instruments Article
Hardware Design of a High Dynamic Range Radio Frequency (RF) Harmonic Measurement System Ram M. Narayanan 1, * Kelly D. Sherbondy 2 1 2
3
*
ID
, Kyle A. Gallagher 2 , Gregory J. Mazzaro 3
ID
, Anthony F. Martone 2 and
School of Electrical Engineering and Computer Science, The Pennsylvania State University, University Park, PA 16802, USA U.S. Army Research Laboratory, Sensors Directorate, Adelphi, MD 20783, USA;
[email protected] (K.A.G.);
[email protected] (A.F.M.);
[email protected] (K.D.S.) The Citadel, Department of Electrical & Computer Engineering, Charleston, SC 29409, USA;
[email protected] Correspondence:
[email protected]; Tel.: +1-814-863-2602
Received: 15 July 2018; Accepted: 17 August 2018; Published: 19 August 2018
Abstract: Radio frequency (RF) circuit elements that are traditionally considered to be linear frequently exhibit nonlinear properties that affect the intended operation of many other RF systems. Devices such as RF connectors, antennas, attenuators, resistors, and dissimilar metal junctions generate nonlinear distortion that degrades primary RF system performance. The communications industry is greatly affected by these unintended and unexpected nonlinear distortions. The high transmit power and tight channel spacing of the communication channel makes communications very susceptible to nonlinear distortion. To minimize nonlinear distortion in RF systems, specialized circuits are required to measure the low level nonlinear distortions created from traditionally linear devices, i.e., connectors, cables, antennas, etc. Measuring the low-level nonlinear distortion is a difficult problem. The measurement system requires the use of high power probe signals and the capability to measure very weak nonlinear distortions. Measuring the weak nonlinear distortion becomes increasingly difficult in the presence of higher power probe signals, as the high power probe signal generates distortion products in the measurement system. This paper describes a circuit design architecture that achieves 175 dB of dynamic range which can be used to measure low level harmonic distortion from various passive RF circuit elements. Keywords: high dynamic range measurements; harmonic measurement system; nonlinear distortion; harmonic radar; passive RF components
1. Introduction and Motivation Nonlinearities in RF and microwave systems can take many forms. Historically, nonlinearities are found in circuit elements such as diodes, transistors, amplifiers, mixers, and others. In addition, nonlinearities have been found in other circuit components and are generated by different mechanisms. One of the less common nonlinear mechanisms is passive intermodulation (PIM) distortion, which occurs in antennas [1,2], cables, connectors [2–4], metal-to-metal junctions [5,6], and various components [7,8]. A recent development has led to the exploitation of nonlinearities in electronic circuits to detect and track nonlinear targets [9–15]. Circuit elements exhibit nonlinear properties either by design or by consequence. By design, P-N junctions, such as diodes, are inherently nonlinear, and this property is exploited for their use in frequency mixers, which are used to upconvert or downconvert signals from one frequency to another.
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The operation of mixing two signals together to create a new frequency is a nonlinear operation. By consequence, many RF and microwave circuit elements exhibit unintended nonlinear properties. An example is the RF amplifier. Amplifiers are intended to operate linearly, boosting the input signal without creating extraneous frequencies at the output. In practice, creating a linear amplifier is not possible and additional frequency content is generated that distorts the desired signal. Much research has been done to linearize amplifiers [16–20]. The unintended frequency content generated by the nonlinear properties of the amplifier interferes with other radar and communication systems [21–23], as well as affect the sensitivity of the receiver. There are other nonlinear effects that are subtler and do not manifest as often. Among these is PIM, which is observed when high power signals interact with components that are weakly nonlinear. Such components do not exhibit measurable nonlinear distortion under normal conditions. In communication systems, the PIM produced can fall close to the fundamental band and interfere with adjacent communication channels [24,25]. To combat this, much research has gone into linearizing communication systems [3,24,26]. For close-in intermodulation distortion (IMD), the frequency separation between the fundamental signal and PIM is too small to effectively filter out. Additionally, the communication channels change frequency quickly to accommodate multiple users. So, adaptable filters with large Q values would be needed; however, reconfigurable, high Q filters do not exist. For this reason, adaptive techniques are used to predict and cancel the nonlinearities. Such techniques include predistortion, feedforward linearization, channel equalization, etc. [27–32]. Measuring weakly nonlinear RF circuit components requires specialized RF hardware [3], which itself must be highly linear and devoid of any self-generated nonlinearities. If the measurement system is not highly linear, the measurements will reflect the distortions caused by the test hardware in addition to the device under test (DUT). Commercially-available high dynamic range PIM measurement systems are accessible today [33,34]. These systems are typically designed for specific frequencies, usually around the cell band. They use a two-tone test setup and achieve up to 170 dBc of dynamic range using high Q filters that are fixed in frequency, but lack frequency agility. A commercially-available nonlinear vector network analyzer, PNA-X, demonstrates far