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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"%matplotlib inline \n", | |
"import warnings\n", | |
"import numpy as np\n", | |
"import scipy.signal\n", | |
"import matplotlib as mpl\n", | |
"import matplotlib.pyplot as plt\n", | |
"\n", | |
"#warnings.filterwarnings(\"ignore\")\n", | |
"mpl.rcParams['lines.linewidth'] = 2\n", | |
"mpl.rcParams.update({'font.size': 12})\n", | |
"\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Bessel low pass multi-feedback (MFB) filter design\n", | |
"==================================================\n", | |
"\n", | |
"_**Software used**: Python/scipy, Mathematica, ltspice_" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The following is a design guide for Bessel low-pass filters of any order using op-amps. The method should be roughly the same for Butterworth filters, which only require the interchange of the Bessel polynomials with Butterworth polynomials (which are also implemented in `scipy.signal`). For Sallen-Key filters, find the transfer function of the circuit $H(s)$ (in terms of $C_1,C_2,R_1,R_2,R_3$) and use it instead of the MFB transfer function (eq. 3).\n", | |
"\n", | |
"Bessel low-pass filters are defined by transfer functions of the form (in the Laplace domain, with $s=j\\omega$):\n", | |
"\n", | |
"$$\\hspace{3cm}H(s) = \\frac{\\theta_n(0)}{\\theta_n(s/\\omega_0)}\\hspace{3cm}(\\text{eq. 1})$$\n", | |
"\n", | |
"where $\\omega_0$ is the cutoff frequency and $\\theta_n(s)$ is a reverse Bessel polynomial of order $n$:\n", | |
"\n", | |
"$$\\theta_n(s) = \\sum_{k=0}^n a_k s^k$$\n", | |
"\n", | |
"with $$a_k = \\frac{(2n-k)!}{2^{n-k}k!(n-k)!}$$\n", | |
"\n", | |
"e.g.\n", | |
"\n", | |
"$$\\begin{align*}\n", | |
"\\theta_1(s) &= s + 1\\\\\n", | |
"\\theta_2(s) &= s^2 + 3s + 3\\\\\n", | |
"\\theta_3(s) &= s^3 + 6s^2 + 15s + 15\\\\\n", | |
"\\theta_4(s) &= s^4 + 10s^3 + 45s^2 + 105s + 105\\\\\n", | |
"\\theta_5(s) &= s^5 + 15s^4 + 105s^3 + 420s^2 + 945s + 945\\\\\n", | |
"\\end{align*}$$\n", | |
"\n", | |
"These Bessel filters are normalized for unit group delay at the cutoff point. Note that the coefficients can be readily reproduced with ``scipy.signal.bessel`` [1]:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"num = [3.]\n", | |
"den = [1. 3. 3.]\n" | |
] | |
} | |
], | |
"source": [ | |
"ω_0 = 1. # [rad/s]\n", | |
"[num, den] = scipy.signal.bessel(2, ω_0, \"lowpass\", analog=True, output=\"ba\", norm=\"delay\")\n", | |
"print(\"num = \" + str(num))\n", | |
"print(\"den = \" + str(den))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"They can also be normalised by magnitude (-3 dB amplitude at $\\omega_0$) or phase (see [1]):" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"num = [1.61803399]\n", | |
"den = [1. 2.20320266 1.61803399]\n" | |
] | |
} | |
], | |
"source": [ | |
"[num, den] = scipy.signal.bessel(2, ω_0, \"lowpass\", analog=True, output=\"ba\", norm=\"mag\")\n", | |
"#[num, den] = scipy.signal.butter(2, ω_0, \"lowpass\", analog=True, output=\"ba\") #added for comparison: very recognisable group delay curve.\n", | |
"print(\"num = \" + str(num))\n", | |
"print(\"den = \" + str(den))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Second-order filter design\n", | |
"--------------------------\n", | |
"\n", | |
"We will begin with a design example for a second-order, magnitude normalized filter. The filter uses the coefficients given by `scipy.signal.bessel` in the previous cell.\n", | |
"\n", | |
"Its transfer function looks like this:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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", | |
"text/plain": [ | |
"<Figure size 800x600 with 3 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"def get_group_delay(num, den, ω):\n", | |
" \"\"\"Calculate group delay from transfer function coefficients.\"\"\" #originally made with Github Copilot, so take with grain of salt. seems to work with unwrap\n", | |
" # H(s) = num(s) / den(s)\n", | |
" # gd = -d/dω arg(H(jω))\n", | |
" # gd = -d/dω arg(num(jω)) + d/dω arg(den(jω))\n", | |
" num_ = np.poly1d(num)\n", | |
" den_ = np.poly1d(den)\n", | |
" num_jw = num_(1j * ω)\n", | |
" den_jw = den_(1j * ω)\n", | |
" \n", | |
" ang_num_jw = np.angle(num_jw)\n", | |
" ang_den_jw = np.angle(den_jw)\n", | |
"\n", | |
" # ang_num_jw = np.unwrap(ang_num_jw, discont=np.pi) #probably needed but not encountered so leave it for now\n", | |
" ang_den_jw = np.unwrap(ang_den_jw, discont=np.pi)\n", | |
"\n", | |
" gd = -np.gradient(ang_num_jw, ω) + np.gradient(ang_den_jw, ω) #e^j arg1 / e^j arg2 = e^j (arg1 - arg2) so just derivate and then signed add angles, instead of dividing, derivating and taking the angle at the end.\n", | |
" \n", | |
" \n", | |
" #print for debugging\n", | |
" # print(\"ω = .. ; gd = .. ; np.angle(num_jw) = .. ; np.angle(den_jw) = ..\")\n", | |
" # for i in range(len(ω)):\n", | |
" # print(\"gd[{}] = {:.4f} ; ω[{}] = {:.4f} ; = ang(num_jw[{}]) = {:.4f} ; ang(den_jw[{}]) = {:.4f}\".format(\n", | |
