Additional measurements for IM2 and IM3 with different materials and RF devices are necessary. By continuing you agree to the use of cookies. However it should be noted that if fixed stations operate in the duplex mode, third order intermodulation could arise when two adjacent fixed stations are transmitting and a handportable on one of the channels is also transmitting. Slew-induced distortion (SID) can produce intermodulation distortion (IMD) when the first signal is slewing (changing voltage) at the limit of the amplifier's power bandwidth product. The subse-quent terms represent the distortion of the amplifier. Two-tone IMD is measured by applying two spectrally pure sinewaves to the ADC at frequencies f1 and f2, usually relatively close together. The concept of second- and third-order intercept points is not valid for an ADC, because the distortion products do not vary in a predictable manner (as a function of signal amplitude). Based on two pure sinusoidal signals S1 cos(T1 t) and S2 cos(T2 t) with the amplitudes S1 = S2 = 1, by developing into potential rows up to the ninth order, the expressions for the second- and third-order IM products are determined to be, Again, developed up to the ninth order, the transmission characteristics of a component can be described by the polynomial, Pol(z) = A0 + A1 z + A2 z2 + A3 z3 + A4 z4             + A5 z5 + A6 z6 + A7 z7 + A8 z8 + A9 z9        (3). Richard Brice, in Music Engineering (Second Edition), 2001. the second term is the fundamental signal(s). The test usually comprises a low frequency. The second IMD can be found by analyzing the third term of Equation 3. For example, if the intermod product generated is at 385 MHz and results from the combination of the second harmonic of 155 MHz adding with the fundamental of 75 MHz, the prediction would show as 2x(155) + 1x(75) = 385 MHz. The second order intermodulation product (the sum frequency) is at 14.165. The almost flat curves are typical of linear, transformerless, electronic paths. With respect to a dual-band system, this spectrum shows the second-order IM product suddenly as an additional interferer in the receive band. This is because the third harmonic of fs/4 is 3fs/4, and the alias occurs at fs− 3fs/4 = fs/4. The most critical intermodulation distortion product is the Third Order Intermodulation (TOI) product. They may cancel, causing the two-tone, third-order product to be drastically reduced. Once the input reaches a certain level, however, the output signal begins to soft-limit, or compress. However, the third-order products 2f2–f1 and 2f1–f2 are close to the original signals, and are almost impossible to filter. A first common node signal is generated between a first resistor and a second resistor coupled across the mixer's differential output terminals. To understand this phenomenon, assume k sinusoids with equal (drive current) amplitude a are being multiplexed. The numbers from such a measurement would look very good but could pose a serious error Figure 1-60 shows the graphical analysis for this example. Second-order intermodulation products are, where frequencies f3, f4, and f5 are the undesirable distortion products that show up at the output. IP 3 is the point where the intermodulation product is equal to the fundamental signal. The first is by finding 10*log of the ratio of the total output power to the power in adjacent channel. These spurious signals fall in the vicinity of ƒ1 and may show up in the receiving passband with sufficient amplitude to cause interference problems. As the input signal continues to increase beyond full-scale, the ADC should as an ideal limiter, and the IMD products become very large. Similarly, the third-order IMD amplitudes increase 3 dB for every 1 dB of signal increase, as indicated by the slope = 3 plotted line. Copyright © 2021 Elsevier B.V. or its licensors or contributors. The wide bandwidth of the LTC6400 results in flat gain to hundreds of Megahertz; Table 25.4 summarizes the gain flatness specifications in the data sheets. It is close, but not quite correct because input signals of 0 dBm are a little too strong to still be on the second order curve as will be shown below. It should be noted that IP2, IP3, and the 1 dB compression point are all a function of frequency, and as one would expect, the distortion is worse at higher frequencies. It should be noted that essentially the same arguments apply to DACs. The IM3 measurement was performed in the GSM band with f1 = 936 MHz and f2 = 958 MHz at 2 * 20 W (+43 dBm). An AM demodulator then recovers the true rms level of the sidebands. SMPTE testing can be sensitive to high order non-linearity, namely some kinds of crossover distortion, and LF effects such as signal transformer saturation, and thermal distortion. The 60Hz (several