EMIT Theory

EMIT's powerful solver engine performs a power flow analysis for wideband signal spectra originating at one or more Transmitter (Tx) and traveling, sometimes via very complex routes, to each victim Receiver (Rx).

Upon arrival at each Rx, EMIT compares the received signal spectrum with the Rx's susceptibility to compute several interference metrics (EMI Margins, Sensitivity, Desense or Availability) and quantify the interference at the Rx. Each time a signal spectrum encounters a component, it is modified by the component's wideband characteristics, including potential nonlinear effects.

Each signal spectrum in EMIT can contain both narrowband and broadband elements. This section provides a brief overview of the methodology used In EMIT's simulation engine.

(1-1) Simulation Theory

EMIT's (1-1) simulation looks at each individual Tx/Rx pair in the design, along with any components (filters, cables, amplifiers, multiplexers, and so on) that may be present. EMIT simulates each Tx/Rx pair separately to compute each of the interference metrics. Each component in the Tx/Rx chain is modeled in EMIT by its frequency-dependent characteristics (called a Spectral Profile) that are either supplied by the user or computed by EMIT.

For predicting cosite interference, EMIT calculates an EMI margin, which is a metric that compares the received interference power level to the susceptibility of the Rx. EMIT calculates three different EMI margins to help identify the cause of any interference:

• Point EMI Margin
• Peak in-channel EMI Margin
• Noise in-channel EMI Margin

Other interference metrics available are Sensitivity, Desense and Availability . Each of these is derived from the computed EMI Margin. All calculations are described in further detail below.

Point EMI Margin

Point EMI Margin calculations proceed by cascading all spectral profiles In the Tx/Rx chain to arrive at the Point EMI Margin (M) for the Tx/Rx pair. This calculation is performed for each Tx/Rx pair In the scene. This is shown conceptually in the figure below.

Where:

• M = Point EMI Margin (dB)
• P_tx = Transmitted Power (dBm)
• T_tx = Sum of all Tx Outboard Component Transfer Functions (dB)
• ATA = Antenna-to-Antenna Coupling (dB)
• T_rx = Sum of all Rx Outboard Component Transfer Functions (dB)
• S_rx = Receiver Susceptibility (dBm)

The Point EMI margin can only be computed over the frequency range for which all spectral profiles in the Tx/Rx chain are defined. EMIT automatically determines the frequency range common to all spectral profiles during simulation. The Point EMI margin will thus be computed from a frequency equal to the largest minimum frequency for all of the spectral profiles up to a frequency equal to the largest maximum frequency for all of the spectral profiles.

An EMI margin that exceeds a set threshold (0 dB by default) indicates interference at the Rx. This occurs when the power at the Rx input exceeds the susceptibility of the Rx. The plot below shows the spectral profiles representing the power at the Rx input (red) and the Rx susceptibility (blue). Assuming a fixed value coupling of 0 dB is used, there will be two frequencies for this case where the Point EMI margin is positive, representing Interference. At 100 MHz and 200 MHz the Rx Input power (red) exceeds the Rx susceptibility (blue).

The Rx Saturation Level for this example is at 0 dBm and the Tx Broadband Noise is at -80 dBm. These extreme values may or may not represent the actual system performance, depending on how the Tx and Rx characteristics were produced. For example, if the susceptibility of the Rx has been measured, the saturation level may represent the maximum power level that could confidently be put Into the Rx front end without damaging it. This does not necessarily indicate that interference will occur at that input power level, but that tests were not performed at higher power levels to determine the interference threshold. On the Tx side, the noise floor could represent the dynamic range of the instruments used for the measurements and not the actual broadband noise emissions of the Tx. In cases like this, the EMIT simulation may produce positive EMI margins when in reality they would not be present.

Consider the plot below, which is similar to the case above except for a different Tx frequency. Computing the Point EMI Margin as outlined above will result In a positive EMI margin at 80 MHz where the Rx Input power (red) exceeds the Rx susceptibility (blue), and at 200 MHz where the Tx noise floor at -80 dBm exceeds the susceptibility of the Rx. If the 0 dB Rx saturation level truly represents a power level that causes Interference then this is a real Interference event. On the other hand, if the 0 dB saturation level is a limitation of the Rx characterization and not a true indicator of interference as described above, then this positive EMI margin could be a false alarm.