" # i, gd[i], i, ω[i], i, np.angle(num_jw[i]), i, np.angle(den_jw[i])))\n", | |
" #this is what it took to realize that I had to unwrap the phase of the denominator\n", | |
" \n", | |
" return gd\n", | |
"\n", | |
"def get_group_delay_scipy(num, den, ω, fs=100):\n", | |
" numd_d, den_d = scipy.signal.bilinear(num, den, fs=fs) # convert to discrete-time. scipy gives group delay function only for discrete-time systems.\n", | |
" [_, gd] = scipy.signal.group_delay(\n", | |
" (numd_d, den_d),\n", | |
" ω / (2*np.pi),\n", | |
" fs=fs)\n", | |
" gd = gd / fs\n", | |
" return gd\n", | |
"\n", | |
"def plot_transfer(ω, h, gd=None, h_=None, gd_=None, line_labels=None):\n", | |
" fig = plt.figure(figsize=(8, 6))\n", | |
" if gd is None:\n", | |
" n_rows = 2\n", | |
" else:\n", | |
" n_rows = 3\n", | |
" gs = mpl.gridspec.GridSpec(n_rows, 1)\n", | |
" ax_mag = plt.subplot(gs[0])\n", | |
" ax_phase = plt.subplot(gs[1])\n", | |
" ax_mag.grid(True)\n", | |
" ax_phase.grid(True)\n", | |
"\n", | |
" ax_delay = None\n", | |
" if not gd is None:\n", | |
" ax_delay = plt.subplot(gs[2])\n", | |
" ax_delay.grid(True)\n", | |
"\n", | |
" # main plot\n", | |
" lines_mag = ax_mag.loglog(ω, np.abs(h)) # N.B. H(s) = H(jω)\n", | |
" angleh = np.unwrap(np.angle(h), axis = 0, discont = np.pi) # unwrap phase to avoid discontinuities (jumps). the plots with discontinuities make it harder to \n", | |
" ax_phase.semilogx(ω, angleh)\n", | |
" if not gd is None:\n", | |
" ax_delay.semilogx(ω, gd)\n", | |
" \n", | |
"\n", | |
" # alternate plot\n", | |
" if not h_ is None:\n", | |
" ax_mag.loglog(ω, np.abs(h_), '--')\n", | |
" angleh_ = np.unwrap(np.angle(h_), axis = 0, discont = np.pi) # unwrap phase to avoid discontinuities\n", | |
" #angleh_ = np.angle(h_)\n", | |
" ax_phase.semilogx(ω, angleh_, '--')\n", | |
" ax_delay.semilogx(ω, gd_, '--')\n", | |
"\n", | |
" ax_mag.set_xticklabels([])\n", | |
" ax_mag.grid(True)\n", | |
" ax_phase.grid(True)\n", | |
" ax_mag.set_ylabel(u\"Magnitude |H| [dB]\")\n", | |
" ax_phase.set_ylabel(u\"Phase ∠H [rad]\")\n", | |
" if not gd is None:\n", | |
" ax_delay.grid(True)\n", | |
" ax_phase.set_xticklabels([])\n", | |
" ax_delay.set_xlabel(u\"Angular frequency [rad/s]\")\n", | |
" ax_delay.set_ylabel(u\"Group delay [s]\")\n", | |
" else:\n", | |
" ax_phase.set_xlabel(u\"Angular frequency [rad/s]\")\n", | |
"\n", | |
" if not line_labels is None:\n", | |
" ax_mag.legend(lines_mag, line_labels, loc=\"best\")\n", | |
" \n", | |
" _ytick = ax_mag.get_yticks()\n", | |
" ax_mag.set_yticks(_ytick)\n", | |
" ax_mag.set_yticklabels(10 * np.log10(_ytick))\n", | |
" \n", | |
" return ax_mag, ax_phase, ax_delay\n", | |
" \n", | |
"# plot using scipy.signal.freqs\n", | |
"ω = scipy.signal.findfreqs(num, den, 1000, kind=\"ba\")\n", | |
"[_, h] = scipy.signal.freqs(num, den, ω)\n", | |
"#[_, gd] = scipy.signal.group_delay([num, den], ω)\n", | |
"gd = get_group_delay_scipy(num, den, ω, fs = 100) #group delay but done the \"correct\" way with scipy\n", | |
"\n", | |
"# alternate way: plot the Bessel polynomial directly\n", | |
"h_ = np.poly1d(den)(0)/np.poly1d(den)(1j * ω)\n", | |
"gd_ = get_group_delay(num, den, ω) # group delay calculated from the transfer function coefficients. this was left as TODO\n", | |
"\n", | |
"#notice the grpup delay looks completely differnet in this implementation. both methods yield the same result, and it looks more like what you expect\n", | |
"#try with Butterworth filter to see the clear peak, and see that the old one wasnt right (since butterworth is easier to find on google)\n", | |
"_ = plot_transfer(ω, h, gd, h_, gd_)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Note that we are plotting using `scipy.signal` (blue lines) and by plotting the Bessel polynomial directly (orange dashed lines). These should match.\n", | |
"\n", | |
"Check that gain is -3 dB at $\\omega_0$:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Gain at ω_0 = 1.0 rad/s: 0.7071067811865474 = -3.0102999566398143 dB, ang = -1.2973090366533402 rad (Bessel poly)\n", | |
"Gain at ω_0 = 1.0 rad/s: 0.7071067811865474 = -3.0102999566398143 dB, ang = -1.2973090366533402 rad (scipy.signal)\n" | |
] | |
} | |
], | |
"source": [ | |
"h_0 = np.poly1d(den)(0)/np.poly1d(den)(1j * ω_0)\n", | |
"print(\"Gain at ω_0 = \" + str(ω_0) + \" rad/s: \" + str(np.abs(h_0)) + \" = \" + str(20 * np.log10(np.abs(h_0))) + \" dB, ang = \" + str(np.angle(h_0)) + \" rad (Bessel poly)\")\n", | |
"\n", | |
"[_, h_0] = scipy.signal.freqs(num, den, ω_0)\n", | |
"h_0 = h_0[0]\n", | |
"print(\"Gain at ω_0 = \" + str(ω_0) + \" rad/s: \" + str(np.abs(h_0)) + \" = \" + str(20 * np.log10(np.abs(h_0))) + \" dB, ang = \" + str(np.angle(h_0)) + \" rad (scipy.signal)\")" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Plot the poles of the filter in the complex plane:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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", | |
"text/plain": [ | |
"<Figure size 800x600 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"[z, p, k] = scipy.signal.tf2zpk(num, den)\n", | |
