Determines the intersection points of the asymptotes of the magnitude of the loopgain with unity. :param loopgainRational: Rational function of the Laplace variable, that represents the loop gain of a circuit. :type LoopgainRational: sympy.Expr :return: Dictionary w
(loopgainRational)
| 411 | return gain |
| 412 | |
| 413 | def findServoBandwidth(loopgainRational): |
| 414 | """ |
| 415 | Determines the intersection points of the asymptotes of the magnitude of |
| 416 | the loopgain with unity. |
| 417 | |
| 418 | :param loopgainRational: Rational function of the Laplace variable, that |
| 419 | represents the loop gain of a circuit. |
| 420 | :type LoopgainRational: sympy.Expr |
| 421 | |
| 422 | :return: Dictionary with key-value pairs: |
| 423 | |
| 424 | - hpf: frequency of high-pass intersection |
| 425 | - hpo: order at high-pass intersection |
| 426 | - lpf: frequency of low-pass intersection |
| 427 | - lpo: order at low-pass intersection |
| 428 | - mbv: mid-band value of the loopgain (highest value at order = zero) |
| 429 | - mbf: lowest freqency of mbv |
| 430 | :rtype: dict |
| 431 | """ |
| 432 | numer, denom = loopgainRational.as_numer_denom() |
| 433 | poles = _numRoots(denom, ini.laplace) |
| 434 | zeros = _numRoots(numer, ini.laplace) |
| 435 | poles, zeros = _cancelPZ(poles, zeros) |
| 436 | numPoles = len(poles) |
| 437 | numZeros = len(zeros) |
| 438 | numCornerFreqs = numPoles + numZeros |
| 439 | gain, coeffsN, coeffsD = coeffsTransfer(loopgainRational) |
| 440 | freqsOrders = np.zeros((numCornerFreqs, 2), dtype='float64') |
| 441 | for i in range(numZeros): |
| 442 | freqsOrders[i, 0] = np.abs(zeros[i]) |
| 443 | freqsOrders[i, 1] = 1 |
| 444 | for i in range(numPoles): |
| 445 | freqsOrders[numZeros + i, 0] = np.abs(poles[i]) |
| 446 | freqsOrders[numZeros + i, 1] = -1 |
| 447 | # sort the rows with increasing corner frequencies |
| 448 | freqsOrders = freqsOrders[freqsOrders[:, 0].argsort()] |
| 449 | for i in range(numCornerFreqs): |
| 450 | if i == 0: |
| 451 | # Initialize variables |
| 452 | value = np.abs(float(gain)) |
| 453 | fcorner = float(freqsOrders[i, 0]) |
| 454 | order = int(freqsOrders[i, 1]) |
| 455 | result = _initServoResults(fcorner, order, value) |
| 456 | elif freqsOrders[i, 0] == 0: |
| 457 | # Update corner frequency and order |
| 458 | fcorner = float(freqsOrders[i, 0]) |
| 459 | order += int(freqsOrders[i, 1]) |
| 460 | else: |
| 461 | new_fcorner = float(freqsOrders[i, 0]) |
| 462 | new_order = int(order + freqsOrders[i, 1]) |
| 463 | # Determine new value at corner frequency |
| 464 | if order == 0: |
| 465 | new_value = value |
| 466 | elif fcorner == 0: # first pole or zero in origin |
| 467 | new_value = value * new_fcorner ** order |
| 468 | else: |
| 469 | new_value = value * (new_fcorner / fcorner) ** order |
| 470 | # Determine unity-gain frequencies |
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