APPLICATION BULLETIN ® Mailing Address: PO Box 11400 • Tucson, AZ 85734 • Street Address: 6730 S. Tucson Blvd. • Tucson, AZ 85706 Tel: (602) 746-1111 • Twx: 910-952-111 • Telex: 066-6491 • FAX (602) 889-1510 • Immediate Product Info: (800) 548-6132 INTERMODULATION DISTORTION (IMD) By Christian Henn, Burr-Brown International, GmbH gains and output voltage swings, group delay time, settling time, rise time, slew rate, harmonic distortion, and IMD performance. In the remaining sections the application note describes the basics of intermodulation distortions, the relationship between fundamental and 3rd IMD, and shows the test setup and test results for the OPA622 and OPA623. The intermodulation distortion (IMD) performance of wideband, DC-coupled amplifiers is a relatively new area for integrated operational amplifier suppliers. New progresses in IC technology extend the application of op amps where some years ago discrete circuits played the major role. Methods to measure and communicate the extent of this distortion to users have been borrowed from traditional “RF” companies which have historically supplied the radar and radio communications industries, where the importance of it was first highlighted. HARMONIC DISTORTION When Flash-A/D users talk about distortion they are generally concerned with the spurs introduced into the spectrum of interest. In laboratory conditions harmonic distortion is a major area of concern and is usually measured by inserting a single-tone fundamental into the DUT, then looking at the relevant frequency (2xf, 3xf) to determine the magnitude of the harmonic tones. While this testing is useful to many customers, it does not always appease everyone. Manufacturers who claim to have amplifiers with –3dB bandwidth in the tens of MHz region often test distortion at relatively low tones. While the results are undoubtedly favorable, the user cannot use it for a circuit design. Harmonic distortion also neglects the magnitude of spurs from other sources. Installed in the equipment for which it was selected, there is no guarantee that it will be exposed to a pure spectrum as it is for harmonic distortion measurements. In many cases the amplifier is asked to operate in spectrally-rich environments where intermodulation distortion properties of the amp are of keen interest. Examples of applications demanding good intermodulation distortion include: • Radar • Satellite Communications • Digital Radio Receivers • Nuclear Particle Research • CAD Monitor Amplifier In radar applications good IMD performance is essential, because interference from other radars and jammers often pollute the spectrum. For satellite communications systems, the usable bandwidth for each transponder is limited and multiple signals are frequency multiplicated onto one carrier so that signals can interfere with each other when IMD performance is low. For Digital Radio Receivers, a small segment of a broader RF spectrum is digitized and scanned by high-speed data signal processors. For CAD Monitor Amplifiers and for Nuclear Particle Research test equipment, the IMD or as later described the intercept point characterize more precisely than harmonic distortion the large signal capabilities of wideband amplifiers. MATHEMATICAL DERIVATION OF INTERMODULATION DISTORTION The usable dynamic range of an amplifier is limited at very small signal levels by the noise floor and at large signal levels by interferences between signal frequencies. Distortions are caused by non-linearities in the amplitude transfer characteristics. As shown later for producing harmonics, the transfer curve exists of a linear and a quadratic portion and the typical output contains not only the fundamental frequency, but integer multiples of it. IMD results from the mixing of two or more signals of different frequencies and the transfer curve contains in addition a cubic portion. The spurious output occurs at the sum and/or difference of integer multiples of the input