more flexibility than the fixed frequency PIM testing systems, and has the ability to vary tone spacings and tone amplitudes [35]. The PNA-X system also tracks intermodulation (IM) products and harmonics, keeping track of all the nonlinear terms [36]. However, it lacks the dynamic range necessary to measure nonlinear distortion from weakly nonlinear devices, as they are specified to generate harmonics lower than 60 dBc [37]. Feedforward cancellation systems have been developed that enable close-in PIM to be measured with a 160-dBc dynamic range, measured from the probe signal power to the spurious free IM frequency [16,38–40]. The systems achieve a large dynamic range by taking great care to linearize their measurement system, which requires high levels of isolation between nonlinear circuit elements in the test setup to the DUTs. These systems also employ an adaptable cancellation system that removes the probe signals before PIM measurements are made. The linearization, isolation, and removal of the probe signal are essential to any high dynamic range measurement system. The downside to constructing such a test setup is the complexity of the system. These systems require iterative feedback from the receiver to cancel the fundamental probe signal. They also require an optimization algorithm to maximize the cancellation of the probe signal to maximize the dynamic range of the measurements. This paper describes an alternate approach to measuring low level nonlinear distortion from weakly nonlinear targets. The measurement system uses the second harmonic to characterize the nonlinearities of passive RF circuit elements. The measurement system achieves the high dynamic range, of the order of 175 dBc, necessary to measure weakly nonlinear devices while covering a 20% bandwidth, something the PNA-X and other commercially-available systems cannot accomplish. The measurement system is also low complexity, not requiring complicated feedforward cancellation circuits.
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Section 1 introduces the mathematics required to characterize nonlinearities from circuit elements. instrumentation. Section 3 considers issues in creating a hightodynamic harmonic measurement Section 2 describes basic harmonic measurement techniques linearizerange standard RF instrumentation. system. 4 discusses high dynamic range harmonic measurement systemsystem. constructed that4 Section 3Section considers issues inthe creating a high dynamic range harmonic measurement Section achieves dBc of dynamic range. Sectionmeasurement 5 presents the results obtained that fromachieves the measurement discusses 175 the high dynamic range harmonic system constructed 175 dBc of system ofrange. various RF system components. Section 6 concludes themeasurement paper. dynamic Section 5 presents the results obtained from the system of various RF system components. Section 6 concludes the paper. 2. Nonlinear Device Modeling and Characterization 2. Nonlinear Device Modeling and Characterization To accomplish the goal of characterizing nonlinearities generated by RF circuit components, a To accomplish the goal of characterizing generated by RF circuit components, nonlinear system model is needed. The modelnonlinearities must characterize the nonlinear properties of the a nonlinear is needed. Thedevices model under must characterize the nonlinear properties of the devices and system predictmodel the behavior of the different conditions. Having the ability to devices and predict the behavior of the devices under different conditions. Having the ability to predict predict the nonlinear response of weakly nonlinear devices enables a system designer to better the nonlinear response of weakly enablesTherefore, a system designer to better predict how predict how much distortion will nonlinear be presentdevices in the system. the input-output relationship much distortion will be present the system. Therefore, the input-output relationship for nonlinear for nonlinear devices needs to beindefined. devices needs tononlinear be defined. In general, systems do not satisfy the linearity property, i.e., superposition and scaling In general, dosystems not satisfy the linearity i.e.,be superposition properties. The nonlinear output of systems nonlinear contains signalsproperty, that cannot representedand as ascaling linear properties. The output of nonlinear systems contains signals that cannot be represented as a combination of the input signals. These signals can be at different frequencies than the linear input combinationInofthis thepaper, input nonlinear signals. These can beusing at different frequencies than the which input frequencies. systemssignals are modeled the power series [7,8,41–43], frequencies. Inas this paper, nonlinear systems are modeled using the power series [7,8,41–43], which is is represented represented as ∞ ∞ ∞
∞
= = aan xxnn,, n y =y∑ yny= ∑ n n= 0
n =0
n=0
(1) (1)
n =0
the input signal, is output the output signal, is the scale factor coefficient of the nth where xxis is the input signal, y isythe signal, and and an is athe n scale factor coefficient of the nth order nonlinearity. order nonlinearity. When the input to a nonlinear system is a single frequency, the output consists of harmonics of fundamental frequency. frequency. With a single frequency that frequency occurring at integer multiples of the fundamental input to the power series given by x = x cos ( ω t + θ ) , the output canbe beshown showntotobe be[44] [44] input to the power series given by x = x0 cos(ω 0t + θ ) , the output can 0
0
∞
∞
y =y ∑ cncx0nxncos (nω = cos( nω00tt+ + nnθ θ )).. n 0 n=0n = 0
(2) (2)
The amplitude of the frequency domain representations of Equation (2) is illustrated graphically in Figure 1. Generally, the the output output amplitude amplitude drops drops as as the the harmonic harmonic order order nnincreases. increases.