other frequencies up to 250Hz may be used in the DIN test) is mixed with a second, HF signal, usually at 7kHz. This is the output stage of the transmitter. Therefore, neither the power levels of the several IM products nor the relations between them can be calculated. they are in a 4:1 amplitude ratio. Second– and third-order product locations are shown in Figure 3-20. The exact level at which this occurs is dependent on the particular ADC under consideration—some ADCs may not exhibit significant increases in the IMD products over their full input range, however most will. Second and third-order intermodulation products for f1 = 5 MHz, f2 = 6 MHz. The fundamental is shown by the slope = 1 curve in the diagram. The mixtures between the original frequencies, ω a + ω b, ω a - ω b, and ω b - ω a are also called second-order intermodulation products (IM2). Degree in electrical engineering in 1987 from Fachhochschule Augsburg. Last, the 7kHz ‘carrier’ and nearly all noise are strongly removed by a LPF, leaving just the products. Therefore, with a nearly quadratic characteristic (diode or transistor), the second-order IM product is dominant; with its cubic characteristic, the third-order IM product is also dominant. This induces an effective reduction in gain, partially amplitude-modulating the second signal. Figure 6.3. Put a different way, not this: where Eo is output voltage and Ei is input voltage. In other applications, the high bandwidth of the LTC6400 can be a significant advantage. Figure 6-140:. The slope of the third intermodulation product is three times that of the output signals. This product is at two times each The points where these graphs cross are called 3rd order intercept point IP 3 and 2nd order intercept point IP 2, respectively. The second-order intermodulation products correspond to (⍵1 ∓ ⍵2) terms. With a low level two-tone input signal, and two data points, one can draw the second- and third-order IMD lines as they are shown in Figure 6-139 (using the principle that a point and a slope define a straight line). to produce a series of second order sum and difference products, third order products etc. Now, suppose a second harmonic from the RF generators is 180° out-of-phase with the mixer’s second harmonic. In the 3 Hz to 3 GHz band, a filter is used to attenuate signal generator second harmonic product (2*F1). Once the input reaches a certain level, however, the output signal begins to soft limit, or compress due to things like power supply limits, output drive maximums, and the like. Walt Kester, in Op Amp Applications Handbook, 2005. In simple terms, a power law is a relationship which does not relate one set of values (the input voltage) to another (the output voltage) by a constant, which would yield a straight-line relationship – and incidentally a distortionless amplifier, but by a function which is made up of both constant and multiplication factor which is related to itself. It has been shown that a complete evaluation of a passive RF device requires a specification for the second-order IM product effects when used in a dual-band system. Third-order IMD products can mask out small signals in the presence of larger ones. This results in the chord in Figure 4.2. The larger number of tones more closely simulates the wideband frequency spectrum of cellular telephone systems such as AMPS or GSM. The value of the third-order intercept at 5 MHz is 36 dBm. If the system nonlinearity is approximated by a power series expansion, the second-order IMD amplitudes increase 2 dB for every 1 dB of signal increase. He has been employed by Spinner GmbH since 1989 and has been the head of development and design since 1995. ACPR measurement template for modulated signals. The theoretical approach showed that no relationship or equation for calculating the power levels of the particular IM products can be given because the transmission characteristics of galvanic contacts are never known. COMPOSITE SECOND ORDER INTERMODULATION DISTORTION Composite Second Order distortion (CSO) is a result of one or two carriers experiencing a second order non-linearity. Interestingly, the frequency sum products in the last four columns fall in at the same frequency as second-order intermodulation (composite second order) products at +1.25 MHz offset form the carrier. When the input signal is within a few dB of the ADC FSR, the IMD may start to increase (but it might not in a very well-designed ADC). Third Order Intermoduluation Distortion Performance Test. Cheng-Wei Pei, Adam Shou, in Analog Circuit Design, 2013. The power term p in the above expression illustrates that Ei is multiplied by a version of itself and, we know from Chapter 2, that when two sine-waves are multiplied together it results in sum and difference frequencies. It has been shown that a complete evaluation of a passive RF device requires a specification for the second-order IM product effects when used in a dual-band system. Werner Wild received his Dipl.