Peak ln-Channel EMI Margin

The second EMI Margin calculated by EMIT is the Peak In-Channel EMI Margin. The Peak In­Channel EMI Margin calculates the total power in the Rx channel due to narrowband (NB) signal components. As shown In the figure below, multiple NB signals can lie within the Rx channel bandwidth. If the amplitude of these signals is below the susceptibility envelope (red) then the Point EMI Margin will be negative. However, the total power at the Rx's detector may be above the susceptibility threshold.

The Peak EMI Margin is calculated by summing the peak power of each NB signal component that falls within the Rx channel's 3-dB bandwidth and comparing it with the in-channel susceptibility:

Where:

• P_i = Peak power (in Watts) of the i^th narrowband signal component
• P_peak = Total power of all N narrowband signal components (dB)
• S_rx = Receiver in-channel susceptibility (dB)
• M_peak = Peak EMI Margin (dB)

As with the Point EMI Margin, a positive Peak EMI Margin indicates interference at the Rx. This occurs when the total power due to NB signal components within the Rx channel exceeds the susceptibility of the Rx. The Peak EMI Margin is plotted as gray triangles in the figure below. Since the Peak EMI Margin is approximately 6 dB, there is marginal interference at the Rx. In this example, a fixed coupling of 0 dB was used so the amplitude of both these narrowband signals at the input to the Rx is -100 dB which is below the Rx's susceptibility envelope, as expected.

Broadband In-Channel EMI Margin

The Broadband In-Channel EMI Margin calculates the potential for interference due to broadband noise In the Rx channel bandwidth. To compute this, the total noise power within the channel bandwidth is calculated and compared to the Rx in-channel susceptibility:

Where the +3 dB in the equation for M_noise converts the average power level to peak power level of the in-channel broadband noise, and:

• P_Noise = Total in-channel average noise power (Watts)
• P_n(f) = Noisepower spectral density (W/Hz)
• f1 =
• f2 =
• BW_rx = 3 dB IF Filter bandwidth
• f_rx = Rx channel center frequency
• S_rx = Rx in-channel susceptibility (dB)
• M_Noise = noise in-channel EMI Margin (db)

A positive Broadband In-Channel EMI Margin indicates interference at the Rx. This occurs when the total power due to broadband noise within the Rx channel exceeds the susceptibility of the Rx. The Broadband In-Channel EMI Margin is plotted as gray stars in the previous figure. Since the Point EMI Margin is approximately 0 dB and the Noise in-channel EMI Margin is approximately -8 dB, only the Point EMI Margin makes a significant contribution to the Peak In-Channel EMI Margin, which is not always the case.

Sensitivity

For many applications, it is desirable to compute the sensitivity of a Rx in the presence of "noise" signals. In this context, "noise" is intended to denote an interference spectrum and generally consists of both narrowband and broadband components. The sensitivity is defined as the minimum power required for the Signal of Interest (Sol) to be able to receive and decode the signal properly. The sensitivity is given by the following equation:

Where:

• S/N = Minimum signal to noise ratio required by the receiver
  • The required S/N ratio (where N is taken to be Noise + Interference) is defined in the Rx Spectral Profile
• P_{Rx - Noise} = Receiver noise floor = kTBF
• kT = Boltzmann's constant * absolute temperature
• B = Receiver bandwidth
• F = Receiver noise factor
• P₁ = Total in-channel interference power

The total interference power, P₁,is the sum of all broadband and narrowband Interference within the Rx bandwidth and is given by:

Where:

• P_BB = Broadband noise power density
• P_NB = Narrowband noise power components

EMIT computes these interfering powers as part of the calculation tor the Noise in-channel EMI Margin and Peak in-channel EMI Margin.

Consider the relationship between the EMI Margin (M) that EMIT traditionally computes and the sensitivity, as defined above. EMIT defines the Rx susceptibility (S_Rx) as the minimum interference power that will cause interference to the Rx. Although S_Rx is a wideband quantity, here we consider only the in-channel susceptibility, which is given by:

From (Equation 1), see that:

So (Equation 3) can be written as:

Solving for sensitivity yields:

EMIT's EMI Margin (M) is by definition given by:

From (Equation 3), this can be rewritten as:

Thus, the simple relationship between EMIT's EMI Margin and Sensitivity:

Once all of the EMI Margins have been computed in EMIT, the Sensitivity is computed using (Equation 9) with the P_min value known from the Rx Spectral Profile definition. However, the sensitivity value will never be permitted to be less than the Rx's P_min since that value is taken to be the absolute smallest signal that the receiver can decode property.

