A method for intermodulation improvement

A new method for reducing the intermodulation interference of frequency division multiplexed signals is described. Examples using 24 carriers illustrate the principle. The carriers are divided into groups which are amplified separately. Each group consists of appropriate carrier allocations which yield few intermodulation products coincident with the carriers of that group.     

Fiber Optic Intermodulation Distortion

In analog frequency-division multiplexed fiber optic systems, laser nonlinearities transfer energy between the different carriers, resulting in intermodulation distortion and interference. A third-order polynomial without memory is used to model the nonlinearity. The FM frequency-division multiplexed (FM/FDM) signal consists of a set of FM carriers at frequencies.N_{omega 0}, whereN = L, L + 1, L +2, ... , M. The video distortion introduced by the nonlinearity is determined for various types of second- and third-order intermodulation terms. The intermodulation distortion frequency spectrum is determined for FM signals with assumed Gaussian spectra.     

A Fast Algorithm for Sorting and Counting Third-Order Intermodulation Products

This paper presents a fast algorithm that performs a selective counting of the third-order intermodulation products generated when several carriers of various types are transmitted through a common nonlinear device. In deriving the algorithm, the carrier configuration and the frequency distribution of intermodulation products are both described by polynomials which are related to each other. The frequency distributions of third-order intermodulation products of the various kinds are then obtained with the aid of an FFT algorithm and a numerical method for solving a set of linear equations. When compared to a direct counting procedure, the proposed algorithm has presented a drastic reduction on the required Computational effort. This advantage is particularly important when the number of carriers sharing the nonlinearity is large. In an example with 1366 carriers of three different types sharing the nonlinearity, the CPU time was reduced from 7 h 46 min. down to 52 s.     

Control of IM3 distortion in helix TWTs by harmonic injection-anEulerian hydrodynamical study

Helix traveling-wave tube equations were formulated under Eulerian-fluid approximations, extending the nonlinearity up to the third-order. Closed-form solutions for the nonlinear equations were obtained by the method of Laplace transforms for the circuit electric field, which was then interpreted, for RF output power. The RF fundamental output power estimated by the present Eulerian theory was validated against that done by the Lagrangian analysis and the regime of agreement of the two theories was ascertained. Then within this range of validity were found the third-order intermodulation products at the frequencies 2f₁-f₂ and 2f₂-f₁, for the case of two-balanced signal inputs, one at the frequency f₁ and the other at f₂. The multisignal output power spectrum predicted by the two theories also showed a fairly close agreement. The role of the two additional second harmonic signals injected at the input, one at the frequency 2f₁ and the other at 2f₂, in controlling the third-order intermodulation products (distortion) was next studied by the simple Eulerian hydrodynamic analysis. By harmonic injection at the signal frequency 2f₁ (2f₂) alone, the intermodulation product at 2f₁-f₂ (2f₂-f₁) could be reduced but not at 2f₂-f₁ (2f₁-f₂). For the reduction of both the intermodulation products, the harmonic inputs at the frequencies 2f₁ and 2f₂, respectively, need to be simultaneously injected. In particular, the optimum values of the RF input power levels and phases of the second harmonic inputs relative to the corresponding fundamental inputs, which would result in a minimum in the third-order intermodulation distortion in the device, were found     

Experimental study and empirical evaluation of carrier compression and third order intermodulation products of unequal carriers in a communication satellite transponder

Carrier compression and third order intermodulation products of two and three unequal carriers have been studied experimentally using a 36 MHz wide C-band transponder of INSAT-1B satellite. From the experimental data, empirical relations for carrier compression for two unequal carriers have been derived, which agree with the measured data within ±0.5 dB. The empirical relations for carrier compression derived for two unequal carriers have been extended to three unequal carriers and good correlations with measured data have been obtained. Empirical relations for third order intermodulation products of two and three (f₁+f₂-f₃ type) unequal carriers have also been derived.     

Intermodulation in multiple fixed beam distributed amplifier phased array antenna systems

In the recent development of phased array/distributed amplifier systems for application to mobile satellite or thin route communication systems, the intermodulation (IM) generated by the element amplifiers is spatially dispersed in such a way that some of the IM radiated energy falls outside the intended beam area. In addition, some of the IM falling inside the beam area has frequencies different from the carriers intended for that area. It is known that for fixed beam systems with frequency reuse, an average IM noise reduction of several dB can be realized. In the specific case under investigation, of four beams, nine frequencies and 12 carriers (1-33 frequency reuse factor), an IM improvement of about 2-0 dB is realized. The improvement in carrier-to-IM-noise ratio can be applied to increase system capacity, or for given capacity it can be used to reduce RF power amplifier back-off, which can be translated into a reduction of spacecraft prime power requirement. The considerable advantage gained from the multiple beam distributed amplifier approach makes it worthwhile to explore the workings of such a system and other benefits it may offer. One of the benefits is a common RF power pool for all carriers and beams, and the other is the spatial dispersion of intermodulation (IM). A satellite multiple beam pattern and the spatial dispersion of IM products are shown in Figure 1.     

