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$P_\\mathrm{out} = 4.867$ kW, 49.33 A RMS per winding", "align": 1 } }, { "type": "rect", "position": { "x": 6231.102, "y": 457.874 }, "size": { "x": 604.724, "y": 22.677 }, "stroke": { "opacity": 0 }, "text": { "text": "$R_\\mathrm{cu}(f)$ denotes frequency-dependent loss; leakage, magnetizing and core-loss branches omitted", "align": 1 } } ] }, { "type": "group", "components": [ { "type": "node", "id": "ocirc", "position": { "x": 250.0, "y": 1650.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 250.0, "y": 1763.386 } }, { "type": "open", "points": [ { "x": 250.0, "y": 1650.0 }, { "x": 250.0, "y": 1763.386 } ], "voltage": { "label": "v_\\mathrm{i}" } }, { "type": "node", "id": "ocirc", "position": { "x": 438.976, "y": 1650.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 438.976, "y": 1763.386 } }, { "type": "open", "points": [ { "x": 438.976, "y": 1650.0 }, { "x": 438.976, "y": 1763.386 } ], "voltage": { "label": "v_\\mathrm{o}" } }, { "type": "wire", "points": [ { "x": 250.0, "y": 1650.0 }, { "x": 287.795, "y": 1650.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 287.795, "y": 1650.0 }, { "x": 363.38599999999997, "y": 1650.0 } ], "label": { "value": "R" } }, { "type": "wire", "points": [ { "x": 363.38599999999997, "y": 1650.0 }, { "x": 438.976, "y": 1650.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "capacitor", "points": [ { "x": 382.283, "y": 1650.0 }, { "x": 382.283, "y": 1763.386 } ], "label": { "value": "C" } }, { "type": "wire", "points": [ { "x": 250.0, "y": 1763.386 }, { "x": 438.976, "y": 1763.386 } ], "directions": [ "--" ] }, { "type": "node", "id": "ground", "position": { "x": 344.488, "y": 1763.386 } }, { "type": "node", "id": "circ", "position": { "x": 382.283, "y": 1650.0 } }, { "type": "node", "id": "circ", "position": { "x": 382.283, "y": 1763.386 } }, { "type": "node", "id": "circ", "position": { "x": 344.488, "y": 1763.386 } }, { "type": "rect", "position": { "x": 231.102, "y": 1793.622 }, "size": { "x": 226.772, "y": 22.677 }, "stroke": { "opacity": 0 }, "text": { "text": "$\\tau = RC;\\; H(s) = 1/(1 + sRC)$", "align": 1 } }, { "type": "path", "id": "european voltage source", "points": [ { "x": 590.1569999999999, "y": 1763.386 }, { "x": 590.1569999999999, "y": 1650.0 } ], "label": { "value": "V_\\mathrm{in} = 5\\,\\mathrm{V}" } }, { "type": "wire", "points": [ { "x": 590.1569999999999, "y": 1650.0 }, { "x": 643.071, "y": 1650.0 }, { "x": 643.071, "y": 1675.89 }, { "x": 707.134, "y": 1675.89 } ], "directions": [ "--", "--", "--" ] }, { "type": "node", "id": "spdt", "position": { "x": 684.646, "y": 1687.795 }, "rotation": 180, "label": { "value": "PWM", "anchor": "south", "position": "north" } }, { "type": "wire", "points": [ { "x": 707.134, "y": 1699.701 }, { "x": 643.071, "y": 1699.701 }, { "x": 643.071, "y": 1763.386 } ], "directions": [ "--", "--" ] }, { "type": "wire", "points": [ { "x": 662.1569999999999, "y": 1687.795 }, { "x": 722.441, "y": 1687.795 }, { "x": 722.441, "y": 1650.0 }, { "x": 741.3389999999999, "y": 1650.0 } ], "directions": [ "--", "--", "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 741.3389999999999, "y": 1650.0 }, { "x": 816.929, "y": 1650.0 } ], "label": { "value": "R = 10\\,\\Omega" } }, { "type": "wire", "points": [ { "x": 816.929, "y": 1650.0 }, { "x": 892.52, "y": 1650.