Desense

The Desense of an Rx channel quantifies how much the sensitivity of an Rx channel is degraded in the presence of an in-channel interference. That is, how much the total in-channel interfering power exceeds the Rx's in-channel susceptibility. This is computed simply as the sum of the Peak in-channel EMI Margin and the Noise in-channel EMI Margin.

This value also reflects how much desensitization ("desense") a Rx experiences in the presence of interference as compared to P_min. Positive (in dB) values of Desense indicate that the Rx's sensitivity has been reduced as compared to P_min,while negative (in dB) values of Desense indicate that the in-channel interference is below the Rx's interference threshold.

Availability

The availability is given as a percentage (%) and quantifies what percentage of Rx channels in a Rx Band are experiencing interference (as defined by the Availability EMI Margin Threshold). The Tx and Rx band or channels for displaying availability are selected in the EMIT analysis window. Availability provides a useful way to mimic frequency-hopping systems.

(N-1) Simulation Theory

EMIT's (N-1) simulation capability computes EMI Margins for Rx channel frequencies that are potential victims of multiple Txs operating simultaneously, including transmitter-to-transmitter intermodulation (Tx-Tx intermod). This analysis looks at the effect of multiple transmitters on the interference at each Rx. It computes the interference at a Rx due to the superposition of all Tx signals and the Intermodulation Products (IMPs) created in one Tx due to radiation of another Tx coupling into its front end. The IMP are then re-radiated and can interfere with a Rx. Alternatively, the spectra of multiple Txs can couple into the Rx's front end, where IMPs are created due to nonlinearities in the low noise amplifier (LNA). The figure below conceptually shows these two scenarios. Signals from all three transmitters are coupling into the receiver, where they can generate MPs in the Rx's front end.

Another potential cause of IMPs are those that arise due to the nonlinear mixing of the two signals that occurs at junctions of dissimilar metals near the Txs (the so-called "rusty bolt effect"). EMIT is currently unable to model the rusty bolt effect or other Passive Intermodulation (PIM) phenomena.

In EMIT, Tx-Tx intermods can be generated for Txs (or RTs) that have outboard amplifiers or that have an internal amplifier defined in the Tx Spectral Profile properties. It should be noted that the generation of IMPs in EMIT is not limited to (N-1) simulations or to computing Tx-Tx intermod. Any time more than one narrowband signal component enters an amplifier that is located anywhere in the signal path (Tx and/or Rx), there is the potential for IMPs and EMIT fully accounts for this.

For the inter-TX intermod described above, the power at the input of an amplifier in a "victim" Tx due to another co-located Tx is calculated according to:

Where:

• P_in,amp = Power at input terminal of the amplifier in the victim Tx (dBm)
• P_tx,i = Transmit power of the interfering Tx (dBm)
• T_tx,i = Sum of all interfering Tx outboard component transfer functions (dB)
• T_tx,v = Sum of all victim Tx outboard component transfer functions, including amplifier reverse isolation (dB)

The output power spectrum of the victim Tx then couples to a Rx in the same manner that a typical Tx output spectrum couples to a victim Rx. The Tx-Tx intermods are also generated in the same manner as MPs in the Rx front end LNA.

In general, the following procedure is used to generate the output of an amplifier for all amplifiers, regardless of their location in the Tx or Rx signal paths:

1. Combine the spectra of all incoming signals. For Tx-Tx intermods this requires combining the spectra of the "victim" Tx with the interfering Tx (or Txs). For amplifiers in the Rx front end, this requires combining the spectra of all Txs that couple into the Rx including any Tx-Tx spectra.
   • Broadband (BB) emissions are converted from dBm/Hz to Volts/Hz (assuming R = 1Ohm) and added together.
   • Narrowband (NB) components are added on a frequency basis. If two or more frequencies overlap, the power levels are combined.
2. The instantaneous voltage level at the input to the amplifier is calculated to check for amplifier saturation. The power levels at all frequencies are converted to voltages. These voltages are summed to compute the instantaneous voltage (assuming all spectra arrive at the Rx simultaneously). If the total voltage is greater than the 1-dB compression point for the amplifier, then the amplifier is saturated and the simulation ends.
3. The center frequency of each NB signal component is determined. Each NB signal component is treated as a tone with an amplitude determined by the peak power of the NB signal component. A "two-tone" nonlinear analysis is then performed for every pair of NB tones at the input to the amplifier.

