How does harmonic balance simulation work




















So if your harmonic balancer is going bad, you could get rough engine vibrations, a cracked crankshaft, or even a serpentine belt that gets thrown off its track.

Replacing one is excellent preventative maintenance, and that's exactly what we'll talk about next. So you want to replace your harmonic balancer, huh? There's good news and bad news. First, the good news: Installing a new balancer is a relatively easy task. And now the bad news: Getting the old one off the crankshaft is not.

It could involve taking apart some of your car's body parts, like the front fender or bumper and probably even the radiator. First, you'll probably need to go out and buy a tool you might not have -- a harmonic balancer puller. That's a specialized tool that's used to safely remove harmonic balancers without damaging your vehicle, and it also works on things like gear pulleys and steering wheels.

Search around to find the right puller for your needs. Every engine is different, so if you want to change the harmonic balancer on your car, you'll need to search around various car forums and Web sites to see how it's done on your specific model. Generally, you'll want to remove the belt from the crankshaft pulley and then take the harmonic balancer mounting bolt off with a socket and ratchet. From there, you'll use the puller tool you just bought to take the balancer itself off the crankshaft [source: Auto MD ].

As far as reinstalling the new harmonic balancer goes, it's pretty much the same steps in reverse. Just be sure to compare the old part and the new part to make sure the bolt hole locations are the same. And don't forget to pay close attention to the proper torque settings, too. If you can start your engine and the vibrations don't jar your tooth fillings loose, you've done the job correctly.

I'll admit that I had no idea this part even existed until I began researching this article. It's just further proof of the complexity of the modern engine and its supporting components.

I've read that a lot of people remove the harmonic balancer because they think it will increase their vehicle's performance, but I don't think this is recommended. Sign up for our Newsletter! Its default unit is dB. It is the reflection coefficient looking into the source that gives the minimum noise figure. Effective noise resistance can be used to plot noise-figure circles or related quantities.

This parameter determines how rapidly the minimum noise figure deteriorates when the source impedance is not at its optimum value. It describes the short circuit noise currents squared at each port, and the correlation between noise currents at different ports. These expressions for noise simulation can be manipulated in equations. At low powers, NFmin agrees with NFssb and both match the noise figure found from a small-signal analysis.

As the input power increases and nonlinear devices compress, this is no longer the case. NFmin and NFssb both deteriorate from their small-signal values. NFmin is an approximation to NFssb which neglects higher order conversion gains, and the difference between NFmin and NFssb expresses the importance of these higher order conversion gains.

For most applications, compression is moderate and NFmin and NFssb are close. For applications driven into severe compression, NFmin and NFssb can differ significantly. Also, note that Sopt is only defined at one frequency and that severe compression may demand a matching network that takes into account other frequencies. Deep into compression, care should be taken when using the noisy two-port parameters for design. This default option requires more memory but delivers more accurate results.

In addition, it may require large kernel swap-size parameters. Only if there is insufficient memory should this option be set to no.

Setting this option to no, causes only half of the small-signal mixer sidebands to be used and also uses one-fourth of the memory, but at the cost of generating potentially inaccurate results. Exercise caution when setting this option to no. Note: If you find you are running out of RAM, either set this parameter to no after reading the paragraph above, or switch to the Krylov option.

Bandwidth BandwidthForNoise Bandwidth for spectral noise simulation. The noise contributor data do not scale with noise bandwidth. Specify the desired value in the Frequency field.

This default option requires more memory and simulation time, but is required for the most accurate simulations. Selecting this option causes the fundamental frequencies to be restored to the dataset, and merges them sequentially. In ADS, if this simulation performs more than one HB analysis from multiple HB controllers , the device operating point data for all HB analyses will be saved, not just the last one.

Default setting is None. None None No information is saved. Brief Brief Saves device currents, power, and some linearized device parameters. Detailed Detailed Saves the operating point values which include the device's currents, power, voltages, and linearized device parameters. Higher levels increase the accuracy of the solution by reducing the FFT aliasing error and improving convergence.