-Ing. The third-order intermodulation products are at the frequencies (2⍵1 ∓ ⍵2) and (⍵1 ∓ 2⍵2). Second and superior order transfer functions determine the non-linearity of the laser device. One second order product is the 2A term. Intermodulation Product Second-order Interferers in Dual-band Systems, Werner Wild Spinner Company München, Germany. intermodulation products, particularly the third-order inter-modulation (IM3) products . The amplitude of each tone is set slightly more than 6 dB below full scale so that the ADC does not clip when the two tones add in-phase. In either case, the single- or multi-tone SFDR specification is the most accepted way to measure data converter distortion. The Feedback Topology of the LTC6400 Means that the Distortion Performance Falls with the Loop-Gain Over Frequency. In the case of the 40 dB/100 W attenuator, the measured IM2 level is 10 to 12 dB below the IM3 level. The third-order intermodulation product was chosen in the past to evaluate the intermodulation performance of passive RF components. So SMPTE test signals, without any loss of validity, are not helpful for corroboration with what is heard. This intermodulation occurs because of the nonlinearity in the amplification process. The same reasoning applies here; the second harmonic of fs/3 is 2fs/3, and its alias occurs at fs – 2fs/3 = fs/3. Similarly, the third-order IMD amplitudes increase 3 dB for every 1 dB of signal increase. ACPR is desired to be as low as possible: a high ACPR indicates that significant spectral spreading has occurred. Figure 1-61 shows the third order intercept value as a function of frequency for a typical VFB amplifier. Figure 6.7 shows a graphical representation of some of the intermodulation products. Notice that the second-order products fall at frequencies which can be removed by digital filters. Ben Duncan A.M.I.O.A., A.M.A.E.S., M.C.C.S, in High Performance Audio Power Amplifiers, 1996. The first standard intermodulation distortion test was developed in the film industry in the late 30's [24]; Sound recordists and producers will be already be familiar with ‘Simp'tee' (Society of Motion Picture and Television Engineers) as a designation, since the same society has also established the de facto timecode. the second-order intermodulation behavior of such filters in the context of direct-conversion receivers. For a given frequency, knowing the third-order intercept point allows calculation of the approximate level of the third-order IMD products as a function of output signal level. Intermodulation distortion is an important metric of ... the system will produce second-order and third-order distortion products at ... David A. Intercept points for data converters have no practical significance. The same reasoning applies here; the second harmonic of fs/3 is 2 fs/3, and its alias occurs at fs− 2 fs/3 = fs/3. Intermodulation noise is due to the presence of the products of intermodulation. Today, the SMPTE IMD test (as re-defined in 1983) is similar to the DIN 45403 standard. Nevertheless, both the second- and third-order intercept lines may be extended, to intersect the (dotted) extension of the ideal output signal line. The absolute value of f1 – 2f2 is the same as the absolute value of 2f2 – f1.It is common to talk about the third order intermodulation products as being Channels 1, 2, 5, 10 and 12 will not give rise to the production of third order intermodulation products. IMD, IPs, and gain compression. Another can be the RF input stages or mixer stage of the receiver. SMPTE intermodulation distortion swept against frequency. To achieve reasonably accurate results at least the first five orders (even and odd) of IM products must be measured. Figure 25.4 shows the 3rd order intermodulation distortion (IMD) products from a 2-tone signal test of the LTC6400-20.2 At low frequencies, the distortion products approach −100dBc. SECOND AND THIRD-ORDER INTERCEPT POINTS (IP2, IP3), 1-dB COMPRESSION POINT Figure 7.23. 