Note: Do not save the schematics after usage because they may be used in later examples.
Note: Opening the schematics from the links is best done with a Click+Drag over an existing opened instance of LTspice.
The following table lists some of the key parameters which, when set to zero, allow various optimizations possible. There can only be one null parameter at a time.
Any of the following examples can be used to verify the table.
  1. With mostly a theoretical value, a LP with a pole @100Hz and unity gain. These are the parameters to change:
    sigma, BWp and G are defined externally to be able to set the two Laplace sources for comparison. The parameter sigma can be varied to provide a smoother, or a sharper knee in phase (and magnitude, for LP). Its effect can be viewed by uncommenting the .step sigma line and re-running the simulation.

  2. A more practical use of this filter is as an integrator over the audio band. For a 0dB@100Hz and considering this:
The log will reveal a much more precise rolloff. If the phase needs to be (better) matched to what V(pure_int) shows, sigma can be lowered, but it will also have an effect on the amplitude.
As mentioned, the parameter N extends or reduces the upper-frequency for the slope. With the last settings active, N=10 will show a zero at approximately 1kHz, marking the maximum frequency the filter can be used at.
This schematic shows how noise from <100Hz..10kHz> is filtered in time domain. The filter at the input is a HP with fc=100Hz and is not a part of the example.
  1. Example

  2. Checking the graphs, this requires setting BWp=BWs with BWp>0. E.g. a unity gain, 8th order AP at an arbitrary frequency of 1kHz:
    As the description for the Bessel filter says, Asc here can be used with 0 and 1 to see the difference. For a better view, Bessel2 can be chosen (a simple adding of a 2 at the end of the name by RClick-ing it) and the parameters changed like this for a .step run:
  3. Example

  4. For the other two all-pole filters, AP is used in the exact same manner as Bessel is, with the exception that, this time, Asc has a full influence on the result. Example of a 4th order Butterworth with BWp=BWs=1k and 2dB@ωc:
  5. (reusing the previous schematic)

  6. Even if Chebyshev APs are rare to nonexistant, it is configured just as Butterworth is with the addition of nT and Ap: for even orders, nT=-1 will show a 0dB-Ap response (given G=1), and for large values of Ap (and N) there will be a minor notch around the center frequency. With the example from the previous point, the only changes are: the name (Butterworth → Chebyshev), nT=0 (unity gain for all orders) and Ap=0.01 which has an impact on the phase response:
    Ap can be changed to Ap={Ap} and the following command added to the schematic for a view on the influence of Ap to the phase: .step param Ap list 0.01 0.1 1 3. Both schematics can be used to show the response for a sine input with the same frequency as the pass-band settings; changing the simulation cards is done with these steps.
It's configured like a LP and only Bessel can be used like this. Here are the parameters for a 1ms@1kHz, but with ~-3dB@ωc:
The time domain response to a 1kHz sine input can be viewed by changing the simulation cards between themselves. For the sake of demonstration, here is another schematic: the alternate Bessel2 is used to show how a train of impulses are filtered for orders ranging from 1 to 32 (the .step command), with (Asc>0) and without (Asc=0) frequency scaling. Bessel cannot be used here because of this.
To make this a -3dB@ωc LP, Asc must be >0. If an exact gain at the corner frequency is needed then Asc={20*log10(gain)}, but the frequency scaling is done by polynomial approximation, which isn't exact.
  1. A minimum order for a -3dB@1GHz and -80dB@1.1GHz InvChebyshev LP:
  2. Using the same values, the second approach, by specifying the order, results in this configuration:
  3. This is a pole-zero filter so the value of As, if not null, matters. For this InvChebyshev case, As=80.
Choosing the first method for a Butterworth with -1dB@1kHz and -60dB@500Hz results in:
An arbitrary Cauer: 20dB gain, unnormalized, 1MHz center frequency, -3dB@150kHz pass-band bandwith, relative to ωc, with 0.01dB ripple and 175kHz stop-band bandwidth @-100dB.
  1. Minimum order:

  2. Stop-bands internally determined (unlike BWs, As needs specifying, it's a pole-zero filter):
As the graphs show, transforming the previous example can be done by simply reversing the settings for the pass-band and stop-band frequencies, if the same values are required; otherwise, BWs<BWp.
The transient response to a swept sine input can be seen by switching the simulation cards. It can be seen that, despite the one or two seconds delay during pre-simulation, the simulation itself isn't slow.
By switching over to the .TRAN card, the test pins can be used. The schematic has been previously used and the order is known to be 23. Since the simulation card is .TRAN 23nsim=23n ⇒ the time scale will be divided into N segments of 23ns/23 = 1ns each; if the poles are denoted as σp[n]+jωp[n] and the zeroes as z[n] then, starting with the first segment of the time scale, V(real[p]) will output σp[1:N], V(imag[p]) will output ωp[1:N] and V(imag[z]) will output ωz[1:N].
But, since this is a LP, any value beyond ceil(N/2) is just symmetry (the same goes for HP). If the filter is "transformed" into a BP (or BS), for example, with fc=1G and BWs=1.25G (to allow an order less than the maximum permitted), then the voltages at the test pins will use all the time scale by having the poles/zeroes for the lower frequencies in the first half and the poles/zeroes for the upper frequencies in the second half.

©Vlad, 2008 - 2015