Memory and speed are affected less when the direct harmonic balance method is used than when the Krylov option is used. Increasing the Oversample can help convergence by ensuring that rapid transitions and sharp features in waveforms are more precisely sampled. This does not increase the problem size, but does increase the number of device evaluations. The computational complexity of the direct Harmonic Balance solver determined by the Order and size of circuit is largely not affected.

As a rule of thumb, try to set the Oversample to 2, 4, etc. For multi-tone Harmonic Balance, the number of samples is equal to the product of the sample sizes of the fundamentals. Oversample[n] Displays a small dialog box. To increase simulation accuracy, enter in the field an integer representing a ratio by which the simulator will oversample each fundamental.

Budget Perform Budget simulation OutputBudgetIV Enables Budget simulation, which reports current and voltage data at the pins of devices following a simulation. Current into the n th terminal of a device is identified as Voltage at the nth terminal of a device is identified as It is both fast and robust, combining capabilities of the Basic and Advanced modes.

This mode will automatically activate advanced features to achieve convergence. The Auto mode also allows for convergence at looser tolerances if the simulation does not meet the default tolerances. A warning message is given in the status window when this occurs, and it includes the tolerance level up to which convergence was achieved.

This mode is extremely robust, and ensures maximal KCL residual reduction at each iteration. It is recommended that the maximum number of iterations MaxIters be increased to the range when this mode is selected. It is fast and performs well for most circuits. For highly nonlinear circuits the basic mode may have difficulties converging. It is then recommended to switch to the Advanced convergence mode. The simulation will iterate until it converges, an error occurs, or this limit is reached.

The default and recommended option is Robust. You can also specify the number manually by choosing the Custom option and entering an integer. The larger the number is, the more robust the simulation will be. Advanced Continuation Parameters Opens dialog to set the arc-length continuation parameters. It is recommended because optimal performance can be achieved for most circuits.

It allows the simulator to choose which solver would be most effective for the active design. The computation time grows with the cube of the problem size and memory grows with the square of the problem size. This bandwidth truncation speeds up the Jacobian factorization, but can lead to convergence problems as the Newton direction is not accurate.

This method greatly reduces memory requirements in large harmonic balance problems, such as those encountered in RFICs or RF System simulations. The computation time grows slightly faster than linear with the number of samples FFT size , and memory grows linearly with the number of harmonics. This is an iterative linear solver that does not require explicit storage of Jacobian. The linear problem can be approximately solved in fewer iterations to a desired loose tolerance and the Newton direction is computed approximately.

This can affect the Newton convergence properties, but not the accuracy of the final solution. Increase this limit if it is often reached. The Krylov solver achieves full convergence if the linear system residual is smaller than the tight tolerance KrylovTightTol, default 0.

The solver fails if residual reduction factor in two adjacent iterations is larger than KrylovConvRatio default 0. It controls how frequently the Jacobian is constructed and factored rather than being reused. The default and recommended option is Fast. The user can specify the number by choosing Custom and entering 0, 1, or 2.

The smaller the number is, the more robust the simulation will be. The larger this parameter, the more memory and CPU time will be required but the more robust the simulation will be as well. Advanced Krylov Parameters Opens dialog to set the Krylov solver's parameters. A block matrix is a matrix whose elements are matrices and vectors.

The blocks of the Jacobian are truncated to a specified threshold by default. The default threshold bandwidth is set by Guard Threshhold, and its default option is Fast. The bandwidth truncation speeds up the Jacobian factorization and saves memory, but can lead to convergence problems due to an inaccurate Newton direction.

In order to get the full bandwidth of the Jacobian blocks and improve the convergence, choose the Robust option. By default, when it is not explicitly set to yes or no by the user, the simulator enables it sets it to yes. Small circuits might simulate a little slower, but not significantly. In the arc-length continuation, the arc-length is increased in steps. The step size is calculated automatically for each problem. However if the ArcMaxStep is specified and is nonzero, it will define an upper-limit for the size of the arc-length step.

The default is 0 which means there is no upper limit for the ArcMaxStep. Display and set this parameter directly on the schematic. The default is 0 which means there is no limit for the ArcLevelMaxStep. ArcMinValue determines the lower limit that is allowed for the continuation parameter p during the simulation. In the arc-length continuation, p can trace a complicated manifold and its value can vary non-monotonically. ArcMinValue specifies a lower bound for p such that if during the arc-length continuation, p becomes smaller than ArcMinValue, the simulation is considered to have failed to converge.