"\n", | |
"def plot_poles_zeros(z, p):\n", | |
" fig, ax = plt.subplots(1, figsize=(8, 6))\n", | |
" ax.scatter(np.real(p), np.imag(p), s=120, linewidth=2, marker='x')\n", | |
" for sp in ax.spines:\n", | |
" ax.spines[sp].set_color('none')\n", | |
" ax.axhline(0., color='black', linewidth=2)\n", | |
" ax.grid(True)\n", | |
" ax.set_xlabel(\"Re\")\n", | |
" ax.set_ylabel(\"Im\")\n", | |
"\n", | |
"plot_poles_zeros(z, p)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Note that the transfer function for a second-order low-pass filter is commonly written in terms of a quality factor $Q$ [2]:\n", | |
"\n", | |
"$$\\hspace{3cm}H(s) = \\frac{\\omega_0^2}{s^2 + \\frac{\\omega_0}{Q} s + \\omega_0^2}\\hspace{3cm}(\\text{eq. 2})$$\n", | |
"\n", | |
"Comparing this form to the Bessel polynomial, e.g. for the delay-normalized second-order coefficients:\n", | |
"\n", | |
"$$ = \\frac{1.6180}{s^2 + 2.2032s + 1.6180}$$\n", | |
"This can be solved for $\\omega_0$ and $Q$ to yield:\n", | |
" \n", | |
"$$\n", | |
"\\begin{align*}\n", | |
"\\omega_0 &= \\sqrt{1.1680}\\\\\n", | |
"Q &\\approx 0.5774\n", | |
"\\end{align*}\n", | |
"$$\n", | |
"\n", | |
"For the circuit implementation, we only need the coefficients. The MFB second-order low-pass circuit looks like:\n", | |
"\n", | |
"<img src=\"https://gist.githubusercontent.com/turingbirds/5fa6275781232c1c4e563a43c4042bf2/raw/85f2cbd652c8d25b7d0b537224d887c020986b0a/multiple_feedback_low_pass_second_order_filter_op_amp.png\">\n", | |
"\n", | |
"The transfer function of this circuit can be derived by circuit analysis:\n", | |
"\n", | |
"$$\\hspace{3cm}H(s) = \\frac{-\\frac{R_3}{R_1}}{C_1 C_2 R_2 R_3 s^2 + C_2 \\frac{R_1R_2 + R_2R_3 + R_3R_1}{R_1} s + 1}\\hspace{3cm}(\\text{eq. 3})$$\n", | |
"\n", | |
"Comparing (eq. 3) with (eq. 2), we can derive the Q value in terms of circuit components:\n", | |
"\n", | |
"$$\\hspace{5cm}Q = \\frac{\\sqrt{C_1C_2R_2R_3}}{C_2 \\frac{R_1R_2 + R_2R_3 + R_3R_1}{R_1}}\\hspace{3cm}(\\text{eq. 4})$$\n", | |
"\n", | |
"Let's continue the running example (magnitude-normalised second-order), for which we computed the following transfer function:\n", | |
"\n", | |
"$$H(s) = \\frac{1.6180}{s^2 + 2.2032s + 1.6180}$$\n", | |
"\n", | |
"This was, however, for a radial frequency of $\\omega_0=1\\,\\text{rad/s}$. Recall that the definition for Bessel filters (eq. 1) contains the factor $1/\\omega_0$, so in general (for any $\\omega_0$):\n", | |
"\n", | |
"$$H(s) = \\frac{\\theta_n(0)}{\\theta_n(s/\\omega_0)}\n", | |
"= \\frac{1.6180}{{\\left(\\frac{s}{\\omega_0}\\right)}^2 + 2.2032{\\left(\\frac{s}{\\omega_0}\\right)} + 1.6180}$$\n", | |
"\n", | |
"Furthermore, note that the this filter has unity gain at DC. However, the op-amp MFB implementation is inverting (the gain is actually negative unity), and in any case can easily be set up to give any non-unity gain, by varying the ratio $R_3/R_1$. To account for DC gain, we include a factor $H_0$ as follows:\n", | |
"\n", | |
"$$H(s) = H_0 \\cdot \\frac{\\theta_n(0)}{\\theta_n(s/\\omega_0)}\n", | |
"= H_0 \\cdot \\frac{1.6180}{{\\left(\\frac{s}{\\omega_0}\\right)}^2 + 2.2032{\\left(\\frac{s}{\\omega_0}\\right)} + 1.6180}\\hspace{3cm}(\\text{eq. 5})$$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"By equating the $H(s)$ obtained from circuit analysis (eq. 3) and $H(s)$ obtained from the Bessel polynomial (eq. 5), we obtain the following relationships:\n", | |
"\n", | |
"$$\n", | |
"\\begin{align*}\n", | |
"H_0 &= -\\frac{R_3}{R_1}\\\\\n", | |
"\\frac{1}{1.6180\\;\\omega_0^2} &= C_1 C_2 R_2 R_3\\\\\n", | |
"\\frac{2.2032}{1.6180\\;\\omega_0} &= C_2 \\frac{R_1R_2 + R_2R_3 + R_3R_1}{R_1}\\\\\n", | |
"\\end{align*}\n", | |
"$$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"When $H_0$ and $\\omega_0$ are known (i.e. picked by design), these equations can subsequently be solved to obtain values for the components. A symbolic mathematics tool makes this very simple; the example below is given for Mathematica.\n", | |
"\n", | |
"Because there are only three equations for 5 unknowns (i.e., the 5 component values), the system is underdetermined, so solving the system without further constraints results in equality relationships. Let's say we are making a filter with a DC gain $H_0=-{}^1/{}_2$ and corner frequency $f_0=50\\,\\text{kHz}$, which corresponds to $\\omega_0\\approx3.1\\cdot10^5\\,\\text{rad/s}$.\n", | |
"\n", | |
"```Mathematica\n", | |
"H0 = -0.5\n", | |
"w0 = 2*Pi*50*^3\n", | |
"Solve[{H0 == -R3/R1, 1/(1.6180*w0^2) == C1*C2*R2*R3, 2.2032/(1.6180*w0) == C2*(R1*R2 + R2*R3 + R3*R1)/R1}, {C1, C2, R1}]\n", | |
"```\n", | |
"\n", | |
"Which yields:\n", | |
"\n", | |
"```Mathematica\n", | |
" -7 -6\n", | |
" 7.22381 10 (3. R2 + 2. R3) 8.66873 10\n", | |
"Out[3]= {{C1 -> ----------------------------, C2 -> -------------, R1 -> 2. R3}}\n", | |
" R2 R3 3. R2 + 2. R3\n", | |
"\n", | |
"```\n", | |
"\n", | |
"\n", | |
