciprocal mixing one of two tones at 100 W each, then with me in such a rational manner. He deserves most of the credit for the that masks the IMD performance of its output IP3 would be 30 / 2 = 15 dB receivers. greater than 100 W, or 15 + 50 = ideas I present. Thanks also to Ed Phase noise is the unwanted phase 65 dBm. Such a figure may be used to Hare, W1RFI; Mike Tracy, KC1SX; modulation of frequency-control ele- compare transmitters much as it is to and Zack Lau, W1VT, for their valu- ments in a receiver. Especially during compare receivers, although that is able input and kind assistance. IMD3 testing, phase noise may limit not often done. It is more sensible to one’s ability to measure dynamic talk about a transmitter’s maximum Notes range. That is because the interfering output power at some level of IMD. 1M. Tracy, KC1SX, ARRL Test Procedures signals are close enough to one’s pass- Tim Pettis, KL7WE, discovered a Manual, ARRL, Rev G, Jan 2002. ARRL members may download the manual at band to cause significant reciprocal unique way of combining (with good www.arrl.org/members-only/prodrev/ mixing. In fact, the effect may prevent isolation) the outputs of two transmit- testproc.pdf. one from actually measuring the IMD ters to produce an IMD-free test sig- 21905 was a good year for Albert Einstein. DR of the receiver under test in the nal for driving high-power amplifiers Along with his papers explaining the pho- usual way. It is an undesirable situa- during IMD testing.8 It uses six l/4 toelectric effect and special relativity came tion, but it is what led Peter to define lengths of coax in two rings. It is a “On the Motion Required by the Molecular Kinetic Theory of Heat of Small Particles phase-noise dynamic range. narrow-band solution, so a separate Suspended in a Stationary Liquid,” Phase noise also comes into play fixture must be constructed for Annalen der Physik, 1905. prominently during measurement of each frequency range tested. Like 3T. Ferris, Ed., The World Treasury of Phys- so-called blocking dynamic range. other combiners, it is sensitive to ter- ics, Astronomy and Mathematics (New That measurement is designed to in- mination impedance, but it includes a York: Little, Brown and Co, 1991). dicate the ability of a receiver to ac- way to adjust isolation for various 4R. Feynman, Six Not-So-Easy Pieces (Read- ing, Massachusetts: Addison-Wesley, commodate a single strong, off-chan- loads. 1997). nel signal while receiving a weak, on- Hum and noise measurements are 5D. Reed, KD1CW, Ed., The 2001 ARRL channel signal. In older rigs, a strong normal parts of transmitter testing. Handbook (Newington, Connecticut: adjacent-channel signal often reduced The dynamic range of a transmitter ARRL, 2001), p 15.20. the output level of the on-channel sig- may also be defined in terms of the 6ARRL Handbook, pp 17.5-17.6. nal. There could have been several maximum signal-to-noise-and-distor- 7P. Chadwick, G3RZP, “HF Receiver Dy- namic Range: How Much Do We Need?” reasons for that, including saturation tion (SINAD) ratio it produces. QEX, May/June 2002, pp 36-41. of some stage or actuation of analog 8T. Pettis, “Hy-Brid Hi-Power,” Proceedings AGC. Modern rigs typically run into Conclusion of the 1998 Central States VHF Confer- the reciprocal-mixing problem before I hope my suggestions help you ence, ARRL Order #6915. (cid:1)(cid:1) other blocking effects rear their heads, though. Reciprocal mixing generally causes receiver output power to in- crease, rather than decrease, because of noise mixed into the passband. Getting back to the case of noise-lim- ited IMD measurements, we are stuck with having to decide how to pick IMD products out of reciprocal-mixing noise. It is not okay to just guess at the IP. I have found an audio spectrum analyzer very useful in digging IMD products out of the noise. The resolu- tion bandwidth of the analyzer may be reduced until a discrete IMD product stands out. So, rather than using a volt- meter to measure receiver output power, a spectrum analyzer is a good tool for measuring the power of a single IMD product alone. When performance is limited by phase noise in every test of interest, though, IMD DR loses much of its relevance. 52 Jul/Aug 2002