4. The Input Intercept Points (IIP) are estimated using the following approximations:

   

   

   

   

   ...

   

   Where:

   • IIP_N = N^th order intercept points referred to the input
   • P_1dB = 1dB compression point referred to the input

5. The IMPs are then calculated from the IIPs according to:

   

   

   Where:

   • = The lower frequency n^th order intermod product (dBm)
   • = The higher frequency n^th order intermod product (dBm)
   • P₁, P₂ = Power level of the two tones (dBm)

6. The bandwidth of each IMP Is computed by:

   

   Where:

   • BW₁ and BW₂ = The bandwidths of the two individual NB components
   • p and q = The order of the two tones

7. This process is repeated for all two-tone pairs at the input to the amplifier.

The approximation used for computing higher order IIPs shown above will eventually result in IIPs in the linear portion of the gain curve, which is nonphysical. In other words, the assumption becomes invalid. For this reason, EMIT computes successive higher order llPs and stops at the last one that is greater than the 1dB compression point. EMIT then proceeds to compute the amplitude of the IMPs and does so for all up to the highest order IIP available. If the amplitude of any of these falls below the noise level, EMIT will discard it.

Alternatively, the nonlinear performance of an amplifier can be specified using the Harmonic Input Intercept Points table. When measuring amplifier performance, it is usually easier to measure the amplitude of harmonics produced by an amplifier being driven by a single-frequency input signal. This allows the harmonics to be characterized by a Harmonic Input Intercept Point (HllP). Measurement of the output harmonic levels yields an HllP_n for each of the n harmonics. The HIIP has the same meaning as an llP but is specific to the harmonics.

Following the formulation presented by R.L.Smith in a paper at Microwave Journal, we can estimate the amplitude of IMPs from the HIIPs using the following equation:

Refer to the referenced paper for full definitions of the variables.

EMIT provides the option of specifying HllPs for an amplifier as an alternative to using the approximate IIP recursion relations shown previously. If an HIIP is defined in EMIT for an amplifier, then the MPs are computed according to the above equation where the HIIPs provided are used directly and others will be approximated according to:

EMIT then calculates the various interference metrics using this combined spectrum (Tx-Tx intermods, Rx generated MPs, etc.) and the simulation proceeds in a similar manner to the (1-1) simulation. Note that the order of the components matters for the nonlinear analysis. For example, if a transmitter has an amplifier and filter, the amplitude of any MPs created In the filter will be highly dependent on whether the filter is between the Radio and the Amplifier or if the filter is between the Amplifier and Antenna.

In general, the number of Tx/Rx channel combinations that need to be simulated can grow very quickly even for moderately sized projects. For example, a simple 5 Tx and 5 Rx scenario with each Tx or Rx operating on 20 channels will contain 10,000 Tx/Rx channel pairs (including self-interactions). Add modeling the (N-1) interactions (that is, Tx-to-Tx intermodulation and multiple Tx spectra arriving at the Rx simultaneously) and the number of channel combinations quickly balloons to almost 20 million.

Individual Tx-to-Rx simulations can be enabled/disabled by Ctrl+clicking on the associated square in the Scenario Matrix. This allows a subset of the project to be simulated.

Memory requirements for extremely large simulations should be considered as well. Users can set the maximum amount of memory that EMIT can use for a simulation in the Preferences panel. This sets the maximum amount of memory that EMIT will use when running a simulation. If during a run the memory used by EMIT reaches this limit, a warning is issued and the simulation is stopped. The default value is 75% of the available memory.

With appropriate add-on Ansys Electronic HPC Packs, EMIT's computational engine can take advantage of computers with multi-core processors and graphical processing units (GPUs) to run parts of the simulation in parallel. Users can specify the number of cores (also called threads) to use for the simulation by selecting the Preferences node in the Project Manager. When Automatic Multithreading is enabled, EMIT uses all available system resources for the simulation. Deselecting this option provides a field to allow the user to select the specific number of threads to be used. For example, on a computer with a four-core CPU, a user may wish to reduce the number of cores used by EMIT to two in order to leave system resources free for other tasks while EMIT is running.

Simulations can be stopped during a run and results for all Band pairs that have completed will be available for analysis (that is, all channel combinations for a given band pair must have completed for EMIT to have the results available). If changes are made to a project after a simulation is completed, only the results for systems affected by the change are purged.