An indirect procedure for counting intermodulation products amongnarrow-band carriers [satellite links]

The problem of computing intermodulation generated by a large number of narrowband carriers is examined. In general, narrowband carriers sharing a nonlinear repeater may have different power levels and different spectral shapes. Therefore, different kinds of intermodulation products will appear. It is well known that replacing identical contiguous carriers by a noise band may lead to a poor approximation when baseband computations involving carriers with peaked spectral shapes (e.g. SCPC/FM) are considered. However, it is shown here that this noise band representation offers an effective way to calculate the total RF intermodulation power corresponding to each kind of product and can therefore be viewed as a means of indirectly counting intermodulation products     

Harmonic and Intermodulation Performance of the Semiconductor Bolometer

A mathematical model for the temperature dependence of the bolometer semiconductor resistance is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the harmonic and intermodulation performance of the acquired interferogram voltage with large-amplitude multisinusoidal variations in the incident radiation. The special case of two-tone equal-amplitude incident radiation is considered in detail. The results show that the intermodulation components are always higher than the harmonic components of the same order. The results also show that the second-order intermodulation is always dominant and is higher than the second-harmonic component by about 6 dB. Moreover, the results show that for relatively small incident amplitudes of the incident radiation the ratio between the second- and third-harmonic components is almost equal to the ratio between the second-harmonic component and the fundamental. The results also show that the ratio between the amplitudes of the second- and third-order intermodulation components is almost equal to the ratio between the amplitudes of the second-order intermodulation component and the fundamental.     

Intermodulation Interference-Minimum Frequency Assignment for Satellite SCPC Systems

This paper addresses frequency assignment for singlelevel and multilevel SCPC systems. In order to obtain the optimum channel allocation, where the influence of intermodulation noise on carriers is minimized, a practical and effective method is proposed. The quasi-optimum, solutions obtained with the proposed method are presented for single-level SCPC systems, showing their advantage in intermodulation noise reduction. Concerning frequency assignment for multilevel SCPC systems, two strategies to realize the-quasi-optimum channel allocation are compared with regard to the improvement in carrier-to-intermodulation noise power ratio. The performance of the obtained channel allocation indicates the effectiveness of the proposed optimization method.     

Intermodulation improvement for multichannel television distribution by appropriate channel allocations and the use of 1/3rd line offsets

In addition to the use of frequency plans to reduce intermodulation interference between carriers, in the case of television distribution further improvement can be obtained by using? line-rate frequency offsets. Some results are tabulated.     

On the capacity optimization in multicarrier channel operation

The transmission plan for a communications channel exploited in multicarrier mode involves the operational parameters and the prediction of the channel impairments with special consideration for the intermodulation noise generated by beating among carriers. The intermodulation noise is a driving factor in the design phase of a transmission plan as it seriously affects the C/N + 1 ratio of the carriers in the channel, being often the dominant factor. The transmission plan of a channel operated in multicarrier mode can be represented as an injective application between two sets: the carriers and the frequency slots of the channel. Classical combinatory laws allow for the prediction of the number of configurations that can be established with sets of unidimensional elements. However, if one of the sets has elements with non‐unidimensional attributes, the classical combinatory laws fail to predict the number of possible configurations. This is the case in multicarrier transmission plans, where the carriers have an associated bandwidth (attribute of the carrier) that typically occupy several frequency slots. In this paper, an expression for the prediction of the number of possible configurations in a transmission plan is derived. This expression permits to select the most appropriate method to achieve transmission plan optimization, as a function of the associated computational resources. The higher the number of configurations, the higher the options for the optimization of the transmission plan. Subsequently, the C/N + I ratio of the carriers can be increased and therefore the quality of the service and the use of the channels resources are improved. Investigation of the space of configurations show that the maximum number of possible configurations is achieved in the range of 70–90% of channel occupation, which converges with the typical operational use of satellite transponders in multicarrier operation. This discussion is applicable not only to the frequency domain but also to any other system where sets of elements with non‐unidimensional attributes have to be considered (time domain, space domain, etc.). Copyright © 2003 John Wiley & Sons, Ltd.     

Intermodulation improvement by appropriate channel allocations

Intermodulation interferences of multicarrier signals can be reduced at the expense of increased bandwidth if the signal carriers are arranged in appropriate frequency plans. The paper investigates in detail the trade-off between bandwidth and intermodulation interference. The results are presented in tabular form.     

