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@turingbirds
Last active March 21, 2024 18:11
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline \n",
"import numpy as np\n",
"import scipy.signal\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"mpl.rcParams['lines.linewidth'] = 2\n",
"mpl.rcParams.update({'font.size': 12})"
]
},
{
"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",
"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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stp5/s23dBTSsf4fE6i+I1dVE1L4Hi95jx6JEnh71CiePimFaeoSsfhCD2tF6DpYCGlAu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\nMWaQ/w+brXr9bZFCGAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f3ad3f45be0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"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",
" ax_phase.semilogx(ω, np.angle(h))\n",
" if not gd is None:\n",
" ax_delay.semilogx(ω, gd)\n",
"\n",
" # alternate plot\n",
" if not h_ is None:\n",
" ax_mag.loglog(ω, np.abs(h_), '--')\n",
" ax_phase.semilogx(ω, np.angle(h_), '--')\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_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",
"\n",
"# alternate way: plot the Bessel polynomial directly\n",
"h_ = np.poly1d(den)(0)/np.poly1d(den)(1j * ω)\n",
"gd_ = np.nan * np.ones_like(ω) # XXX: TODO\n",
"\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: 0.707106781187 = -3.01029995664 dB, ang = -1.29730903665 rad (Bessel poly)\n",
"Gain at ω_0 = 1.0 rad/s: 0.707106781187 = -3.01029995664 dB, ang = -1.29730903665 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": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAg0AAAF9CAYAAACH0lvIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n1WLlGwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f3ad19d3908>"
]
},
"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": {
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RVctEZBbwoqqmtivzbeAyVc3u5PxmYKyqbvJuDwc2A56O/VREZB5OUxEpKSmnPPfccz79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fL/DL8v5p398wcTMG/5AfzjBxNx91ubkOb3YUh38+nQAPDOzdMxWTFzR0tZrXgwQz2ICIO65Qgt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\nFTMzM2tZ/wfwgOV+wng6BwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f3ad1a63128>"
]
},
"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",
"[_, gd] = scipy.signal.group_delay([num, den], ω)\n",
"\n",
"_ = plot_transfer(ω, h, gd)"
]
},
{
"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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ASJ+Oo9EiYjGwDrg0M1uZeTfwOeBXZ/fIJEmae6Zz5eNS4E8i4vcyc3e/DqihTgZ+kJkP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\nJElFGT4kSVJRhg9JklSU4UOSJBX1/wEkWbJW1Fn7+AAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f3ad1b07ef0>"
]
},
"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+128883.74986156j -430419.50313801-128883.74986156j]\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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AhlvuPW3v1y7rqZRSJ/Y70FrPBGaC0SGxvo4eSUlJp9WxsKU7JO7atYvMzEwG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\ntQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f3ad1c0c908>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"h_partial = np.empty((len(ω), len(_den)), dtype=np.complex)\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] = scipy.signal.group_delay([_num[i], _den[i]], ω)[1]\n",
"\n",
"h_reconstructed = np.prod(h_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",
"_ = plot_transfer(ω, h_plot, gd_plot, line_labels=[\"full\", \"stage 1\", \"stage 2\", \"reconstructed\"])"
]
},
{
"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": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Gain at ω_0 = 314159.2653589793 rad/s: 0.707106781187 = -3.01029995664 dB, ang = -2.42642478822 rad (Bessel poly)\n"
]
},
{
"data": {
"image/png": 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IxZ9EZD+Qf4IiCcChdp5LAQ6cYmgd6UQ/U7DUfzJ1tOeatpRtrUwotg0I/vZx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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f3ad1c85fd0>"
]
},
"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",
"\n",
"_ = plot_transfer(ω, 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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SpCwYSiRJUhayCCURMRQR10XEzojYGxF/ExGrW455S0TcHxH7I+KOiDixpf+XIuLJiNgd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\ngGtSSje2e63GS9K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"text/plain": [
"<matplotlib.figure.Figure at 0x7f3ad1ca9c88>"
]
},
"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+225537.948643j -433815.40624319-225537.948643j]\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: (-471966.576175+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\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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LUe/IkPAhfDzwYzaN2cTTNz9NmEcYqYWpfHrkU6JWRPGnjX9i7bm1FFnql5m2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HCgXUQ0kRWtZ2Q0yiwliqGbTkUi8OtTcekyaFFSaSCV2ngyldEk9oYc7A05aPAl0+rTs7fJd8Tf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\n/ZvR3Kv/BpwIpBhjilppe0q1qiP6P7pSrWgK8D/gB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"text/plain": [
"<matplotlib.figure.Figure at 0x7f3ad1ca4da0>"
]
},
"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=np.complex)\n",
"\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",
"\n",
"ax = plot_transfer(ω, h.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": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.4.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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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