"How to fix the remaining degrees of freedom depends on you. You can choose to hand-pick e.g. $R_1$, if the input impedance is a constraint, and then compute $R_3$ and pick $R_2=R_3$. A popular alternative is to first pick $C_1$ and $C_2$ as standard values, and then calculate the resistors; the motivation behind this is that resistors at the computed values are generally easier to obtain than capacitors.\n", | |
"\n", | |
"```Mathematica\n", | |
"H0 = -0.5\n", | |
"w0 = 2*Pi*50*^3\n", | |
"R1 = 100*^3\n", | |
"C2 = 47*^-12\n", | |
"Solve[{H0 == -R3/R1, 1/(1.6180*w0^2) == C1*C2*R2*R3, 2.2032/(1.6180*w0) == C2*(R1*R2 + R2*R3 + R3*R1)/R1}, {C1, R2, R3}]\n", | |
"```\n", | |
"\n", | |
"Which yields:\n", | |
"\n", | |
"```Mathematica\n", | |
" -11\n", | |
"Out[5]= {{C1 -> 9.46719 10 , R2 -> 28147., R3 -> 50000.}}\n", | |
"```\n", | |
"\n", | |
"Simulation with ltspice confirms a gain of $-6\\,\\text{dB}$ at DC and, at the crossover frequency, a gain of $-9\\,\\text{dB}$ and phase shift of approximately $1.84\\,\\text{rad}$. (Note that ltspice also computes the group delay.) Calculating the Q using equation 4 indeed yields $Q\\approx0.5774$.\n", | |
"\n", | |
"Note that if you get negative or otherwise nonsensical results from Mathematica, it probably means that the values selected for the fixed components (e.g. $R_1$ and $C_2$ in the previous example) are either too high or too low." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Fourth-order filter design\n", | |
"--------------------------\n", | |
"\n", | |
"Let's do the same thing for a fourth-order filter. The filter will be implemented by cascading (placing in series) two MFB circuits, the first of which implements one pole pair, and the second the second pair. Note that this is not the same as independently designing two second-order filters and placing them in series.\n", | |
"\n", | |
"In addition, note that the `scipy.signal.bessel` function has an argument for the corner frequency $\\omega_0$, which so far we have left at a normalised frequency of $1\\,\\text{rad/s}$. The frequency was later normalised (or un-normalised, if you will) for the chosen corner frequency of $f_0=50\\,\\text{kHz}$. We will now begin immediately with the real corner frequency of $\\omega_0=2\\pi\\cdot{}50\\,\\text{kHz}\\approx3.1\\cdot10^{5}\\,\\text{rad/s}$." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 800x600 with 3 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"ω_0 = 2 * np.pi * 50E3 # [rad/s]\n", | |
"[num, den] = scipy.signal.bessel(4, ω_0, \"lowpass\", analog=True, output=\"ba\", norm=\"mag\")\n", | |
"\n", | |
"# plot the Bessel polynomial directly\n", | |
"ω = scipy.signal.findfreqs(num, den, 1000, kind=\"ba\")\n", | |
"h = np.poly1d(den)(0)/np.poly1d(den)(1j * ω)\n", | |
"\n", | |
"#[_, gd] = scipy.signal.group_delay([num, den], ω)\n", | |
"gd = get_group_delay_scipy(num, den, ω, fs = 2 * np.pi * 50E3 * 10) #not sure whats the right way to pick fs, generally higher seems to work.\n", | |
"gd_ = get_group_delay(num, den, ω) # group delay calculated from the transfer function coefficients. this was left as TODO\n", | |
"\n", | |
"_ = plot_transfer(ω, h, gd, h, gd_) #plot both gd and gd_ for sanity check. still same." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The fourth-order filter has two pairs of complex conjugate poles:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 800x600 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"[z, p, k] = scipy.signal.tf2zpk(num, den)\n", | |
"plot_poles_zeros(z, p)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Each pair of poles is implemented by one second-order stage. For simplicity we select pole pairs manually—it should be obvious which numbers belong together as each pair contains a number $a+bi$ and its complex conjugate $a-bi$." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Poles for stage 0: [-312654.0542871+394931.41558563j -312654.0542871-394931.41558563j]\n", | |
"\tnum = 2.537234E+11, den = [1.00000000e+00 6.25308109e+05 2.53723381e+11]\n", | |
"Poles for stage 1: [-430419.50313801+128883.74986157j -430419.50313801-128883.74986157j]\n", | |
"\tnum = 2.018720E+11, den = [1.00000000e+00 8.60839006e+05 2.01871970e+11]\n" | |
] | |
} | |
], | |
"source": [ | |
"_p = [p[:2], p[2:]] # N.B. manually select pole pairs\n", | |
"filt_ord = len(p) // 2\n", | |
"_num = filt_ord * [None]\n", | |
"_den = filt_ord * [None]\n", | |
"for i in range(filt_ord):\n", | |
" print(\"Poles for stage \" + str(i) + \": \" + str(_p[i]))\n", | |
" [_num[i], _den[i]] = scipy.signal.zpk2tf(z, _p[i], k)\n", | |
" print(\"\\tnum = \" + \"{0:E}\".format(_den[i][-1]) + \", den = \" + str(_den[i]))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Let's compute the values for the first pair of poles first.\n", | |
"\n", | |
"The transfer function for this stage is:\n", | |
"\n", | |
"$$H(s) = H_0 \\cdot \\frac{2.5373\\cdot10^{11}}{s^2 + 6.2531\\cdot10^{5}s + 2.5373\\cdot10^{11}}$$\n", | |
"\n", | |
"which is again equal to the transfer function derived by circuit analysis (equation 3). By equating the two, we obtain the following relationships:\n", | |