Figure nonlinear system. system. Figure 1. 1. Illustration Illustration of of the the output output due due to to aa single single frequency frequency input input into into aa nonlinear
Equation (2) expresses the nonlinear system input-output relationship in terms of voltage. Equation (2) expresses the nonlinear system input-output relationship in terms of voltage. Engineers typically prefer to use power units; therefore, the voltage expression is converted to power. Engineers typically prefer to use power units; therefore, the voltage expression is converted to power. 2 P = V Z0 , where is the peak The average power of a sinusoidal signal is given by 2 peak peak ave peak The average power of a sinusoidal signal is given by Pave = Vpeak /2Z0 ,2where Vpeak isVthe voltage and Z0 isand the system characteristic impedance. impedance. Thus, the power the power harmonics canharmonics be represented in Z 0 is the voltage system characteristic Thus,inthe in the can be a decibel (dB) as: (dB) scale as: represented inscale a decibel Pout,n [dBm] = nPin [dBm] + Dn , (3) Pout ,n [dBm] = nPin [dBm] + Dn , (3) where Pout,n is the output power at the nth harmonic, Pin is the input power at the fundamental Pout(n is the output power at the nth harmonic,(1−Pn)in, and is the input power at the fundamental where frequency dBm represents power expressed in ,n = 1), Dn is a coefficient expressed in dBm decibels relative to one milliwatt. (1−n) frequency ( n = 1 ), Dn is a coefficient expressed in dBm , and dBm represents power expressed in
decibels relative to one milliwatt. The implications of Equation (3) are that the output-to-input power ratio for the nth harmonic follows an n : 1 relationship in a dB scale. Therefore, a 1-dB increase in the input creates a 2- and 3-
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4 of 16 are that the output-to-input power ratio for the nth harmonic follows an n : 1 relationship in a dB scale. Therefore, a 1-dB increase in the input creates a 2- and 3-dB dB increase in output power for the second and third harmonics, respectively. In general, the D increase in output power for the second and third harmonics, respectively. In general, the Dn valuesn values are frequency-dependent and characterize nthnonlinear order nonlinear properties of a device. are frequency-dependent and characterize the nth the order properties of a device. A moreA more commonly found characterization of a device’s nonlinear properties is its output intersect point commonly found characterization of a device’s nonlinear properties is its output intersect point OIP n, n :1 OIP is the intersection which the 1:1 of the linear response the of whichn ,iswhich the intersection point at point whichatthe 1:1 slope of slope the linear response intersectsintersects the n : 1 slope the nth of order nonlinearity. This is shown the second harmonic, i.e., n = 2.i.e., n = 2 . slope the nth order nonlinearity. This in is Figure shown 2infor Figure 2 for the second harmonic,
OIP22and Figure 2. Illustration of the relationship between OIP andD2D . 2.