frequencies. INTERMODULATION DISTORTION IN THE OPA622 AND OPA623 The IMD test results in this application note center on new ultra high-speed operational amplifiers available from BurrBrown—notably, the OPA622 voltage feedback amplifier and the OPA623 current-feedback amplifier. While the specifications are important and are fully tested, the targeted market segments for these amplifiers clearly called for superior AC performance. Enhanced testing for these parts includes –3dB bandwidth curves for various © 1994 Burr-Brown Corporation AB-194 Printed in U.S.A. April, 1994 1 2 3 4 5 6 Remembering that [sin2x = (1 – cos2x)/2] and [sin(x)sin(y) = (cos(x – y) – cos(x + y))/2] and substituting into Equation 4 provides: K 2 (V IN )2 = K 2 (E12 + E 22 ) / 2 − (5a) (K 2 / 2)(E12 cos 2ω1t + E 22 cos 2ω 2 t) + (5b) 2K 2 E1E 2 (cos(ω1t − ω 2 t) − cos(ω1t + ω 2 t)) (5c) I The first and second terms in Equation 5 represent DC offset and second-order harmonics. The third term is the secondorder IMD. This exercise can be repeated with the fourth term of Equation 3 to study third-order effects. K 3 (V IN )3 = K 3 (E13 sin 3 ω1t + E 32 sin 3 ω 2 t + IA BP 3E12 E 2 sin 2 ω1t(sin ω 2 t) + Bias Point 3E1E 22 sin ω1t(sin 2 ω 2 t) VK Utilizing the identities, sin3x = 1/4(3sin – sin3x) and sin2xsiny = 1/2(siny – 1/2(sin(2x + y) – sin(2x – y))), Equation 6 reduces to: K 3 (V IN )3 = VB V (3K 3 / 4)(E13 sin ω1t + E 32 sin ω 2 t + FIGURE 1. Nonlinear Transfer Characteristics. The non-ideal characteristics of an amplifier can be described by using the Power Series Expansion: V OUT = K 0 + K1 (V IN ) + K 2 (V IN ) + K 3 (V IN ) + L (1) 2 3 A one-tone input signal (VΙΝ = Esinωt) produces harmonic distortion, a two-tone input signal produces harmonic distortion and intermodulation distortion. V IN = E1 sin ω1t + E 2 sin ω 2 t (2) Combining equations 1 and 2 results in the following identity: V OUT = K 0 + K1 (E1 sin ω1t + E 2 sin ω 2 t)2 + K 2 (E1 sin ω1t + E 2 sin ω 2 t)2 + K 3 (E1 sin ω1t + E 2 sin ω 2 t)3 + L (3) The first term (K0) represents the DC offset of the amplifier, the second term is the fundamental signal(s). The subsequent terms represent the distortion of the amplifier. The second IMD can be found by analyzing the third term of Equation 3. 2E12 E 2 sin ω 2 t + 2E 22 E1 sin ω1t) (7a) (K 3 E 32 / 4)(E13 sin 3ω1t + E 32 sin 3ω 2 t) + (7b) (3K 3 E12 E 2 / 2)(sin(2ω1t − ω 2 t) − 12 sin(2ω1t + ω 2 t)) +(7c) (3K E 2 E / 2)(sin(2ω t − ω t) − 1 sin(2ω t + ω t)) (7d) 3 2 1 2 1 2 2 1 Term (a) from Equation 7 represents amplitude offset at the fundamental frequencies. Term (b) signifies the third-order harmonics. Term (c) and (d) represent third-order IMD. The result clearly indicates that IMD and crossmodulation only occur on a curved transfer characteristic with cubic terms like term (c) and (d) in Equation 7. In contrast a transfer characteristic with a linear and quadratic portion generates the mixing products (sum and difference) and the harmonics of the input signals. SOME SIMPLE RELATIONSHIPS Intermodulation distortion occurs at frequencies that are the sum and/or difference of integer multiple of the fundamental frequencies. For example, assume a composite signal has fundamental frequencies ωl and ω2. Distortion products will occur at frequencies aωl±bω2 where a and b = 0, 1, 2, 3, … The following table illustrates this relationship. K 2 (V IN )2 = K 2 (E12 sin 2 ω1t + E 22 sin 2 ω 2 t + 2E1E 2 sin 2 ω1t(sin ω 2 t)) (6) (4) 2nd-Order Frequencies ω1 – ω2 ω1 + ω2 TABLE I. 2 3rd-Order Frequencies 2ω1 + ω2 2ω1 – ω2 2ω2 + ω1 2ω2 – ω1 Amplitude of 3rd IMD Tones = 3K 3 E12 E 2 / 2 Most IMD can be filtered out. However, if the input tones are of similar frequencies, the third-order IMD (2ωl – ω2, 2ω2 – ωl) will be very close to the fundamental frequencies and cannot be easily filtered. Third-order IMD is of most concern in narrow bandwidth applications. Second-order IMD is of greater concern in broad bandwidth applications. Figure 2 below