"\n", | |
"$$\n", | |
"\\begin{align*}\n", | |
"H_0 &= -\\frac{R_3}{R_1}\\\\\n", | |
"\\frac{1}{2.5373\\cdot10^{11}} &= C_1 C_2 R_2 R_3\\\\\n", | |
"\\frac{6.2531\\cdot10^5}{2.5373\\cdot10^{11}} &= C_2 \\frac{R_1R_2 + R_2R_3 + R_3R_1}{R_1}\\\\\n", | |
"\\end{align*}\n", | |
"$$\n", | |
"\n", | |
"These are indeed of the same form as the relations obtained by equating eq. 3 and eq. 5, except that the corner frequency has now been worked into the coefficients by `scipy.signal.bessel` instead of being explicit; note that $1/(2.5708\\cdot\\omega_0^2)\\approx 2.5373\\cdot10^{11}$ and $1/(1.9904\\cdot\\omega)\\approx6.2531\\cdot10^5$, where 2.5708 and 1.9904 are the Bessel coefficients returned by `scipy.signal.bessel` for the normalised filter with $\\omega_0=1$.\n", | |
"\n", | |
"\n", | |
"```Mathematica\n", | |
"H0 = -0.5\n", | |
"w0 = 2*Pi*50*^3\n", | |
"R1 = 100*^3\n", | |
"C2 = 47*^-12\n", | |
"Solve[{H0 == -R3/R1, 1/(2.53723381*^11) == C1*C2*R2*R3, 6.25308109*^5/2.53723381*^11 == C2*(R1*R2 + R2*R3 + R3*R1)/R1}, {C1, R2, R3}]\n", | |
"```\n", | |
"\n", | |
"```Mathematica\n", | |
"\n", | |
" -9\n", | |
"Out[5]= {{C1 -> 1.03241 10 , R2 -> 1624.5, R3 -> 50000.}}\n", | |
"\n", | |
"```\n", | |
"Similarly, for the second pair of poles:\n", | |
"\n", | |
"```Mathematica\n", | |
"H0 = -1\n", | |
"w0 = 2*Pi*50*^3\n", | |
"R1 = 100*^3\n", | |
"C2 = 33*^-12\n", | |
"Solve[{H0 == -R3/R1, 1/(2.01871970*^11) == C1*C2*R2*R3, 8.60839006*^5/2.01871970*^11 == C2*(R1*R2 + R2*R3 + R3*R1)/R1}, {C1, R2, R3}]\n", | |
"```\n", | |
"\n", | |
"```Mathematica\n", | |
"\n", | |
" -11\n", | |
"Out[5]= {{C1 -> 4.79938 10 , R2 -> 46915.5, R3 -> 100000.}}\n", | |
"```\n", | |
"\n", | |
"The partial and full transfer functions are plotted in the following figure. We also compute the full transfer function reconstructed from the two partial transfer functions (the line labeled \"reconstructed\"); this line should overlap with the original (\"full\")." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 800x600 with 3 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"h_partial = np.empty((len(ω), len(_den)), dtype=complex) #np.complex deprecated\n", | |
"gd_partial = np.empty((len(ω), len(_den)))\n", | |
"gd_partial_ = np.empty((len(ω), len(_den)))\n", | |
"for i in range(len(_den)):\n", | |
" h_partial[:, i] = np.poly1d(_den[i])(0)/np.poly1d(_den[i])(1j * ω)\n", | |
" gd_partial[:, i] = get_group_delay_scipy(_num[i], _den[i], ω, fs=10**7) # still not sure how to pick fs.\n", | |
" gd_partial_[:, i] = get_group_delay(_num[i], _den[i], ω) # group delay calculated from the transfer function coefficients. this was left as TODO\n", | |
"\n", | |
"h_reconstructed = np.prod(h_partial, axis=1)\n", | |
"gd_reconstructed = np.sum(gd_partial, axis=1)\n", | |
"gd_reconstructed_ = np.sum(gd_partial_, axis=1) \n", | |
"\n", | |
"h_plot = np.hstack([h[:, np.newaxis], h_partial, h_reconstructed[:, np.newaxis]])\n", | |
"gd_plot = np.hstack([gd[:, np.newaxis], gd_partial, gd_reconstructed[:, np.newaxis]])\n", | |
"gd_plot_ = np.hstack([gd_[:, np.newaxis], gd_partial_, gd_reconstructed_[:, np.newaxis]])\n", | |
"_ = plot_transfer(ω, h_plot, gd_plot, h_plot, gd_plot_, line_labels=[\"full\", \"stage 1\", \"stage 2\", \"reconstructed\"])\n", | |
"# for i in range(h_plot.shape[1]):\n", | |
"# _ = plot_transfer(ω, h_plot[:, i], gd_plot[:, i], h_plot[:, i], gd_plot_[:, i], line_labels=[\"full\", \"stage 1\", \"stage 2\", \"reconstructed\"][i:i+1])\n", | |
"# plt.title(\"Stage \" + str(i))\n", | |
"# plt.show()\n", | |
"\n", | |
"\n", | |
"#this one is actually really cool you can see the stage one alone has a group delay peak around cutoff.\n", | |
"#sadly im still learning from your demo so im not exactly sure how to look at it but yea, more instructive than before.\n", | |
"#also would help if we could fix the colors. otherwise we have to print without gd_plot_ which is fine too, thats just a sanity check. (it should be idnetical to gd_plot)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Note that the Q factor (eq. 4) is 0.8055 for the first pair of poles, and 0.5219 for the second. In general, when cascading higher-order filters, the filter with the lowest Q (most wide filter) should be closest to the input, and the highest Q (most narrow filter) closest to the output. This is done to avoid saturation, as high-Q filters can exhibit gain peaking, which is less likely to lead to saturation in later stages because of the attenuation the signal has undergone prior to it.\n", | |
"\n", | |
"So, in the current example, the first stage of the filter (the first op-amp circuit, nearest the input) should be the circuit corresponding to the second pair of poles, and the second stage (nearest the output) should correspond to the first pair of poles. The easiest course of action is to recompute the component values with poles switched." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Fifth-order filter design\n", | |
"-------------------------\n", | |
"\n", | |