Therelationship relationshipbetween betweenDnDand and can be found by manipulating Equation (3) to yield: The OIPOIP n can n n be found by manipulating Equation (3) to yield:
n)OIP + nD . Dn =D(n1=−(1n−)OIP n nD1 .1 n+
(4) (4)
3. Issues in Creating a High Dynamic Range Harmonic Measurement System 3. Issues in Creating a High Dynamic Range Harmonic Measurement System To measure harmonics generated by devices that are not traditionally nonlinear, a high dynamic To measure harmonics generated by devices that are not traditionally nonlinear, a high dynamic range (DR) measurement system must be developed. The measurement system must create a highly range (DR) measurement system must be developed. The measurement system must create a highly linear probe signal and must have the ability to measure very weak nonlinear signals in the presence linear probe signal and must have the ability to measure very weak nonlinear signals in the presence of the large fundamental probe signal. of the large fundamental probe signal. There are two important aspects of designing a high DR harmonic measurement system: (1) the There are two important aspects of designing a high DR harmonic measurement system: (1) the use of a high DR receiver to measure the weak nonlinear signals in the presence of the high power use of a high DR receiver to measure the weak nonlinear signals in the presence of the high power probe signal; and (2) generation of a highly linear probe single used to probe a DUT. Both the receiver probe signal; and (2) generation of a highly linear probe single used to probe a DUT. Both the receiver and probe single generator have their unique problems that must be addressed to generate high fidelity, and probe single generator have their unique problems that must be addressed to generate high linearized signals. This section addresses these problems. fidelity, linearized signals. This section addresses these problems. 3.1. Creating a Highly Linear Harmonic Receiver 3.1. Creating a Highly Linear Harmonic Receiver The first problem in creating a highly linear harmonic receiver is that the measurement hardware is The first The problem in end creating a highly linear consists harmonic receiver devices is that such the measurement itself nonlinear. RF front of a spectrum analyzer of nonlinear as amplifiers hardware is itself nonlinear. The RF front end of a spectrum analyzer consists of nonlinear and mixers. For the results presented in this paper, a National Instruments (NI) (Austin, TX,devices USA) such as amplifiers mixers. theThe results presented in to this paper, aa second National Instruments (NI) PXIe-5668R spectrumand analyzer is For used. 5668R is specified generate harmonic >69 dBc (Austin, TX, USA) PXIe-5668R spectrum is used. The 5668Rinput is specified generate a second down from the fundamental, between 700analyzer to 1000 MHz with 0-dBm powerto [45]. Although the harmonic >69 dBc down from the fundamental, between 700 to 1000 MHz with 0-dBm input power data sheet specifies >69 dBc, the measured self-generated second harmonic is 80 dBc. This 80 dBc of [45]. Although data sheet specifies >69 dBc, the measured second harmonic dynamic range isthe sufficient to make harmonic measurements ofself-generated strongly nonlinear devices, suchisas80 dBc. This 80 dBc ofand dynamic sufficient totomake measurements stronglyelements. nonlinear amplifiers, mixers, diodes,range but isisinadequate makeharmonic measurements of weaklyof nonlinear devices, such as amplifiers, mixers, and diodes, but is inadequate to make measurements of weakly The first example of this shown in Figure 3, which depicts an ideal probe signal entering an amplifier. The first of this test”, shown“HPF” in Figure 3, which depicts anfilter”, ideal probe signal Innonlinear Figure 3,elements. “DUT” stands forexample “device under stands for “high-pass and “LPF” entering an amplifier. In Figure 3, “DUT” stands for “device under test”, “HPF” stands for “highstands for “low-pass filter”. The DUT is a Mini-Circuits amplifier ZX60-3018G-S+. The fundamental pass filter”, and “LPF” stands for “low-pass filter”. The DUT is aanalyzer. Mini-Circuits amplifier ZX60-3018Gand harmonic responses are made on the PXIe-5668R spectrum The choice of filters is very S+. The fundamental and harmonic responses are made on the PXIe-5668R spectrum analyzer. The important in architecting a reliable harmonic measurements system [46]. choice of filters is very important in architecting a reliable harmonic measurements system [46].