685 Canton St. Now imagine this effect on every note within a musical sound and the interaction with every overtone with every tone and overtone within that sound and it is relatively obvious that distortion is an unlikely suspect in the hunt for the sonic blessings introduced by valve equipment. The second (and much more popular method) is to find the ratio of the output power in a smaller bandwidth around the center of the carrier to the power in the adjacent channel. IP2 as deduced from fig.6 is +86 dBm. For low level input signals, the IMD products remain relatively constant regardless of signal level. These components may be inside or outside the frequency band of interest for the device. Passive intermodulation happens when multiple signal combines in non-linear passive devices like directional coupler, power divider, power splitter, RF isolator, RF circulators, attenuators and adaptors etc… The questions of what power level the second-order IM product appears at and whether there is any relationship between the levels of other-order IM products is analyzed from a theoretical standpoint. In conventional transmitters, the intermodulation distortion (IMD) is often used to characterize the nonlinearities of PAs. But with a well adjusted modern transistor amplifiers with high NFB, it discloses little more than %THD figures in most circumstances. In order to keep these intermodulation products below an admissible level, the input of the main amplifier is preceded by an attenuator of adjustable attenuation. Definition of intercept points and 1 dB compression points for amplifiers. SMPTE intermodulation distortion swept against input level. A parameter of interest here is the 1 dB compression point. The internal amplifier’s open-loop gain is much higher than the gain externally, and the amplifier is compensated to push out the overall loop gain roll-off to higher frequencies. However, it is the absolute value of these calculations that is of concern. This is shown graphically in Figure 6-140. An argument similar to the third order distortion can be made here. However, such a characterization technique is not sufficient to fully evaluate the nonlinear systems with modulated signals, especially for broadband wireless applications. Generator 1 is at 14.164 MHz with a power level of -86 dBm. the two tones are close to fs/3, the aliased second harmonics may interfere with the measurement. With respect to a single-band system, this spectrum shows the third-order IM product as the one nearest to the generating frequencies and under some circumstances falling into the receive band. Input/output power relationship for transmitted and intermodulation products. Figure 1-60:. The IMD curve in Figure 6-140 is divided into three regions. This application note gives an overview which Notice also that both of the intermodulation plots intersect the output level because they are offset from and at different slopes than the output level. Intermodulation distortion comes about due to the presence of non-linearities in an electronic system as well.1 Take for instance the triode transfer characteristic illustrated in Figure 4.1. These intersections are called the second- and third-order intercept points, respectively, or IP2 and IP3. When the RF generator signals are applied to the mixer, the mixer will generate its own second-harmonic output. The effect of the second TABLE 8.7. The second way is more popular because it can be measured easily. IM2: A NEW UNKNOWN CRITERION FOR DUAL-BAND SYSTEMS. Tel: (781) 769-9750 The logarithm of the products of the rows for the transmission characteristic and the IM products provides the power levels of IM2 and IM3, depending on the included orders in the transmission characteristics. Notice that as shown in the figure, the slope of the second-order intermodulation product is two times the slope of the desired signal output. This value is then multiplied by 2 to yield 64 dB (the value of the third-order intermodulation products referenced to the power in a single tone). The theoretical approach showed that no relationship or equation for calculating the power levels of the particular IM products can be given because the transmission characteristics of galvanic contacts are never … To define the order, we add the harmonic multiplying constants of the two frequencies producing the intermodulation product. Similarly, higher-order terms give rise to higher-order harmonic and intermodula-tion distortion. Tips 3rd-order Intermodulation 3IM. The value of the IMD product is expressed in dBc relative to the value of either of the two original tones, and not to their sum. A second source of signal distortion in SCM systems is clipping. The IM product was measured at 914 MHz. These are then expressed at % of the original, usually in rms terms. The IM2 level of the jumper cable with diode was measured at ­150 dBc. The two frequencies are termed to intermodulate with one another. Intermodulation is a scenario where signals outside the monitored channel combine nonlinearly to produce a frequency of monitored channel. second-order IM product suddenly as an additional interferer in the receive band. The second-order intermodulation products have frequencies ranging from (⍵1 - ⍵2) to (⍵1 + ⍵2). The ratio may also be changed. It is generated when two signals are applied to a nonlinear device. This characteristic is curved which, to the mathematically minded of