The default is p min - delta , where delta is p max - p min , p min is the lower end of the parameter sweep, and p max is the upper end of the parameter sweep. ArcMaxValue determines the allowed upper limit of the continuation parameter p during the simulation. ArcMaxValue specifies an upper bound for p such that if during the arc-length continuation, p becomes greater than ArcMaxValue, the simulation is considered to have failed to converge. Max Shrinkage MaxShrinkage Controls the minimum size of the arc-length step default is 1e It is used to interrupt an otherwise infinite, loop in the case of poor or no convergence.

The default is intentionally set to a large value of to accommodate even slowly convergent iterations. You can still increase this number in cases where poor convergence may be improved and you are willing to allow more time for it. It needs to be tight, and the default value is 1e Larger values may lead to less accurate results, while further tightening may require longer simulation times.

Packing Threshold sets the bandwidth threshold for the packing. The default value is 1e Set this to a larger value to increase the memory reduction. When the number of Loose Iterations is reached, the solver then uses the Loose Tolerance value to achieve partial convergence. The penalty is a longer computation time if no swapping is required.

By default, this feature is turned off. You should turn on for extremely large problems in which the available RAM would not be able to accommodate the Jacobian. Preconditioner KrylovPrec The Krylov solver requires a preconditioner for robust and efficient convergence. Preconditioners matrices approximating the Jacobian are used to speed up the Krylov solver's convergence.

It uses a DC approximation on the entire circuit. Due to its block-diagonal nature, it can be factored once and applied inexpensively at each linear solve step. This preconditioner approximates the Jacobian by ignoring all but the DC Fourier coefficients consists of the diagonal blocks of the Jacobian.

Two solvers are available currently: the general solver that is preferable for smaller or typical-size circuits and the large-circuit solver that is preferable for larger circuits. On circuits that fail with the DCP, using the BSP option will often achieve convergence at the cost of additional memory usage. This is a robust choice for highly nonlinear circuits. The most nonlinear parts of the circuit are excluded, and are instead factored with a specialized Krylov solver.

The complex technology of the SCP preconditioner results in a memory usage overhead. This overhead is due to a construction of a knowledge base that enables the SCP to be much more efficient in the later phase of the harmonic balance solution process.

Source Frequency Order Fund 1 Frequency Combination Order 0. Note For circuits involving large numbers of frequencies, consider using the Circuit Envelope simulator. Note Since harmonic balance simulations also use the DC solution, for optimum speed improvement, both the DC solution and the HB solution should be saved and re-used as initial guesses.

Note To edit this parameter, select the Display tab in the Harmonic Balance Simulation component and set SamanskiiConstant to display on the schematic page. Order Fundamental Oversample Number of Samples 7 1 16 7 2 32 7 3 32 7 4 64 7 5 7 6 Order Fundamental Oversample Number of Samples 8 1 32 8 2 64 8 3 64 8 4 8 5 8 6 Order[1] Order[2] Fundamental Oversample Number of Samples 3 4 1 3 4 2 3 4 3 3 4 4 7 3 1 7 3 2 7 3 3 7 3 4 Order[1] Order[2] Oversample[1] Oversample[2] Number of Samples 5 3 1 4 5 3 2 3 7 4 3 2 7 4 4 1 No labels.

Powered by Atlassian Confluence 6. Setting Fundamental Frequencies. Setting Up the Initial Guess. Enabling Oscillator Analysis. Selecting Nonlinear Noise Analysis. Setting Up Small-Signal Simulations. Defining Simulation Parameters. Selecting a Harmonic Balance Solver Technique. Edit the Frequency and Order fields, then use the buttons to Add the frequency to the list displayed under Select. The frequency of the fundamental s.

The maximum order harmonic number of the fundamental s that will be considered. Contains the list of fundamental frequencies. The maximum order of the intermodulation terms in the simulation. The name of the parameter to be swept. A linear sweep works best in most cases Make sure Restart on the HB Initial Guess tab is not checked so that the sweep is used as a continuation solution from previous sweep step used as an initial guess for the next step.