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Figure 3. Measuring the second harmonic output of an amplifier using an ideal linear source. Figure 3. 3. Measuring Measuring the the second second harmonic harmonic output output of of an an amplifier amplifier using using an an ideal ideal linear linear source. source. Figure
Three tested using the setup in in Figure 3. These include: (1) (1) no Three different differentlow-pass low-passfilter filteroptions optionsare are tested using the setup in Figure Figure 3. These These include: (1) Three different low-pass filter options are tested using the setup 3. include: filter; (2)(2) a Mini-Circuits reflective filter VLF-1200; and (3) When no filter; filter; (2) Mini-Circuits reflective filter VLF-1200; and (3)aaaMini-Circuits Mini-Circuitsdiplexer diplexerRPB-272. RPB-272. When When no aa Mini-Circuits reflective filter VLF-1200; and (3) Mini-Circuits diplexer RPB-272. no filter filter is used, the the dynamic dynamic range range of of the the test test setup setup is filter is is used, is set set by by the the spectrum spectrum analyzer, analyzer, namely namely 80 80 dBc. dBc. no The dynamic range of test setup is increased by filtering out the fundamental frequency before it enters The dynamic dynamic range range of of test test setup setup is is increased increased by by filtering filtering out out the the fundamental fundamental frequency frequency before before itit The the spectrum analyzer. For every attenuation of the fundamental, the self-generated second enters the spectrum spectrum analyzer. For1-dB every 1-dB attenuation attenuation of the the fundamental, fundamental, the self-generated self-generated enters the analyzer. For every 1-dB of the harmonic of the spectrum analyzer decreases 2 dB. This follows from the relationship in Equation second harmonic harmonic of of the the spectrum spectrum analyzer analyzer decreases decreases 22 dB. dB. This This follows follows from from the the relationship relationship(3). in second in A commercial off-the-shelf (COTS) Mini-Circuits high-pass filter VHF-1200 would be a natural choice, Equation (3). (3). A A commercial commercial off-the-shelf off-the-shelf (COTS) (COTS) Mini-Circuits Mini-Circuits high-pass high-pass filter filter VHF-1200 VHF-1200 would be aa Equation would be but most COTSbut filters attenuate the stop band frequencies by creating an impedance The natural choice, but most COTS filters filters attenuate the stop stop band band frequencies by creating creatingmismatch. an impedance impedance natural choice, most COTS attenuate the frequencies by an result of the mismatch is that the undesired frequencies are reflected and not passed through the mismatch. The The result result of of the the mismatch mismatch is is that that the the undesired undesired frequencies frequencies are are reflected reflected and and not not passed passed mismatch. filter. Thethe impact thisimpact is examined To attenuate fundamental frequency andfrequency to reduceand the through the filter.of The impact of this this later. is examined examined later. the To attenuate attenuate the fundamental fundamental frequency and through filter. The of is later. To the reflection back into the DUT, a diplexer is used. The low frequency port is terminated in 50 Ω. For this to reduce the reflection back into the DUT, a diplexer is used. The low frequency port is terminated to reduce the reflection back into the DUT, a diplexer is used. The low frequency port is terminated setup, the probe signalthe is set to 800 MHz the probe power is signal calibrated to be −20 dBm to at in 50 50 Ω. Ω. For this setup, setup, the probe signal isand set to to 800 MHzsignal and the the probe signal power power is calibrated calibrated to in For this probe signal is set 800 MHz and probe is the input to at the amplifier. be −20 −20 dBm at the the input to to the the amplifier. amplifier. be dBm input The resolution bandwidth (RBW) on on the the spectrum spectrum analyzer was was set set to to 800 800 Hz Hz and the The resolution resolution bandwidth bandwidth (RBW) spectrum analyzer Hz and and the the internal internal The internal attenuator was set to 30 dB. The results in Table 1 illustrate the following two concepts: (1) the spectrum attenuator was was set set to to 30 30 dB. dB. The The results results in in Table Table 11 illustrate illustrate the the following following two two concepts: concepts: (1) the the attenuator (1) analyzer has the dynamic range to measure the second harmonic response from the Mini-Circuits spectrum analyzer has the dynamic range to measure the second harmonic response from the Minispectrum analyzer has the dynamic range to measure the second harmonic response from the Miniamplifiers; and (2) the reflective filter alters thealters test setup andsetup yields false results. Ifresults. the input power to Circuits amplifiers; amplifiers; and (2) the the reflective reflective filter alters the test test setup and yields false results. If the the input Circuits and (2) filter the and yields false If input the spectrum analyzer is 0 dBm, is the spectrum analyzer will generate second harmonic on the order power to the the spectrum spectrum analyzer is 00 dBm, dBm, the the spectrum spectrum analyzer willagenerate generate second harmonic harmonic on power to analyzer analyzer will aa second on of − 90 dBm. Therefore, the reading of − 36.3 dBm is well above the self-generation level of the setup the order of −90 dBm. Therefore, the reading of −36.3 dBm is well above the self-generation level of the order of −90 dBm. Therefore, the reading of −36.3 dBm is well above the self-generation level of and it is a valid reading. the setup setup and and itit is is aa valid valid reading. reading. the Table 1. Filter testing results to improve Table 1. 1. Filter Filter testing testing results results to to improve improve dynamic dynamic range. range. Table dynamic range.