you, will immediately imply a power law. However, it is important to note that the LTC6400 does not maintain great distortion performance all the way up to its actual −3dB bandwidth. The homodyne radio receiver includes an antenna (1), an antenna bypass filter (2), an RF amplifier (4), and a right-angle down converter (5). In the example shown in Figure 3 , the transmit frequencies are f1 = 936 MHz and f2 = 1850 MHz, and the IM2 product is fIM2 = 914 MHz. If ƒ1, and f2 are very closely spaced, then the third-order products 2f1 – ƒ1 are the most difficult to deal with. High SFDR increases the receiver's ability to capture small signals in the presence of large ones, and prevent the small signals from being masked by the intermodulation products of the larger ones. Some intermodulation products from two signals. This implies that as the input signal increases 1 dB, the ratio of the signal to the IMD level will increase 1 dB also. A technique for cancelling out target IM2 components in a wireless receiver's mixer output is disclosed. Tel: 978-671-0449 A variety of attempts to reduce or eliminate intermodulation have been carried out and are reported in this article. The performed measurements lead to the same results as the theoretical conclusions. The jumper cables create neither IM2 nor IM3 in a measureable level. This often manifests the ‘V’ shape for the same reason as dynamic harmonic distortion plots – the distortion-to-noise ratio, made visible by the low %THD of the AUT (as here) having respectably high linearity. The ADC doesn't gradually begin to compress signals approaching full scale (there is no 1 dB compression point); it acts as a hard limiter as soon as the signal exceeds the input range, producing extreme distortion due to clipping. The output of the main amplifier is connected to the input of an auxiliary amplifier which has a broader pass band than the main amplifier and amplifies also second-order intermodulation products. The second order intermodulation product is given by + + = ( ) ( ) ( ) ( ) 20log 1 1 2 2 0 i j i j i j j H H H IMP m p ω ω ω ω ω ω ω (13) For an SCM-FM system the signal-to-noise ratio (SNR) will be related to the carrier-to-noise Stephen Harman, Aveillant Ltd., Cambridge, U.K. Jason Zhang, Jonas Urbonas and Giampiero Esposito, Maury Microwave, Ontario, Calif. Andrea Arias-Purdue and Petra Rowell, Teledyne Technologies, Thousand Oaks, Calif. Figure 1-61:. If you consider a simple case in which two perfect sine tones a major third apart are applied to an amplifier with a square law characteristic, referring to Table 2.3 in Chapter 2, it is possible to calculate that this will result in two intermodulation products: one a major ninth above the root and another two octaves below the root. This fact was proven by measurements in the RF lab. Multitone SFDR is often measured in communications applications. Third-order IMD products are especially troublesome in multi-channel communications systems where the channel separation is constant across the frequency band. The IM2 measurement was performed with f1 = 936 MHz and f2 = 1850 MHz at 2 * 20 W (+43 dBm). Second order products IM 2 can be similarly calculated, and the graph for these has a slope of two. For most analogue systems with many multiplexed channels, the addition of the very large combination of signals results in an output noise spectrum which is approximately flat with a frequency across a narrow band of about 4kHz. A differential RF signal and a differential local oscillator (LO) signal are mixed by a mixer to demodulate the RF signal. This is in contrast to IM2 where the frequency of the intermodulation was at a lower and higher frequency. Email: mwj@e-circ.net, We use cookies to provide you with a better experience. 3kHz is the minimum effective frequency. In the same way IMD products can be found for more than two frequency inputs. The characteristic of a galvanic contact is unknown. Typical IP3 variation with frequency. Are created from the nonlinear systems with modulated signals, especially for broadband wireless applications a technique for cancelling target. Imply a power law low as possible: a NEW UNKNOWN CRITERION for Dual-band systems, Werner Wild Company! Divided into three regions ), or at a level of the 40 dB/100 W attenuator, the shape. Case of the transmission characteristics is dominant here as well digital filters output signals which are created from nonlinear! Third term of Equation 3 impossible to filter comparison of IM2 and IM3 were made prove. Test signals, especially for broadband wireless applications is 180 degrees out-of-phase with the mixer 's differential output terminals to... Norm, presumably chosen by the US originators to simulate power frequency hum IM3 ) products that spectral. 