illustrates on a spectrum analyzer the output spectrum of two frequencies (fl, f2) applied to the non-linear transfer characteristic of a mixer with an overdrive level of 10dB. Converting to dB provides: Amplitude of 3rd IMD tone = 20 log(3K 3 / 2) + 20 log(E12 ) + 20 log(E 2 ) Amplitude of 3rd IMD Tone (dB) = constant + 2E1 + E 2 (8) where E1 and E 2 are expressed in dB Equation 8 shows that if the input level (dB) increases, the level of the third-order IM products increases three times faster. Figure 4 shows the graphic presentation of the theoretical increase of the IMD products when the level increases. The desired output of an amplifier and any IMD can be represented by two straight lines of different slopes. The desired output lines have a slope of +1, any IMD has a slope of n, where n is the order of IMD. Consequently, the third-order IMD has a slope of 3. As can be seen in Figure 4 for low level input signals the output tracks the input. At higher input levels Gain Compression occurs at the point where the actual output power drops below the ideal. The –1dB gain compression point is a well accepted performance parameter for RF amplifiers. The intercept point can be found at the intersection of the theoretical line extension of output signal and IMD. The intercept point can be determined from the value of the harmonic suppression (∆IM) which must be determined experimentally. Equation 9 illustrates this relationship. FIGURE 2. Generation of Harmonics and IMD. Figure 3 shows the 2nd and 3rd IMDs for the condition in which the fundamental terms (ωl and ω2) are 20 and 21MHz sinewaves. 70 60 Fundamental Signals 20MHz = ω1; 21MHz = ω2 50 30dBm IP2 30 20 3rd IMD Harmonic Suppression 2nd IMD 1MHz = ω2 – ω1 5dBm IP3 2 10 IM 3rd IMDs 22MHz = 2ω2 – ω1 19MHz = 2ω1 – ω2 0 2nd IMD 41MHz = ω2 + ω1 1dB Compression –10 dBm Amplitude 40 –20 IM 3 –30 –70 FIGURE 3. Relationship Between Fundamentals and IMDs. –80 al gn ≥70dBc IM3 –60 Si –50 ≥60dBc IM2 –40 Frequency –90 INTERCEPT POINT –100 The location of the IMDs relative to the fundamental tones has now been defined. The relationship of amplitudes of the IMD tones depends on the order of the IMD. The coefficients of the third-order IMD term in Equation 7 can be used as a starting point in the analysis. –120 –60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 –70 –18dBm 5dBm FIGURE 4. Relationship Between Fundamental and 3rd IMD. 3 Intercept Point = (Hamonic Suppression) / (N – 1) + (Power of One Fundamental at Output of Amplifier) (9) By rearranging the Equation 9 the magnitude of third-order products can be easily calculated for any output power (dBm) when the intercept point is known. Third IMD = 2 (OIP3 – PO) Third IMD = third-order intermodulation ration below each output tone (dB) (10) One can also make a judgment about the dynamic range of an amplifier with the knowledge about the IP value and the sensitivity (amplifier noise power). A limit for the best distortion-free dynamic range is available when the IM products equal the sensitivity. For a sensitivity of P N = –140dBm at measurement BW = 10Hz for an input mixer and OIP3 = +5dBm, the best input level can be calculated with Equation 11. (N − 1) • OIP + P N N 2 • 5 + (−140) = = − 43dBm 3 P IN = 1. Set the amplitude of the two inputs equal with the power meter. 2. Check for gain compression by reducing the signal power of both fundamentals by 1dB, then checking to make sure that the 3rd IMD tone is reduced by 3dB. If past the compression point (see Figure 2), then the amplitude of the input to the amplifier should be reduced (repeat Step 1). 3. Measure the harmonic suppression of the 3rd IMD tone on the spectrum analyzer. This is the difference between the magnitude of the fundamental and the 3rd IMD (See Figure 1). 4. Measure the amplitude of a fundamental signal at the output of the DUT by disconnecting one of the signal generators. 