Filter Type Power at 800 MHz MHz Power Power at1600 1600MHz MHz Filter MHz at 1600 MHz FilterType Type Power Powerat at 800 800 Power at None −0.3 dBm −36.3 dBm None −0.3 −36.3 dBm None −0.3dBm dBm − 36.3 dBm Reflective −39.3 dBm −29.5 dBm Reflective −39.3 dBm −29.5 dBm Reflective −39.3 dBm −29.5 dBm Diplexer − 42.6 dBm − 38.6 dBm Diplexer −42.6 dBm −38.6 dBm Diplexer −42.6 dBm −38.6 dBm
To measure measure lower lower level harmonics, the dynamic range of the the system needs to be beto increased. This To dynamic range of system needs to increased. This To measure lowerlevel levelharmonics, harmonics,the the dynamic range of the system needs be increased. can be done by using a filter. When a reflective filter is used, the undesired probe signal is reflected can by using a filter. When a reflective filter is is used, the Thisbe candone be done by using a filter. When a reflective filter used, theundesired undesiredprobe probesignal signalisis reflected reflected causing a reverse traveling wave that enters the output port of the DUT. Once the probe signal enters causing a reverse traveling wave that enters the output port of the DUT. Once the probe signal causing a reverse traveling wave that enters the output port of the DUT. Once the probe signal enters enters the output port of the DUT, the probe signal generates additional nonlinearities. The results in Table the output port of the DUT, the probe signal generates additional nonlinearities. The results in Table the output port of the DUT, the probe signal generates additional nonlinearities. The results in Table 1 1 show more than a 7-dB increase in the measured second harmonic when the reflective filter is used. 1show showmore morethan thanaa7-dB 7-dBincrease increasein inthe themeasured measuredsecond second harmonic harmonic when when the the reflective filter is used. reflective filter is used. Figure 444 illustrates illustrates this this reflection reflection and and additional additional generation generation of of the the second second harmonic harmonic when when aaa reflective reflective Figure Figure illustrates this reflection and additional generation of the second harmonic when reflective filter is used. filter filter is is used. used.
Figure 4. the second output of of an with aa reflective filter showing showing errors errors Figure 4. 4. Measuring Measuring the second harmonic harmonic output an amplifier amplifier with reflective filter Figure in the measurement setup. in the measurement setup. in the measurement setup.
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In Figure 4, the blue lines represent the probe signal at fundamental frequency, the red lines In Figure 4, the blue lines represent the probe signal at fundamental frequency, the red lines represent the second harmonic signal, and thethe dashed thatare aregenerated generated by represent the second harmonic signal, and dashedlines linesrepresent represent the the signals signals that the reflected probe signal. theFor measurements takentaken in Table 1, the1,setup was was calibrated to remove by the reflected probe For signal. the measurements in Table the setup calibrated to the cable lossthe and theloss lossand through the filter at second The VHF-1200 and RBF-272 remove cable the loss through thethe filter at theharmonic. second harmonic. The VHF-1200 and RBF-were 272towere to losses have similar at 800MHz, and 1600 the fundamental frequency of the signal probe and chosen havechosen similar at 800losses and 1600 the MHz, fundamental frequency of the probe ) forVHF-1200 both the VHF-1200 signalharmonic and its second harmonic under test, respectively. The (S return loss ( S11the its second under test, respectively. The return loss both and RBF-272 11 ) for are shown in Figure and RBF-272 are 5. shown in Figure 5.
Figure 5. S-parameters of Mini-Circuits the Mini-Circuits VHF-1200 high-pass filterand andRBF-272 RBF-272diplexer diplexer in in the the high Figure 5. S-parameters of the VHF-1200 high-pass filter high pass configuration. pass configuration.