Second-order intermodulation mechanisms in CMOS downconverters

An in-depth analysis of the mechanisms responsible for second-order intermodulation distortion in CMOS active downconverters is proposed in this paper. The achievable second-order input intercept point (IIP2) has a fundamental limit due to nonlinearity and mismatches in the switching stage and improves with technology scaling. Second-order intermodulation products generated by the input transconductor or due to self-mixing usually contribute to determine the IIP2 even though they can, at least in principle, be eliminated. The parasitic capacitance loading the switching-stage common source plays a key role in the intermodulation mechanisms. Moreover, the paper shows that, besides direct conversion and low intermediate frequency (IF), even superheterodyne receivers can suffer from second-order intermodulation if the IF is not carefully chosen. The test vehicle to validate the proposed analysis is a highly linear 0.18-/spl mu/m direct-conversion CMOS mixer, embedded in a fully integrated receiver, realized for Universal Mobile Telecommunications System applications.     

Broadband analogue predistortion using a distortion generator based on two-stage RF mixer topology

An analogue predistorter using a distortion generator based on a two-stage radio frequency mixer topology is presented. The proposed distortion generator achieves fundamental signal cancellation without using a signal cancellation loop or a resonant circuit, thus it generates an error signal that predominantly consists of unwanted intermodulation distortion (IMD). Measurements are performed using multi-tones, WLAN- and Terrestrial Trunked Radio (TETRA)-modulated signals. Distortion generator provides high levels of IMD and achieves more than 40 dB fundamental signal cancellation across a bandwidth of 120 MHz. A proof-of-concept predistorter was constructed to validate the usefulness of the proposed distortion generator, which achieves up to 15 dB suppression of IMD and adjacent channel power ratio at the output of a power amplifier. Distortion generator and predistorter gave similar results at multiple frequencies between 920 MHz and 2 GHz, with different test signals having bandwidths ranging from 25 kHz to 120 MHz.     

A note on the intermodulation performance of SCPC satellite links using a dominant carrier

The intermodulation performance of satellite links using a dominant carrier side-by-side with many small SCPC/FDMA carriers is considered. Closed-form expressions which are easy to evaluate are obtained for the amplitudes of the output carriers and intermodulation products. Using these expressions the carrier-to-intermodulation performance of the satellite link can be evaluated using personal computers or pocket calculators.     

Intermodulation properties of double- and triple-circuit parametric amplifiers with nonlinear barrier capacitance

There have been performed an experimental investigation of intermodulation effects in narrowband regenerative double- and triple-circuit parametric amplifiers (RDPA and RTPA) with nonlinear barrier capacitance. It has been obtained that their single-signal and double-signal intermodulation characteristics are of the conventional form, and their phase shifts in the vicinity of the resonance frequency are close to 90°, that is not enough for the compensation of nonlinear distortions in the case of amplifiers cascading. It has been demonstrated that the introduction of the additional oscillatory circuit at the double signal frequency into RDPA does allow effective compensation of the intermodulation interferences of odd order in the single-stage parametric amplifier.     

Prediction of Mixer Intermodulation Levels as Function of Local Oscillator Power

During intermodulation testing with diode mixers an increase of intermodulation interference was observed due to an increase of LO power incident to the mixer. This phenomenon conflicted with the theory that increase of LO power reduces intermodulation output of the diode mixer. In these tests the intermodulation decreased as expected when the LO power was further increased. Results of a theoretical and experimental study of how the level of incident LO power affects the intermodulation output levels emanating from the mixer are presented. The predicted results lead to the following experimentally verified conclusions. 1) A drop in power at some intermodulation frequencies occurs for an increase of LO power, depending on LO operating point and order of intermodulation. 2) Power at each intermodulation frequency will repeatedly increase, reach a maximum, and then decrease as power in LO signal increases, where the number of repetitions follows the orders of intermodulation. 3) The maximum intermodulation power at low-order intermodulation frequencies occurs for higher LO power than higher order intermodulation frequencies. LO power operating point is shown to be a significant factor in mixer intermodulation consideration. Application of these results to receiver intermodulation improvement is discussed.     

Intermodulation Effects in the Transmission of Voice-Activated SCPC/FM Carriers Through a Nonlinear Repeater

When several voice-activated SCPC/FM carriers are transmitted through a nonlinear satellite repeater, a large number of intermodulation products appear at the output. An analysis of the baseband effect of these products is presented, taking into account the random on-off pattern followed by each carrier, the random nature of the level of each modulating speech signal, and a precise definition of the carrier power spectral density which is conditioned on the fact that the carrier is on, assuming that this is the circumstance under which we want to examine interference effects on any particular carrier. The analysis shows that computing intermodulation baseband noise, simply by introducing a penalty factor into the noise that would result by treating intermodulation as if it were thermal noise, may lead to very conservative estimates of intermodulation effects. The paper is restricted to the situation in which all carriers have equal amplitudes, but the general analysis is still valid when this is not so. The extension is straightforward except for the difficulties in counting the number of products of each type.     

Effects of intermodulation, AM-PM conversion, and additive noise in multicarrier TWT systems

The intermodulation due to the traveling-wave tube (TWT) is analyzed for the case where arbitrarily modulated carriers and Gaussian noise are amplified through the TWT. Both AM-PM conversion effects and nonlinear amplification in the TWT are considered. The possibility of reducing intermodulation for system improvement is also discussed.