5. Calculate the intercept point using Equation 9. (11) The distortion free dynamic range results with Equation 12 to 90dB for narrow spaced input signals. (N1 ) • (OIP − P N ) N 2 •135 = = 90dB 3 DETERMINING HARMONIC SUPPRESSION The test system used to measure harmonic suppression is diagrammed below. ∆IM = THIRD-ORDER RESULTS FOR THE OPA622 AND OPA623 The 3rd IMD intercept points are measured for the OPA622/ 623 using fundamental input frequencies from 5MHz to 250MHz with 1MHz spacing between tones. All parts were set up in a gain of +2 and were driven into a 100Ω load. (12) Signal Generator A 6dB Attenuator Spectrum Analyzer Filter Power Divider 6dB Attenuator 3dB Attenuator Power Divider DUT Filter Power Meter Signal Generator B (Attenuators are used to limit the IMD of the signal generator setup; for every 1dB attenuation of the fundamental signs, the nth order IMD is reduced by n dB.) FIGURE 5. Test Setup to Measure Harmonic Suppression. 4 Power Meter Non Inverting R3 100Ω RI 180Ω In+ OPA623 R2 100Ω RO 51Ω 7 3 2 6 Out 4 R´O R1 300Ω +5V R2 300Ω 7 C1 470pF C3 10nF + C5 2.2µF C2 470pF C4 10nF + C6 2.2µF Gnd –5V 4 FIGURE 6. Circuit Schematic DEM-OPA623-1GC Used for IMD Performance Tests. OPA623 IM3 AND IP3 vs FREQUENCY (0dBm Input) OPA623 IM3 AND IP3 vs FREQUENCY (–10dBm Input) 40 40 20 20 IP3 0 IP3 P0 –20 dB dB 0 P0 –20 IM3 IM3 –40 –40 –60 –60 –80 –80 0 50 100 150 200 250 0 300 50 100 150 200 250 Frequency (MHz) Frequency (MHz) FIGURE 8. IM3 and IP3 vs Frequency (0dBm Input). FIGURE 7. IM3 and IP3 vs Frequency (–10dBm Input). 5 300 OPA623 IM3 AND IP3 vs FREQUENCY (10dBm Input) 40 20 20 IP3 P0 30 IP3 25 0 20 dB IM3 –20 35 –20 P0 15 IM3 –40 –40 10 IQ –60 –60 5 0 –80 –80 –40 0 50 100 150 200 250 Quiescient Current, (IQmA) 40 0 dB OPA623 IM3 AND IP3 vs INPUT LEVEL (100MHz) –30 –20 300 –10 0 10 20 Input Level (dBm) Frequency (MHz) FIGURE 9. IM3 and IP3 vs Frequency (10dBm Input). FIGURE 11. IM3 and IP3 vs Input Level (100MHz). OPA623 IM3 AND IP3 vs INPUT LEVEL (50MHz) OPA623 IM3 AND IP3 vs INPUT LEVEL (200MHz) P0 80 25 0 dB 20 –20 Iq 15 IM3 –40 10 –60 5 –40 –30 –20 –10 0 10 50 60 IQ 40 40 20 30 IP3 0 P0 –20 20 IMD –40 10 –60 0 –80 60 0 –80 20 –40 Input Level (dBm) –30 –20 –10 0 10 20 Input Level (dBm) FIGURE 10. IM3 and IP3 vs Input Level (50MHz). FIGURE 12. IM3 and IP3 vs Input Level (200MHz). 6 Quiescient Current, (IQmA) 20 100 30 dB IP3 35 Quiescent Current, IQ, (mA) 40 –VCC +VCC +VCC OUT 1pF COTA 5 RQC 390Ω –VCC 2 12 10 11 Biasing RL 50Ω 9 Out Z O = 50 OB RIN 50Ω OPA622 ZO = 50 In POS RSOURCE = 50Ω RL2 100Ω RLR 150Ω 4 OTA R1 330Ω RL1 100Ω 3 FB 8 13 6 ROG 150Ω –VCC OUT R2 330Ω 12 R9 10Ω 11 C1 470pF C2 10nF C6 470pF C5 10nF + +5V C3 2.2µF Gnd R8 10Ω + C4 2.2µF –5V 6 5 FIGURE 13. Circuit Schematic DEM-OPA622-1GC Used for IMD Performance Tests. 7 OPA622 IM3 AND IP3 vs FREQUENCY (–10dBm Input) 60 35 40 30 20 10 20 IP3 dB dB 0 –10 –20 P0 –30 25 IP3 20 0 IQ P0 –20 IM3 15 IM3 –40 –50 –40 10 –60 5 Quiescent Current, IQ (mA) OPA622 IM3 AND IP3 vs INPUT LEVEL (50MHz) 30 –60 0 –80 –70 100 150 200 250 –40 300 –30 –20 FIGURE 14. IM3 and IP3 vs Frequency (–10dBm Input). 10 20 FIGURE 17. IM3 and IP3 vs Input Level (50MHz). OPA622 IM3 AND IP3 vs FREQUENCY (0dBm Input) OPA622 IM3 AND IP3 vs INPUT LEVEL (100MHz) 30 50 30 20 20 10 10 IP3 0 P0 –10 –10 –20 dB 0 dB 0 Input Level (MHz) Frequency (MHz) IM3 IP3 30 P0 25 IQ –30 –40 –40 –50 –50 –60 –60 20 IM3 –20 –30 15 10 5 0 –70 –70 0 50 100 150 200 250 –40 300 –30 –20 –10 0 10 20 Input Level (dBm) Frequency (MHz) FIGURE 15. IM3 and IP3 vs Frequency (0dBm Input). FIGURE 18. IM3 and IP3 vs Input Level (100MHz). OPA622 IM3 AND IP3 vs FREQUENCY (10dBm Input) OPA622 IM3 AND IP3 vs INPUT LEVEL (200MHz) 30 30 20 50 20 10 IP3 0 P0 25 0 –10 IM3 –20 30 10 dB dB –10 –30 IP3 –10 15 –30 –40 –50 –50 –60 –60 20 IM3 –20 –40 IQ P0 10 5 0 –70 –70 0 50 100 150 200 Quiescent Current, IQ (mA) 50 250 –40 300 –30 –20 –10 0 10 20 Input Level (dBm) Frequency (MHz) FIGURE 16. IM3 and IP3 vs Input Level (50MHz). FIGURE 19. IM3 and IP3 vs Input Level (200MHz). 8 Quiescent Current IQ (mA) 0