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "capacitor", "points": [ { "x": 835.827, "y": 1650.0 }, { "x": 835.827, "y": 1763.386 } ], "label": { "value": "C = 10\\,\\mu\\mathrm{F}" } }, { "type": "wire", "points": [ { "x": 590.1569999999999, "y": 1763.386 }, { "x": 892.52, "y": 1763.386 } ], "directions": [ "--" ] }, { "type": "node", "id": "ground", "position": { "x": 741.3389999999999, "y": 1763.386 } }, { "type": "open", "points": [ { "x": 892.52, "y": 1650.0 }, { "x": 892.52, "y": 1763.386 } ], "voltage": { "label": "v_\\mathrm{o}" } }, { "type": "node", "id": "ocirc", "position": { "x": 892.52, "y": 1650.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 892.52, "y": 1763.386 } }, { "type": "node", "id": "circ", "position": { "x": 835.827, "y": 1650.0 } }, { "type": "node", "id": "circ", "position": { "x": 835.827, "y": 1763.386 } }, { "type": "node", "id": "circ", "position": { "x": 643.071, "y": 1763.386 } }, { "type": "node", "id": "circ", "position": { "x": 741.3389999999999, "y": 1763.386 } }, { "type": "rect", "position": { "x": 627.953, "y": 1714.252 }, "size": { "x": 75.591, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "0 V", "align": 1, "fontSize": "normalsize" } }, { "type": "rect", "position": { "x": 571.26, "y": 1793.622 }, "size": { "x": 340.157, "y": 22.677 }, "stroke": { "opacity": 0 }, "text": { "text": "100 kHz; $D = 0.4$; $\\tau = 100\\,\\mu$s. The low state connects to 0 V, it does not open the input.", "align": 1 } } ] }, { "type": "group", "components": [ { "type": "node", "id": "ocirc", "position": { "x": 2250.0, "y": 1650.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 2250.0, "y": 1763.386 } }, { "type": "open", "points": [ { "x": 2250.0, "y": 1650.0 }, { "x": 2250.0, "y": 1763.386 } ], "voltage": { "label": "v_\\mathrm{i}" } }, { "type": "node", "id": "ocirc", "position": { "x": 2514.567, "y": 1650.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 2514.567, "y": 1763.386 } }, { "type": "open", "points": [ { "x": 2514.567, "y": 1650.0 }, { "x": 2514.567, "y": 1763.386 } ], "voltage": { "label": "v_\\mathrm{o}" } }, { "type": "wire", "points": [ { "x": 2250.0, "y": 1650.0 }, { "x": 2287.795, "y": 1650.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "cute inductor", "points": [ { "x": 2287.795, "y": 1650.0 }, { "x": 2363.386, "y": 1650.0 } ], "label": { "value": "L = 22.51\\,\\mu\\mathrm{H}" }, "current": { "label": "i_L" } }, { "type": "wire", "points": [ { "x": 2363.386, "y": 1650.0 }, { "x": 2514.567, "y": 1650.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "capacitor", "points": [ { "x": 2401.181, "y": 1650.0 }, { "x": 2401.181, "y": 1763.386 } ], "label": { "value": "C = 0.7034\\,\\mu\\mathrm{F}" } }, { "type": "path", "id": "european resistor", "points": [ { "x": 2457.874, "y": 1650.0 }, { "x": 2457.874, "y": 1763.386 } ], "label": { "value": "R = 4\\,\\Omega" } }, { "type": "wire", "points": [ { "x": 2250.0, "y": 1763.386 }, { "x": 2514.567, "y": 1763.386 } ], "directions": [ "--" ] }, { "type": "node", "id": "circ", "position": { "x": 2401.181, "y": 1650.0 } }, { "type": "node", "id": "circ", "position": { "x": 2457.874, "y": 1650.0 } }, { "type": "node", "id": "circ", "position": { "x": 2401.181, "y": 1763.386 } }, { "type": "node", "id": "circ", "position": { "x": 2457.874, "y": 1763.386 } }, { "type": "rect", "position": { "x": 2231.102, "y": 1793.622 }, "size": { "x": 302.362, "y": 22.677 }, "stroke": { "opacity": 0 }, "text": { "text": "Class-D example; the load supplies the damping, winding resistance omitted", "align": 1 } } ] }, { "type": "group", "components": [ { "type": "rect", "position": { "x": 4250.0, "y": 1650.0 }, "size": { "x": 151.181, "y": 113.386 }, "text": { "text": "Ideal supply\n+ source / input filter\n(source subsystem)", "align": 1, "fontSize": "normalsize" } }, { "type": "rect", "position": { "x": 4514.567, "y": 1650.0 }, "size": { "x": 151.181, "y": 113.386 }, "text": { "text": "Regulated converter\n(closed-loop