The Use of Intermodulation Tables for Mixer Simulations

Technical Feature

The Use of Intermodulation Tables for Mixer Simulations

The use of intermodulation table (IMT) files can lead to accurate prediction of the output frequency content of an up-converting or down-converting mixer in system simulations. For best results, custom IMT files should be constructed from mixer output spectrum measurements made at or close to the desired input signal and local oscillator frequency and power conditions.

Daniel Faria, Lawrence Dunleavy and Terje Svensen
University of South Florida
Tampa, FL

Mixers are nonlinear devices used, among other things, to convert signals from one frequency to another. They are characterized by how much conversion gain or loss they introduce in this translation, and also by how much distortion and noise they introduce. In addition to the desired output frequency signal, mixers produce many other frequencies, due to the nonlinear mixing, or intermodulation of the input signal (RF or IF) frequency and the local oscillator (LO) signal frequency. This article covers the use of intermodulation tables to better model the broadband frequency output of mixers used as down- or up-converters in communication systems. A system level mixer model, available in Agilent Advanced Design System 1.5 (ADS™) computer-aided-engineering (CAE) software, is used to explore and overcome some of the potential difficulties involved with obtaining accurate predictions of mixer intermodulation product signal levels using such system simulation models. Specifically, the MixerIMT model was used in ADS to predict observations made on a commercial mixer (Mini-Circuits® ZEM-4300MH) before and after customized characterization, using IMT files. The mixer model available in ADS only requires the conversion loss as an input parameter to model the device under investigation, thus predicting only the upper and lower sideband frequency content (see Figure 1 ). On the other hand, the IMT file represents a custom table of mixer intermodulation product levels resulting from given local oscillator (LO) and input signal frequencies and powers. The predicted output signal results in a direct mapping of each input signal with each LO signal. This study is a continuation from previous investigations of a 915 MHz receiver used in the University of South Florida's Wireless Circuits and Systems Design course^1,2 , as well as a recent paper that describes a complete communications systems test bed constructed to identify and resolve issues affecting system simulation accuracy for transmitter and receiver hardware.³

Fig. 1 Simplified ADS model.

Mixer Product Simulation Using IMT Tables

The simulation results obtained in a related preceding work¹ use mixer models that produce the desired up-converted RF or down-converted IF at the mixer output, but do not predict the other harmonic and intermodulation (IM) products. Intermodulation products are unwanted signals generated by the mixer and exiting from any port. There are two types of intermodulation products - single-tone and multi-tone.

Single-tone intermodulation products consist of a single input (RF or IF) signal mixing with the LO and generating the following frequencies:

f_OUT = |Mf_LO ± Nf_RF | (1)

where

f_OUT = output signal for the mixer
f_RF = input signal for the mixer
f_LO = LO frequencies for the mixer
M,N = integers (0,1,2,…)

Multi-tone intermodulation products consist of two or more input signals mixing with the LO and generating the following frequencies

f_OUT = |±M₁ f_RF1 ±M₂ f_RF2 ±M₃ f_RF3 … ±Nf_LO | (2)

where M₁ , M₂ , M₃ and N are integers (0,1,2...). Multi-tone intermodulation is outside the scope of this article.

The ADS system mixer model MixerIMT can predict multiple IM products at a mixer's output. It requires the use of an IMT file. The IMT file provides information related to the mixer's IM generation properties as a function of single-tone signal and LO mixing order with their respective relative power level (dBc) to the desired output signal (IF or RF). The frequencies at which to expect IM products are given by Equation 1. An example IMT table is shown in Figure 2 .

Fig. 2 Intermodulation table for a double-balanced mixer.⁴

The IMT file ideally applies for a specific reference power level for both P_SIG (RF or IF) and P_LO signals. If the input signals power levels vary from the values specified in the IMT table, interpolation is performed. The recommended ranges for which interpolation is applicable are P_SIG ≤ P_SIGREF (dBc) + 3 and P_LO (dBc) - 10 ≤ P_LO ≤ P_LO (dBc) + 3.⁴ A related consequence is that the Mixer IMT model does not appear useful for predicting 1 dB conversion gain compression in mixer simulations. Further study is needed to explore accuracy of such extrapolations of mixer product amplitude simulations.

In the example IMT file shown

• Each position in the IMT table is occupied by the amplitude in dBc relative to the desired output frequency (IF or RF) expected at the mixer output.
• The vertical column number N (0,1,2 to 15) shows the harmonic number of either input signal used.
• The horizontal row number M (0,1,2 to 15) shows the harmonic number of the LO signal used.
• Notice that a 0 appears in the table at the position of the fundamental signal (N = 1, M = 1). The frequency corresponding to this position could be either the sum or difference frequency (i.e. |f_LO ≈ f_SIG |), or the IF frequency for a down-converter.
• All other entries are specified in dBc relative to the power at the mixer output at the fundamental sum or difference frequency. The power level is assumed lower at this frequency unless the numeric entry is negative, which represents a power level higher than the fundamental sum or difference frequency.
• In row M = 1, column N = 3, the data is 11. This shows for an input signal at -10 dBm and an LO signal of +7 dBm there will be an IM product at |3f_signal ± 1f_LO |, with a power level of 11 dB below the signal at the desired sum or difference frequency.
• Notice that there are missing entries in the IMT. These missing entries have assigned values of 99 dB below the fundamental reference.