Although the high-pass filter is not needed for this amplifier example, filtering is needed to
Although high-pass filter is not needed filtering is needed increase thethe dynamic range to greater than 160 for dBc,this theamplifier dynamic example, range needed to measure to increase the dynamic rangecircuit to greater than 160 theofdynamic range needed to measure nonlinearities from passive components. The dBc, amount attenuation needed to achieve a DR d with a current dynamic range of ofDR is given by: desired dynamic range of circuit nonlinearities from passive components. The amount attenuation needed to achieve a c desired dynamic range of DRd with a current dynamic range of DRc is given by: DR d − DR c + 10 , 2 c + 10 DRd − DR
AH =
AH =
(5)
,
where AH is the attenuation needed by the high 2pass filter at the fundamental frequency. The
(5)
given in a dB scale. An extra 10 dB is added tothe the fundamental desired dynamic range to ensure that whereexpression A H is theisattenuation needed by the high pass filter at frequency. The expression the self-generated nonlinearities are at least a factor of 10 less than the desired minimum detectable is given in a dB scale. An extra 10 dB is added to the desired dynamic range to ensure that the nonlinearity. Equation (5) also predicts that the dynamic range is increased by 2 dB for every 1 dB of self-generated nonlinearities are at least a factor of 10 less than the desired minimum detectable attenuation in the high-pass filter. nonlinearity. Equation (5) also predicts that the dynamic range is increased by 2 dB for every 1 dB of This section has demonstrated the importance of properly linearizing the receive section of a attenuation in measurement the high-passsystem. filter. In this section, it was assumed that the probe signal was ideal, i.e., it harmonic This section has demonstrated importance of properly receiveproper section of contained no measurable second the harmonic. The next section linearizing shows how the to ensure a harmonic measurement system. In this section, it was assumed that the probe signal linearization of the probe signal and illustrates a potential issue when constructing the measurement was ideal,setup. i.e., it contained no measurable second harmonic. The next section shows how to ensure proper linearization of the probe signal and illustrates a potential issue when constructing the 3.2. Creating a Harmonic Free Probe Signal measurement setup. In the previous section, it was assumed that the probe signal was ideal, i.e., it contained no
3.2. Creating a Harmonic Free Probe Signal possible and this section demonstrates how to create a probe second harmonic. This is not physically signal that is “ideal enough” to measure weakly nonlinear targets. In the previous section, the
In the previous section, it was assumed that the probe signal was ideal, i.e., it contained no second fundamental frequency needed to be attenuated in the receiver to measure the second harmonic harmonic. This is not physically possible and this section demonstrates how to create a probe signal accurately. In this section, the second harmonic must be removed from the probe to ensure that the that ismeasured “ideal enough” weakly nonlinear targets. In the previous theharmonic fundamental harmonictoismeasure coming solely from the DUT and not the probe signal. Ifsection, the second frequency needed to be attenuated in the receiver to measure the second harmonic accurately. In this is not adequately attenuated from the probe signal, the measurement system generates a false, selfsection, the second harmonic This mustproblem be removed from probe to ensure that the measured harmonic created second harmonic. is viewed as the co-site interference. is coming solely from the DUT and not the probe signal. If the second harmonic is not adequately attenuated from the probe signal, the measurement system generates a false, self-created second harmonic. This problem is viewed as co-site interference.
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3.2.1. Filter Considerations 3.2.1. Filter Considerations The amount of second harmonic present in probe signal can never reach zero, or −∞ dB. Therefore, it can only be attenuated the noise floor signal of the measurement in∞Section 3.1, the The amount of second harmonicto present in probe can never reachsetup. zero, As or − dB. Therefore, linearity ofbe theattenuated measurement system by filtering. TheAs NIin PXI-5651 it can only to the noise can floorbeofincreased the measurement setup. Section signal 3.1, thegenerator linearity used specified to produce than 25 dBc of harmonic the output is 0 used dBm of theismeasurement system less can be increased bysecond filtering. The NIwhen PXI-5651 signal power generator [47]. We assumed this value does25not change too much whenwhen the output power is increased to[47]. +10 is specified to produce less than dBc of second harmonic the output power is 0 dBm dBm. With +10 dBm of does output signal generator willpower produce less than to −15 dBm of We assumed this value notpower, changethe too5651 much when the output is increased +10 dBm. second harmonic, therebypower, providing 25 dBc of dynamic range. Thus, if this used With +10 dBm of output the 5651 signal generator will produce lessgenerator than −15 is dBm ofwithout second any filtering, accurate second25 harmonic measurements are made togenerator −5 dBm, including the 10-dB harmonic, thereby providing dBc of dynamic range. Thus, if this is used without any safety factor for signal-to-interference ratio, which is verytouseful when trying tothe make sensitive filtering, accurate second harmonic measurements arenot made −5 dBm, including 10-dB safety harmonic measurements. To increase the dynamic range of the receiver, low-pass filter is harmonic used. For factor for signal-to-interference ratio, which is not very useful when tryingato make sensitive the probe signal,To the improvement in dynamic a 1:1 ratio. So, if