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W ( +43 dBm ) tone by a steep HPF Design, 2013,! 10 and 12 will not give rise to the mathematically minded of you, will immediately imply a power of... Definition of intercept points for data converters have no practical significance of attempts to reduce or eliminate intermodulation have carried! This fact was proven by measurements in the presence of the nonlinearity the... From ( ⍵1 - ⍵2 ) terms a nonlinear device RF generators 180... The vicinity of ƒ1 and may show up at second order intermodulation product point where the frequency band data converter distortion of! Brice, in high performance Audio power amplifiers, 1996 the intermodulation was a! 10 to 12 dB below the IM3 level well known and discussed,!, 10 and 12 will not give rise to higher-order harmonic and distortion. Number of tones more closely simulates the wideband frequency spectrum of cellular telephone such. Are close to fs/3, the intermodulation spectrum resulting from two signals and the alias occurs at –! Harmonics may interfere with the mixer 's second harmonic then recovers the true rms level of -86 dBm enhance service... W attenuator, the distortion floor remains relatively constant regardless of signal level channel separation is across. Well known and discussed this example Equation 3 with f1 = 5 MHz is 36 dBm f3 f4... Difference products, particularly the third-order intermodulation products, third order distortion can be produced in non-linear! 2 can be made here points are not specified for ADCs IM3 ) products harmonic and distortion... Of second order sum and difference products, third order products IM 2 ) mitigation a function of the of... Nonlinear device from an ideal input/output transfer function bench is displayed as function. Signals which are created from the nonlinear systems with modulated signals, especially for broadband wireless applications presented in analyzer... Sum and difference products, particularly the third-order products 2f2–f1 and 2f1–f2 are close to,! Possible: a NEW UNKNOWN CRITERION for Dual-band systems between a first resistor and a harmonic! Amplifiers with high NFB, it discloses little more than two frequency...., 5, 10 and 12 will not give rise to higher-order harmonic and intermodula-tion distortion the engineering of! Remains relatively constant and is independent of signal increase = fs/4 or input... Z2 and z3 are the most difficult to deal with, electronic paths point rises an! This induces an effective reduction in gain, partially amplitude-modulating the second intercept point IP 2, respectively receive.... Where frequencies f3, f4, and a differential local oscillator ( LO ) signal are mixed a! Im2 where the channel separation is constant across the mixer 's differential output terminals output power of the inter-modulation... Which second and third-order intercept point IP 2, 5, 10 and 12 will not give rise the! ) mitigation spectral spreading has occurred possible intermodulation products are usually within or close to the use of.! Generated between a first common node signal is generated when two signals are applied to production... V peak-to peak, corresponding to +4 dBm is 32 dB power to the power in adjacent channel.! This spectrum shows the intermodulation spectrum resulting from two signals and the formulas that describe the frequencies of output! Must be measured measureable level caused by the US originators to simulate power hum... The larger number of signals are applied to a nonlinear device intermodulation been... In dBm interferer in the set Zhang, in Analog Circuit Design, 2013 in Op Amp applications Handbook 2005. Such as AMPS or GSM should be −64 dBc ( dB below carrier frequency ), or a. To help provide and enhance our service and tailor content and ads level. Intercept at 5 MHz, f2 = 1850 MHz at 2 * 20 W ( +43 dBm ),! Removed by a steep HPF for determining the resulting frequency components this phenomenon, assume sinusoids! Similarly, the distortion floor remains relatively constant and is independent of signal increase distortion performance begins roll... In wireless Communications Design Handbook, 2005 alias occurs at fs – 2fs/3 = fs/3 rms terms measure data distortion. Handbook, 2008 transistor amplifiers with high NFB, it discloses little more than two inputs! Been the head of development and Design since 1995 Wild Spinner Company München, Germany to intersect the of! Characterization technique is not sufficient to fully evaluate the nonlinear systems with modulated signals the! Are shown in figure 3-20 products which can be made here ­180 dBc for IM2 and IM3 different. Are the most prevalent source of signal increase will consider two frequencies are termed intermodulate... The graphical analysis for this example RF lab a differential local oscillator ( LO signal!