The simulator assigns identical values for sum and difference frequencies at the mixer output. This is consistent with the conventional assumption of a symmetrical mixer as far as output spectrum amplitudes are concerned. To the extent that a real mixer is non-symmetric, this assumption generates unavoidable errors in the simulations as will be shown in the examples below.

The frequencies corresponding to the IMT file content are sometimes referred as a "spur table" (see Appendices A and B ). These spur tables show the expected frequencies at the mixer output. Each cell shows the frequency corresponding to the intermodulation of the LO harmonic and RF harmonic represented by the occupied row and column number.

For example, the fundamental sum and difference frequencies for the given down-converter example are 70 MHz and 1900 MHz, respectively, which can be seen by looking at the cell corresponding to M = 1; N = 1 in the tables. Because of the symmetrical mixer requirement discussed, the IMT file does not allow for separate entries for these two frequencies. The same is true for any pair of frequencies occupying the same cell position.

Fig. 3 Harmonic balance test bench schematic (up-converter configuration).

Mixer IM Product Characterization Measurements

Unfortunately, "one size does not fit all" when it comes to IMT files. Hence, the use of the IMT file example in an attempt to predict the output spectrum of the ZEM4300 mixer will be useful only in showing the frequencies at which IM products can be expected, but with very inaccurate amplitudes. Therefore, for the MixerIMT model to be useful, files must be available that properly represent the specific mixer model to be used under the desired operating signal and LO frequencies and powers. Here, the construction of custom IMT files for a given mixer is briefly described.

Up-converter Mixer Characterization

The measurements involved two signal sources, test accessories and a spectrum analyzer (SA). The configuration is reflected in the simulation schematic, as shown in Figure 3 , with the load at the right side of the network replaced with the SA, a bandpass filter and three attenuators pads around the mixer (10 dB - RF, 3 dB - LO, 6 dB - IF). The IF signal was generated by a HPESG D4000A signal generator (P_IF = 3.2 dBm) and the LO signal was generated by a HP8753D VNA (P_LO = 10.80 dBm). This set-up presented an input power of -10.07 dBm at the RF port of the mixer, and an input power of 7.01 dBm at the LO port. The loss of both the 6 dB pad and the output cable, as measured separately with the HP8753D network analyzer, was taken into account at each IM product frequency when calculating the output power from the mixer IF port measured remotely with a HP8595E spectrum analyzer. The settings of the SA are shown in Table 1 .

The measured results for IM products observed for this up-converting mixer are listed in Table 2 , along with the simulation results.

The conversion loss was determined from a subset of these measurements to be 6.04 dB. It was found important to specify the conversion loss in the mixer model as determined from the same measurement data set used to construct the IMT file in order to obtain the best simulation/measurement consistency. For various reasons, the conversion loss measurements, made in different ways, typically vary by several tenths of a decibel difference between results while obtained for the same mixer.⁵

Down-converter Mixer Characterization

The measurement procedure was essentially the same as that described above, this time using the configuration of Figure 4 . A 915 MHz bandpass filter was used along with the same three attenuators pads around the mixer (10 dB - RF, 3 dB - LO, 6 dB - IF). The RF signal was generated by the HPESG D4000A signal generator (P_RF = 4.8 dBm) and the LO signal was generated by the HP8753D VNA (P_LO = 10.80 dBm). This set-up presented an input power of -10.02 dBm at the RF port of the mixer, and an input power of 7.01 dBm at the LO port. The loss of both the 6 dB pad and the output cable is taken into account when calculating the output power from the IF port at each IM product frequency, based on the remotely measured product levels observed on the HP8595E SA. The conversion loss was measured to be 6.05 dB. The settings of the SA are the same as for the up-converter case. The measured results are shown in Table 3 , along with the simulation results obtained.

Fig. 4 Harmonic balance test bench schematic (down-converter configuration).

Simulation of Mixer IM Products Using Custom IMT Files

Up-converter Simulation
The measured results obtained for the up-converting mixer configuration were used to generate the custom IMT file for the ZEM-4300MH mixer shown in Figure 5 . It is important to mention that since the IMT file only allows one value for either the sum or difference frequency, the highest power level between the two was chosen. The file, once generated, needs to reside in the data folder, then pointed to from the mixer model itself prior to simulation. The simulated results are shown in Figure 6 . The comparison between measurement and simulated results is facilitated by the tabulation given in Table 2 . Note that for most frequencies exact agreement is possible. Those frequencies where discrepancies are indicated correspond to sum (or difference) frequencies whose corresponding difference (or sum) frequency pair had higher observed amplitude. Note that these pairs are easily identified in the simulated results column of the table by looking for pairs of frequencies with the exact same predicted power level.