"An experiment is described in [3] where the transfer function of a Butterworth low-pass filter was measured, before and after the addition of an RC filter at the circuit output. The RC filter was found to considerably reduce the high-frequency feed-through, leading to much higher attenuation at high frequencies (frequencies well above the cutoff frequency). The resistance was chosen low (100 Ω) so as to minimise the attenuation introduced by the series resistance. In general the feasibility of this approach depends on the input resistance of the next stage, which will have to be much higher than the value of R in the RC filter.\n", | |
"\n", | |
"Rather than adding an RC filter post-hoc, we simply design a fifth-order filter from the start. We begin in the same manner as for the fourth-order filter: compute the poles of the transfer function, and the corresponding coefficients." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Gain at ω_0 = 314159.2653589793 rad/s: 0.7071067811865475 = -3.0102999566398125 dB, ang = -2.426424788222964 rad (Bessel poly)\n" | |
] | |
}, | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 800x600 with 3 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"filt_ord = 5\n", | |
"[num, den] = scipy.signal.bessel(filt_ord, ω_0, \"lowpass\", analog=True, output=\"ba\", norm=\"mag\")\n", | |
"\n", | |
"# plot the Bessel polynomial directly\n", | |
"ω = scipy.signal.findfreqs(num, den, 1000, kind=\"ba\")\n", | |
"h = np.poly1d(den)(0)/np.poly1d(den)(1j * ω)\n", | |
"#[_, gd] = scipy.signal.group_delay([num, den], ω)\n", | |
"gd = get_group_delay_scipy(num, den, ω, fs = 2 * np.pi * 10E5) #still guessing fs. this actually gives a warning with bad values... oh well whatever. just dont use the scipy version and its safe.\n", | |
"gd_ = get_group_delay(num, den, ω) \n", | |
"\n", | |
"_ = plot_transfer(ω, h, gd, h, gd_)\n", | |
"\n", | |
"h_0 = np.poly1d(den)(0)/np.poly1d(den)(1j * ω_0)\n", | |
"print(\"Gain at ω_0 = \" + str(ω_0) + \" rad/s: \" + str(np.abs(h_0)) + \" = \" + str(20 * np.log10(np.abs(h_0))) + \" dB, ang = \" + str(np.angle(h_0)) + \" rad (Bessel poly)\")" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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", | |
"text/plain": [ | |
"<Figure size 800x600 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"[z, p, k] = scipy.signal.tf2zpk(num, den)\n", | |
"plot_poles_zeros(z, p)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Observe that there is now one pole that is purely real (imaginary component equal to zero). This pole will be implemented by the RC circuit at the end." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Poles for stage 0: [-433815.40624319+225537.94864299j -433815.40624319-225537.94864299j]\n", | |
"\tnum = [3.43134875e+28], den = [1.00000000e+00 8.67630812e+05 2.39063173e+11]\n", | |
"Poles for stage 1: [-300862.96094798+462167.33585239j -300862.96094798-462167.33585239j]\n", | |
"\tnum = [3.43134875e+28], den = [1.00000000e+00 6.01725922e+05 3.04117168e+11]\n", | |
"Poles for stage 2: [np.complex128(-471966.57617477863+0j)]\n", | |
"\tnum = [3.43134875e+28], den = [1.00000000e+00 4.71966576e+05]\n" | |
] | |
} | |
], | |
"source": [ | |
"_p = [p[3:], p[:2], [p[2]]] # N.B. manually select pole pairs #replaced p[2] with [p[2]] because zpk2tf expect array (even with single element)\n", | |
"_num = filt_ord * [None]\n", | |
"_den = filt_ord * [None]\n", | |
"for i in range(len(_p)):\n", | |
" print(\"Poles for stage \" + str(i) + \": \" + str(_p[i]))\n", | |
" [_num[i], _den[i]] = scipy.signal.zpk2tf(z, _p[i], k)\n", | |
" print(\"\\tnum = \" + str(_num[i]) + \", den = \" + str(_den[i]))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We again choose $H_0=-0.5$ for the first stage and $H_0=-1$ for the second. For the first pair of poles we obtain:\n", | |
"\n", | |
"```Mathematica\n", | |
"H0 = -0.5\n", | |
"w0 = 2*Pi*50*^3\n", | |
"R1 = 100*^3\n", | |
"C2 = 47*^-12\n", | |
"Solve[{H0 == -R3/R1, 1/(2.42221637*w0^2) == C1*C2*R2*R3, 2.76175465/(2.42221637*w0) == C2*(R1*R2 + R2*R3 + R3*R1)/R1}, {C1, R2, R3}]\n", | |
"```\n", | |
"\n", | |
"```Mathematica\n", | |
"\n", | |
" -11\n", | |
"Out[5]= {{C1 -> 9.8093 10 , R2 -> 18146., R3 -> 50000.}}\n", | |
"\n", | |
"```\n", | |
"For the second pair of poles:\n", | |
"\n", | |
"```Mathematica\n", | |
"H0 = -1\n", | |
"w0 = 2*Pi*50*^3\n", | |
"R1 = 10*^3\n", | |
"C2 = 33*^-12\n", | |
"Solve[{H0 == -R3/R1, 1/(3.08135114*w0^2) == C1*C2*R2*R3, 1.9153531/(3.08135114*w0) == C2*(R1*R2 + R2*R3 + R3*R1)/R1}, {C1, R2, R3}]\n", | |
"```\n", | |
"\n", | |
"```Mathematica\n", | |
"\n", | |
" -10\n", | |
"Out[5]= {{C1 -> 3.98909 10 , R2 -> 24978.8, R3 -> 10000.}}\n", | |
"```" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The third stage is different because it has only a single pole. \n", | |
"\n", | |
"The corresponding form of the transfer function based on the Bessel polynomial (eq. 1) is:\n", | |
"\n", | |
"$$\\hspace{3cm}H(s) = \\frac{\\theta_1(0)}{\\theta_1(s/\\omega_0)} = \\frac{1.5023}{\\frac{s}{\\omega_0} + 1.5023}\\hspace{3cm}\\text{(eq. 6)}$$\n", | |