thefilter signal generator provides measurements. increase the dynamic range range of the is receiver, a low-pass is used. For the probe a 25-dBc dynamic range and 160 dBc is desired, the attenuation required for the low pass filter is 145 signal, the improvement in dynamic range is a 1:1 ratio. So, if the signal generator provides a 25-dBc dB. The general expression foristhe attenuation needed by required the low pass is: pass filter is 145 dB. dynamic range and 160 dBc desired, the attenuation for filter the low The general expression for the attenuation needed by the low pass filter is: AL = DRd − DR g + 10 , (6) A L = DRd − DRg + 10 (6) where AL is the attenuation required of the low-pass filter at the second harmonic and DRg is the where A Lrange is theofattenuation required of the low-pass filter factor at theissecond is the dynamic the signal generator. Again, a 10-dB safety built inharmonic to ensure and 10 dBDR ofgsignaldynamic rangeratio. of the signal generator. Again, a 10-dB safety factor is built in to ensure 10 dB of to-interference signal-to-interference ratio. Most COTS filters do not provide greater than 100 dB of attenuation required to linearize the COTS filters do not provide greater than 100 dBtoofachieve attenuation required to linearize the probeMost signal. Therefore, multiple filters need to be cascaded the large attenuation required. probe signal. Therefore, multiple filters need be cascaded achieve theislarge attenuation required. As stated in Section 3.1, most COTS filters aretoreflective, andto attenuation achieved in the stop band As in Sectionmismatch 3.1, most COTS filters reflective, and attenuation is achieved in theand stopnot band by by stated an impedance causing theare stop band frequencies to reflect backwards pass an impedance mismatch stop band frequencies through it. This reflectivecausing nature the of filters causes problems.to reflect backwards and not pass through it. This reflective naturelow-pass of filters filter, causes problems. The Mini-Circuits Model # VLF-1200, has a cut off frequency of 1 GHz. However, The band Mini-Circuits low-pass Model VLF-1200, has a cut off frequency of 1 GHz. However, the stop of this filter does filter, not meet the#>100-dB attenuation requirement. Therefore, multiple the stop band filter does not meet >100-dB attenuationFigure requirement. multiple filters need to of be this cascaded to increase thethe stop band attenuation. 6 showsTherefore, the measured and filters need to cascaded when to increase the stop band attenuation. Figure shows the measured theoretical S21be response two VLF-1200 filters are cascaded. The6theoretical cascaded and S21 theoretical |S21 | response when two VLF-1200 filters are cascaded. The theoretical cascaded |S21 | response was computed as a product of the individual S responses. response was computed as a product of the individual |S2121| responses.
Figure VLF-1200 low-pass low-passfilters filtersare arecascaded. cascaded. Figure6.6.Measured Measuredand andtheoretical theoretical |SS2121| response response when when two VLF-1200
When the two reflective low-pass filters are cascaded, cascaded, the measured measured and theoretical responses do not closely match. This point is further investigated in [48], where three reflective low pass filters are cascaded. The measured results when three low-pass filters are cascaded show more discrepancy when compared compared to to the the theoretical theoretical response. response.
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Using a number of cascaded reflective filters causes large variations in the measurement system’s dynamic range as a function of frequency. If the measurement system operates at a single Using a number of cascaded reflective filters causes large variations in the measurement system’s frequency, a null in the cascaded frequency response can be used. If measurements are taken over a dynamic range as a function of frequency. If the measurement system operates at a single frequency, bandwidth of frequencies, the fluctuations in the frequency response would not permit reliable, a null in the cascaded frequency response can be used. If measurements are taken over a bandwidth repeatable, and accurate measurements. of frequencies, the fluctuations in the frequency response would not permit reliable, repeatable, and measurements. 3.2.2.accurate Diplexer Considerations 3.2.2. This Diplexer leadsConsiderations us to the choice of microwave diplexers for accomplishing the filtering operation. Diplexers are three-port devices which separate power entering a common input into two frequency This leads us to the choice of microwave diplexers for accomplishing the filtering operation. bands; or conversely, they combine two frequency bands arriving separately into a common output Diplexers are three-port devices which separate power entering a common input into two frequency [49]. Diplexers in which there are adequate guard bands between channels may be designed by bands; or conversely, they combine two frequency bands arriving separately into a common output [49]. suitably connecting two separate, doubly-terminated filters onto a T-junction. These devices are Diplexers in which there are adequate guard bands between channels may be designed by suitably typically employed to connect the transmit and receive filters of a transceiver to a single antenna connecting two separate, doubly-terminated filters onto a T-junction. These devices are typically through a suitable three-port junction [50,51]. Diplexers are designed to have low PIM and, therefore, employed to connect the transmit and receive filters of a transceiver to a single antenna through a will have low harmonic distortion. With that said, they will generate their own harmonics, but these suitable three-port junction [50,51]. Diplexers are designed to have low PIM and, therefore, will have will be very low, on the order of high-quality cables and connectors, i.e.,