Fig. 5 Custom measurement based IMT for ZEM 4300 mixer in up-converter configuration.

Fig. 6 Measured and simulated results using generic and custom IMT files for an up-converter mixer.

Down-converter Simulation
A custom IMT file for the ZEM-4300MH mixer in the down-converter configuration was constructed from measured results. This file is shown in Figure 7 . A simulation was performed using the schematic previously shown, and instructing the mixer model to reference this file. The simulated results are shown graphically in Figure 8 . The comparison between measurement and simulated results are more clearly summarized in Table 5. Again the remaining discrepancies are due to sum and difference frequency pairs that had different observed amplitudes. Note that the discrepancy at 1900 MHz (whose corresponding difference frequency pair is 70 MHz) is significant as the observed signal level is fairly high (-23 dBm or -7.8 dBc) and the error is on the order of 30 percent.

Conclusion

The use of intermodulation table (IMT) files can lead to accurate prediction of the output frequency content of an up-converting or down-converting mixer. For best results, custom IMT files should be constructed from accurate mixer output spectrum measurements made at or close to the desired input signal and local oscillator frequency and power conditions. Still, discrepancies can occur due to the inability of current IMT file mixer models to assign different amplitudes to sum and difference frequency components. The ability of a system mixer model, such as the ADS MixerIMT, to extrapolate beyond the specific measurement conditions used to characterize the IMT file is one aspect of on-going work in this area by this research group. Also, IMT file mixer models may not be useful for simulating all parameters of interest such as system gain compression, in which case a different system mixer model can be used to produce the desired simulation. In short, CAE system mixer models are useful, but care must be taken to use them properly and understand their limitations and range of validity.

Fig. 7 Customer measurement based IMT for ZEM 4300 mixer in down-converter configuration.

Fig. 8 Measured and simulated results using generic and custom IMT files for a down-converter mixer.

Acknowledgments

This work was sponsored in part by separate grants from Intersil Corp. and Anritsu Co. The authors thank Mini-Circuits for contributing components and test accessories, and Agilent Technologies for providing the Advanced Design System software and for helpful consultations. The instruments utilized in this work were acquired from combined grants from Agilent Technologies, the National Science Foundation and the University of South Florida.

References
1. L. Dunleavy, P. Flikkema, T. Weller, A. Kuppusamy and E. Benabe, "Characterization and Simulation of a 915 MHz Wireless Receiver," Applied Microwave & Wireless , July 1999, pp. 84-100.
2. T. Weller, P. Flikkema, L. Dunleavy, H. Gordon and R. Henning, "Educating Tomorrow's RF/Microwave Engineer: A New Undergraduate Laboratory Uniting Circuit and System Concepts," IEEE MTT-S International Microwave Symposium Digest , Baltimore, MD, June 1998, pp. 563-566.
3. L. Dunleavy, D.B. Lassesen, T. Svensen and D. Faria, "CAE Challenges for Wireless Transceivers," Submitted to Journal on RF and Microwave CAD , K.C. Gupta Ed., John Wiley & Sons, New York, NY.
4. Advanced Design System Version 1.5 Documentation, Agilent Technologies Inc., Palo Alto, CA.
5. L. Dunleavy, T. Weller, E. Grimes and J. Culver, "Use Network and Spectrum Analysis for Mixer Measurements," Microwaves & RF , Part I, May 1997, pp. 143-152; Part II, June 1997, pp. 71-80.
6. B.C. Henderson, "Mixers Part I: Characteristics and Performance," WJ Tech Notes , Vol. 8, No. 2, March/April 1981, Watkins-Johnson Co., 1981, http://www.wj.com.

Some of these references are available for download at http://ee.eng.usf.edu/WAMI/ library/papers.html.

Daniel Faria received his BSEE degree from the University of South Florida in May 2000. He is currently studying for his master's degree in electrical engineering in wireless communication subsystems. He worked as an intern for Intersil Corp. during the summers of 2000 and 2001, and is currently a research assistant for Dr. Lawrence Dunleavy.

Lawrence Dunleavy received his BSEE degree from Michigan Technological University in 1982, and his MSEE and PhD degrees from the University of Michigan in 1984 and 1988, respectively. He has worked for both E-Systems and Hughes Aircraft Co., and was a Howard Hughes doctoral fellow. In 1990, he joined the electrical engineering department at the University of South Florida, where he is now an associate professor. His current research interests are in the area of accurate microwave and millimeter-wave measurements, measurement-based active and passive component modeling, MMIC design, and wireless systems characterization and CAD. Dunleavy is a senior member of IEEE, and is very active in the IEEE MTT Society and the Automatic RF Techniques Group (ARFTG). He has authored or co-authored more than 80 technical articles.

Terje Svensen graduated with a BSEE degree from the University of South Florida in May 2000. He is currently pursuing a master's degree in electrical engineering with an emphasis on wireless communication systems and a minor in engineering management. He is an active member of IEEE, SBTA, Eta Kappa Nu and Phi Kappa Phi.