"\n", | |
"The transfer function of the circuit is now that of an RC filter (which replaces the transfer function of the MFB filter, that is, eq. 3).\n", | |
"\n", | |
"<img src=\"https://gist.github.com/turingbirds/5fa6275781232c1c4e563a43c4042bf2/raw/f914b95490d06ac91e847c9957d2ab4a1bcb8062/rc_lowpass_filter.png\">\n", | |
"\n", | |
"The transfer function for an RC filter is:\n", | |
"\n", | |
"$$\\hspace{3cm}H(s) = \\frac{1}{1 + RCs}\\hspace{3cm}\\text{(eq. 7)}$$\n", | |
"\n", | |
"By equating the $H(s)$ obtained from circuit analysis (eq. 7) and $H(s)$ obtained from the Bessel polynomial (eq. 5), we obtain the following relationship:\n", | |
"\n", | |
"$$\n", | |
"\\begin{align*}\n", | |
"RC=\\frac{1}{1.5023\\omega_0}\n", | |
"\\end{align*}\n", | |
"$$\n", | |
"\n", | |
"Which can be trivially solved to yield the value for $C$:\n", | |
"\n", | |
"```Mathematica\n", | |
"w0 = 2*Pi*50*^3\n", | |
"R = 100\n", | |
"Solve[{R*C == 1/(1.5023*w0)}, {C}]\n", | |
"```\n", | |
"\n", | |
"```Mathematica\n", | |
"\n", | |
" -8\n", | |
"{{C -> 2.11882 10 }}\n", | |
"```\n", | |
"\n", | |
"As a final check, note that $Q$ for the first stage is approximately $Q_1\\approx0.5635$, and $Q_2\\approx0.9164$ for the second. Given that $Q_1<Q_2$, the order of the stages is appropriate. (Note that a Q factor is not defined for a first-order system such as the RC filter at the end)." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Filling in all the component values, the final circuit looks as below. It is designed for a single supply of 3.3 V and an ADC reference voltage of 2.5 V. Each op-amp is biased by half the reference (1.25 V). Op-amps were simulated at SPICE \"level 2\" with an open-loop gain of 10E6 V/V, gain-bandwidth product equal to 100 MHz and slew rate 100 V/µs.\n", | |
"\n", | |
"After simulating the circuit, it is easy to verify the -3 dB point at 50 kHz and the overall roll-off of 30 dB/octave (see the next section regarding roll-off).\n", | |
"\n", | |
"<img src=\"https://gist.github.com/turingbirds/5fa6275781232c1c4e563a43c4042bf2/raw/f914b95490d06ac91e847c9957d2ab4a1bcb8062/multiple_feedback_low_pass_fifth_order_filter_op_amp.png\">\n", | |
"\n", | |
"The group delay is indeed perfectly flat up until near the cutoff point:\n", | |
"\n", | |
"<img src=\"https://gist.github.com/turingbirds/5fa6275781232c1c4e563a43c4042bf2/raw/f914b95490d06ac91e847c9957d2ab4a1bcb8062/multiple_feedback_low_pass_fifth_order_filter_op_amp_response.png\">\n", | |
"\n", | |
"Clearly, the given component values are unrealistic for real-life applications. To find more practical values might require experimenting a bit with the fixed component values fed to the numerical solver in Mathematica. For example, if we had picked $C_1=390\\,\\text{pF}$ and $C_2=33\\,\\text{pF}$ in the second MFB stage, one solution is $R_1=R_3=10287\\,\\text{Ω}$ and $R_2=24835\\,\\text{Ω}$, both of which are within 5% of standard values ($10\\,\\text{kΩ}$ and $25\\,\\text{kΩ}$)." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Design for target attenuation\n", | |
"-----------------------------\n", | |
"\n", | |
"In general, we might want to our design to achieve a certain, given, attenuation at a certain frequency, say:\n", | |
"\n", | |
"$$H(j\\omega_1) = \\alpha\\,\\text{dB}$$\n", | |
"\n", | |
"Every pole in the filter contributes a roll-off of 6 dB/octave. So for a second-order filter the roll-off will be 12 dB/octave, and for the fifth-order filter designed above the roll-off is 30 dB/octave.\n", | |
"\n", | |
"In general, a visual method is probably easiest. Plot the point ($\\omega_1$, $\\alpha$) on top of the transfer functions for a given $\\omega_0$ and increasing filter order. Then pick the first filter order for which the transfer function lies below the point. In the example below, we would need at least a fifth-order filter:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 14, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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", | |
"text/plain": [ | |
"<Figure size 800x600 with 3 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"ω_0 = 2*np.pi*50E3 # [rad/s]\n", | |
"ω_1 = 2*np.pi*1E6 # [rad/s]\n", | |
"ω = scipy.signal.findfreqs(num, den, 1000, kind=\"ba\")\n", | |
"α = -50 # dB\n", | |
"N = 6 # plot filter orders 1..N\n", | |
"\n", | |
"h = np.empty((N, ω.size), dtype=complex) #np.complex deprecated\n", | |
"gd = np.empty((N, ω.size), dtype=float) #for consistency i guess\n", | |
"for n in range(1, N+1):\n", | |
" [num, den] = scipy.signal.bessel(n, ω_0, \"lowpass\", analog=True, output=\"ba\", norm=\"mag\")\n", | |
" h[n - 1, :] = np.poly1d(den)(0)/np.poly1d(den)(1j * ω)\n", | |
" gd[n - 1, :] = get_group_delay(num, den, ω) # group delay calculated from the transfer function coefficients. this was left as TODO\n", | |
"\n", | |
"ax = plot_transfer(ω, h.T, gd.T, line_labels=[\"Order \" + str(i) for i in range(1, N+1)])\n", | |