Enables simulation at a single frequency point. Enables sweeping a range of values based on a linear increment. Enables sweeping a range of values based on a logarithmic increment. Note: Changes to any of the Start, Stop, etc. Enables use of an existing sweep plan component. This is the transient stop time.

This is the earliest point in time that the transient simulator starts checking for steady state conditions. This is the transient relative voltage and current tolerance. Enables ability to set other transient simulation parameters that are not found in this dialog box. Tells the simulator to perform a single tone transient simulation for a multitone harmonic balance simulation. When enabled, the transient simulation data used in generating the initial guess is output to the dataset, in addition to the final harmonic balance data.

Check this box to enter a file name for a solution to be used as initial guesses. Instructs the simulator to not use the last solution as the initial guess for the next solution. Check this box to save your final HB solution to the output file. This is the required name of a named node in the oscillator. This second node name should only be specified for a differential balanced oscillator. Specifies which of the fundamental frequencies is to be treated as the unknown oscillator frequency which the simulator will solve for.

Specifies which harmonic of the fundamental frequency is to be used for the oscillator. Specifies the number of octaves used in the initial frequency search during oscillator analysis. Specifies the number of steps per octave used in the initial frequency search. The NoiseCons check-box in the tab must be clicked to enable noise simulation with NoiseCons. Holds the names of the NoiseCon items to be simulated.

Enables use of an existing sweep plan component SweepPlan. Because the simulator uses a single-sideband definition of noise figure, the correct input sideband frequency must be specified here. Number of the source port at which noise is injected. Number of the Term component at which noise is retrieved. The fewer the number of nodes requested, the quicker the simulation and the less memory required. Holds the names of the nodes the simulator will consider.

Causes no individual noise contributors to be selected. Sorts individual noise contributors, from largest to smallest, that exceed a user-defined threshold see below. Causes individual noise contributors to be identified and sorts them alphabetically. A threshold below the total noise, in dB, that determines what noise contributors are reported. Causes port noise to be included in noise currents and voltages.

Causes an S-parameter simulation to be performed. Use all small-signal frequencies causes the simulator to solve for all small-signal mixer sidebands. Bandwidth for spectral noise simulation. Solves for all small-signal mixer frequencies in both sidebands. By default, the simulator reports only the small-signal upper and lower sideband frequencies in a mixer or oscillator simulation.

Enables you to save all the device operating-point information to the dataset. Saves the operating point values which include the device's currents, power, voltages, and linearized device parameters. Sets the FFT oversampling ratio. Displays a small dialog box.

Well, HB does this first on small signal frequency domain components and then on larger signals which generate many new frequency components Harmonics. It does sufficient small signal steady state calculations on the harmonics so that the shape of the final transient signal is produced to within an extremely small error tolerance.

Note in each case HB is used when the circuit exploits non-linearity in some form to get the performance required in the circuit design. For the more analytically minded, the following explanation of the basics of HB is in order. With reference to Figure 1, note that the entire circuit to be simulated is first separated into its linear and non linear sections as shown.

The interface is a set of voltages and currents as indicated. Two transadmittance matrices are defined; Y, that maps the signal voltages VsM to the interconnection currents iN and Y1 that maps the voltages vN to the currents iN.

Thus the composite current is:. Since Vsi are known and constant the current Is input linear region currents can be readily computed. These functions are transformed into frequencies by the use of the Fourier transform and provide frequency domain vectors I1 and Q1. A harmonic balance solution is found if the interconnect currents for the linear section are the same as the interconnect currents for the non-linear section.

Therefore the currents of the linear and the non-linear sections are balanced at each harmonic frequency. The inverse Fourier transform is applied at each iteration to convert to time domain quantities.

Then these time domain solutions v1, ……vk and v1,……vq are inserted into the solution i t. A further Fourier transform provides the charge and current vectors as above. After several iterations a solution is found, i. These provide the means to calculate the voltages at all the nodes. Inserting current sources at the interconnect points and doing an AC simulation provides the complete simulation. In conventional frequency-domain linear analysis, nonlinear devices are represented by linearized equivalent circuit models around the dc operating point.

Such models can be inadequate or even unsuitable for large-signal simulation.



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