"_ = ax[0].scatter(ω_1, 10**(α/10), s=80, marker=\"x\")" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"References\n", | |
"==========\n", | |
"\n", | |
"1. SciPy reference on Bessel functions: https://docs.scipy.org/doc/scipy-0.19.0/reference/generated/scipy.signal.bessel.html\n", | |
"2. Wikipedia on Q factor: https://en.wikipedia.org/wiki/Q_factor\n", | |
"3. Texas Instruments Application Report SLOA049B - Active Low-Pass Filter Design - September 2002: http://www.ti.com/lit/an/sloa049b/sloa049b.pdf \n", | |
"4. Ron Mancini, Op Amps for Everyone, chapter 16: Active Filter Design Techniques. Texas Instruments, August 2002: https://focus.ti.com/lit/ml/sloa088/sloa088.pdf\n", | |
"5. Circuit Design: Know It All, Ashby et al. Elsevier 2008" | |
] | |
} | |
], | |
"metadata": { | |
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"display_name": ".venv", | |
"language": "python", | |
"name": "python3" | |
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"name": "ipython", | |
"version": 3 | |
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"version": "3.11.3" | |
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Version 4 | |
SHEET 1 1496 1228 | |
WIRE -48 256 -160 256 | |
WIRE 128 256 32 256 | |
WIRE -336 272 -336 256 | |
WIRE 384 272 272 272 | |
WIRE 560 272 464 272 | |
WIRE 32 336 16 336 | |
WIRE 128 336 128 256 | |
WIRE 128 336 96 336 | |
WIRE 464 352 448 352 | |
WIRE 560 352 560 272 | |
WIRE 560 352 528 352 | |
WIRE 64 416 64 400 | |
WIRE -320 432 -336 432 | |
WIRE -272 432 -320 432 | |
WIRE -160 432 -160 256 | |
WIRE -160 432 -192 432 | |
WIRE -112 432 -160 432 | |
WIRE 16 432 16 336 | |
WIRE 16 432 -32 432 | |
WIRE 32 432 16 432 | |
WIRE 496 432 496 416 | |
WIRE -336 448 -336 432 | |
WIRE 128 448 128 336 | |
WIRE 128 448 96 448 | |
WIRE 160 448 128 448 | |
WIRE 272 448 272 272 | |
WIRE 272 448 240 448 | |
WIRE 320 448 272 448 | |
WIRE 448 448 448 352 | |
WIRE 448 448 400 448 | |
WIRE 464 448 448 448 | |
WIRE 32 464 16 464 | |
WIRE 560 464 560 352 | |
WIRE 560 464 528 464 | |
WIRE 608 464 560 464 | |
WIRE 720 464 688 464 | |
WIRE 784 464 720 464 | |
WIRE 800 464 784 464 | |
WIRE 16 480 16 464 | |
WIRE 464 480 448 480 | |
WIRE 448 496 448 480 | |
FLAG -336 352 0 | |
FLAG -336 256 vcc | |
FLAG 64 480 0 | |
FLAG 64 400 vcc | |
FLAG 16 560 0 | |
FLAG -336 528 0 | |
FLAG -160 496 0 | |
FLAG 496 496 0 | |
FLAG 496 416 vcc | |
FLAG 448 576 0 | |
FLAG 272 512 0 | |
FLAG 720 528 0 | |
FLAG 784 464 Vout | |
FLAG -320 432 Vin | |
SYMBOL voltage -336 256 R0 | |
WINDOW 0 45 43 Left 2 | |
WINDOW 3 46 73 Left 2 | |
WINDOW 123 0 0 Left 2 | |
WINDOW 39 0 0 Left 2 | |
SYMATTR InstName V1 | |
SYMATTR Value 3.3 | |
SYMBOL res -288 448 R270 | |
WINDOW 0 32 56 VTop 2 | |
WINDOW 3 0 56 VBottom 2 | |
SYMATTR InstName R1 | |
SYMATTR Value 100k | |
SYMBOL Opamps\\UniversalOpamp2 64 448 R0 | |
SYMATTR InstName U1 | |
SYMATTR Value2 Avol=10Meg GBW=100Meg Slew=100Meg | |
SYMBOL voltage -336 432 R0 | |
WINDOW 123 36 90 Left 2 | |
WINDOW 0 39 62 Left 2 | |
WINDOW 3 36 120 Left 2 | |
SYMATTR Value2 AC 1 | |
SYMATTR InstName V2 | |
SYMATTR Value SINE(1.25 1.25 50E3 0 0) | |
SYMBOL voltage 16 464 R0 | |
WINDOW 0 43 68 Left 2 | |
WINDOW 3 39 94 Left 2 | |
SYMATTR InstName V3 | |
SYMATTR Value 1.25 | |
SYMBOL cap 96 320 R90 | |
WINDOW 0 12 58 VBottom 2 | |
WINDOW 3 -13 -3 VTop 2 | |
SYMATTR InstName C2 | |
SYMATTR Value 47p | |
SYMBOL res -128 448 R270 | |
WINDOW 0 32 56 VTop 2 | |
WINDOW 3 0 56 VBottom 2 | |
SYMATTR InstName R2 | |
SYMATTR Value 18146 | |
SYMBOL res -64 272 R270 | |
WINDOW 0 32 56 VTop 2 | |
WINDOW 3 0 56 VBottom 2 | |
SYMATTR InstName R3 | |
SYMATTR Value 50k | |
SYMBOL res 144 464 R270 | |
WINDOW 0 32 56 VTop 2 | |
WINDOW 3 0 56 VBottom 2 | |
SYMATTR InstName R4 | |
SYMATTR Value 10k | |
SYMBOL Opamps\\UniversalOpamp2 496 464 R0 | |
SYMATTR InstName U2 | |
SYMATTR Value2 Avol=10Meg GBW=100Meg Slew=100Meg | |
SYMBOL voltage 448 480 R0 | |
WINDOW 0 45 63 Left 2 | |
WINDOW 3 43 90 Left 2 | |
SYMATTR InstName V4 | |
SYMATTR Value 1.25 | |
SYMBOL cap 528 336 R90 | |
WINDOW 0 11 64 VBottom 2 | |
WINDOW 3 -13 -5 VTop 2 | |
SYMATTR InstName C4 | |
SYMATTR Value 33p | |
SYMBOL res 304 464 R270 | |
WINDOW 0 32 56 VTop 2 | |
WINDOW 3 0 56 VBottom 2 | |
SYMATTR InstName R5 | |
SYMATTR Value 24979 | |
SYMBOL cap 256 448 R0 | |
WINDOW 0 47 62 Left 2 | |
WINDOW 3 48 89 Left 2 | |
SYMATTR InstName C3 | |
SYMATTR Value 398.90p | |
SYMBOL res 368 288 R270 | |
WINDOW 0 32 56 VTop 2 | |
WINDOW 3 0 56 VBottom 2 | |
SYMATTR InstName R6 | |
SYMATTR Value 10k | |
SYMBOL cap -176 432 R0 | |
WINDOW 0 44 53 Left 2 | |
WINDOW 3 45 79 Left 2 | |
SYMATTR InstName C1 | |
SYMATTR Value 98.093p | |
SYMBOL res 704 448 R90 | |
WINDOW 0 0 56 VBottom 2 | |
WINDOW 3 32 56 VTop 2 | |
SYMATTR InstName R7 | |
SYMATTR Value 100 | |
SYMBOL cap 704 464 R0 | |
WINDOW 0 52 20 Left 2 | |
WINDOW 3 51 46 Left 2 | |
SYMATTR InstName C5 | |
SYMATTR Value 21.188n | |
TEXT -344 152 Left 2 !;tran 0 1.08E-3 1e-3 1E-6 | |
TEXT -344 176 Left 2 !.ac oct 100 1 100E6 |
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