input model)", "align": 1, "fontSize": "normalsize" } }, { "type": "rect", "position": { "x": 4703.543, "y": 1678.346 }, "size": { "x": 56.693, "y": 56.693 }, "text": { "text": "Load", "align": 1, "fontSize": "normalsize" } }, { "type": "wire", "points": [ { "x": 4401.181, "y": 1672.677 }, { "x": 4514.567, "y": 1672.677 } ], "directions": [ "--" ] }, { "type": "wire", "points": [ { "x": 4401.181, "y": 1740.709 }, { "x": 4514.567, "y": 1740.709 } ], "directions": [ "--" ] }, { "type": "wire", "points": [ { "x": 4665.748, "y": 1706.693 }, { "x": 4703.543, "y": 1706.693 } ], "directions": [ "--" ] }, { "type": "wire", "points": [ { "x": 4423.858, "y": 1672.677 }, { "x": 4491.89, "y": 1672.677 } ], "directions": [ "--" ] }, { "type": "rect", "position": { "x": 4435.197, "y": 1648.11 }, "size": { "x": 45.354, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "$i_\\mathrm{in}$", "align": 1, "fontSize": "normalsize" } }, { "type": "open", "points": [ { "x": 4457.874, "y": 1672.677 }, { "x": 4457.874, "y": 1740.709 } ], "voltage": { "label": "v_\\mathrm{in}" } }, { "type": "node", "id": "ocirc", "position": { "x": 4457.874, "y": 1672.677 } }, { "type": "node", "id": "ocirc", "position": { "x": 4457.874, "y": 1740.709 } }, { "type": "rect", "position": { "x": 4344.488, "y": 1778.504 }, "size": { "x": 151.181, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "$Z_\\mathrm{s}(s)$: look back $\\leftarrow$", "align": 1 } }, { "type": "rect", "position": { "x": 4450.315, "y": 1778.504 }, "size": { "x": 151.181, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "$\\rightarrow$ $Z_\\mathrm{in}(s)$: look in", "align": 1 } }, { "type": "rect", "position": { "x": 4382.283, "y": 1619.764 }, "size": { "x": 151.181, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "Input interface", "align": 1 } }, { "type": "rect", "position": { "x": 4231.102, "y": 1808.74 }, "size": { "x": 491.339, "y": 30.236 }, "stroke": { "opacity": 0 }, "text": { "text": "For $Z_\\mathrm{s}$: deactivate the independent source and disconnect the converter. For $Z_\\mathrm{in}$: keep the operating point and control.", "align": 1 } } ] }, { "type": "group", "components": [ { "type": "path", "id": "european voltage source", "points": [ { "x": 6250.0, "y": 1801.181 }, { "x": 6250.0, "y": 1650.0 } ], "label": { "value": "V_\\mathrm{s} = 12.25\\,\\mathrm{V}" } }, { "type": "wire", "points": [ { "x": 6250.0, "y": 1650.0 }, { "x": 6287.795, "y": 1650.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 6287.795, "y": 1650.0 }, { "x": 6344.488, "y": 1650.0 } ], "label": { "value": "r = 0.05\\,\\Omega" } }, { "type": "path", "id": "cute inductor", "points": [ { "x": 6344.488, "y": 1650.0 }, { "x": 6420.079, "y": 1650.0 } ], "label": { "value": "L = 100\\,\\mu\\mathrm{H}" }, "current": { "label": "i_L" } }, { "type": "wire", "points": [ { "x": 6420.079, "y": 1650.0 }, { "x": 6590.157, "y": 1650.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "capacitor", "points": [ { "x": 6457.874, "y": 1650.0 }, { "x": 6457.874, "y": 1801.181 } ], "label": { "value": "C = 100\\,\\mu\\mathrm{F}" } }, { "type": "path", "id": "european resistor", "points": [ { "x": 6533.465, "y": 1650.0 }, { "x": 6533.465, "y": 1718.031 } ], "label": { "value": "R_\\mathrm{d} = 1\\,\\Omega" } }, { "type": "path", "id": "capacitor", "points": [ { "x": 6533.465, "y": 1733.15 }, { "x": 6533.465, "y": 1801.181 } ], "label": { "value": "C_\\mathrm{d} = 400\\,\\mu\\mathrm{F}" } }, { "type": "wire", "points": [ { "x": 6533.465, "y": 1718.031 }, { "x": 6533.465, "y": 1733.15 } ], "directions": [ "--" ] }, { "type": "wire", "points": [ { "x": 6250.0, "y": 1801.181 }, { "x": 6590.157, "y": 1801.181 } ], "directions": [ "--" ] }, { "type": "rect", "position": { "x": 6590.157, "y": 1668.898 }, "size": { "x": 113.386, "y": 113.386 }, "text": { "text": "Converter\n$P_\\mathrm{in} = 60$ W\n$I = 5$ A DC\nlocal $Z_\\mathrm{in} = -2.4\\,\\Omega$", "align": 1, "fontSize": "normalsize" } }, { "type": "wire", "points": [ { "x": 6590.157, "y": 1650.0 }, { "x": 6609.055, "y": 1650.0 }, { "x": 6609.055, "y": 1668.898 } ], "directions": [ "--", "--" ] }, { "type": "wire", "points": [ { "x": 6590.157, "y": 1801.181 }, { "x": 6609.055, "y": 1801.181 }, { "x": 6609.055, "y": 1782.283 } ], "directions": [ "--", "--" ] }, { "type": "open", "points": [ { "x": 6575.039, "y": 1665.118 }, { "x": 6575.039, "y": 1786.063 } ], "voltage": { "label": "v = 12\\,\\mathrm{V}" } }, { "type": "node", "id": "circ", "position": { "x": 6457.874, "y": 1650.0 } }, { "type": "node", "id": "circ", "position": { "x": 6533.465, "y": 1650.0 } }, { "type": "node", "id": "circ", "position": { "x": 6457.874, "y": 1801.181 } }, { "type": "node", "id": "circ", "position": { "x": 6533.465, "y": 1801.181 } }, { "type": "node", "id": "circ", "position": { "x": 6590.157, "y": 1650.0 } }, { "type": "node", "id": "circ", "position": { "x": 6590.157, "y": 1801.181 } }, { "type": "rect", "position": { "x": 6488.11, "y": 1619.764 }, "size": { "x": 113.386, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "optional damping", "align": 1 } }, { "type": "rect", "position": { "x": 6231.102, "y": 1831.417 }, "size": { "x": 491.339, "y": 30.236 }, "stroke": { "opacity": 0 }, "text": { "text": "C belongs to the source/filter side. Without damping omit only $R_\\mathrm{d}$-$C_\\mathrm{d}$; $r$ remains in both cases.", "align": 1 } } ] }, { "type": "group", "components": [ { "type": "node", "id": "ocirc", "position": { "x": 250.0, "y": 3050.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 250.0, "y": 3163.386 } }, { "type": "open", "points": [ { "x": 250.0, "y": 3050.0 }, { "x": 250.0, "y": 3163.386 } ], "voltage": { "label": "v_\\mathrm{a}" } }, { "type": "node", "id": "ocirc", "position": { "x": 514.567, "y": 3050.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 514.567, "y": 3163.386 } }, { "type": "open", "points": [ { "x": 514.567, "y": 3050.0 }, { "x": 514.567, "y": 3163.386 } ], "voltage": { "label": "v_\\mathrm{v}" } }, { "type": "wire", "points": [ { "x": 250.0, "y": 3050.0 }, { "x": 287.795, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "capacitor", "points": [ { "x": 287.795, "y": 3050.0 }, { "x": 363.38599999999997, "y": 3050.0 } ], "label": { "value": "C_\\mathrm{m} = 3.54\\,\\mathrm{pF}" } }, { "type": "wire", "points": [ { "x": 363.38599999999997, "y": 3050.0 }, { "x": 514.567, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 401.18100000000004, "y": 3050.0 }, { "x": 401.18100000000004, "y": 3163.386 } ], "label": { "value": "R_\\mathrm{v} = 50\\,\\Omega" } }, { "type": "path", "id": "capacitor", "points": [ { "x": 457.874, "y": 3050.0 }, { "x": 457.874, "y": 3163.386 } ], "label": { "value": "C_\\mathrm{v} = 10\\,\\mathrm{pF}" } }, { "type": "wire", "points": [ { "x": 250.0, "y": 3163.386 }, { "x": 514.567, "y": 3163.386 } ], "directions": [ "--" ] }, { "type": "node", "id": "ground", "position": { "x": 382.283, "y": 3163.386 } }, { "type": "node", "id": "circ", "position": { "x": 401.18100000000004, "y": 3050.0 } }, { "type": "node", "id": "circ", "position": { "x": 457.874, "y": 3050.0 } }, { "type": "node", "id": "circ", "position": { "x": 401.18100000000004, "y": 3163.386 } }, { "type": "node", "id": "circ", "position": { "x": 457.874, "y": 3163.386 } }, { "type": "node", "id": "circ", "position": { "x": 382.283, "y": 3163.386 } }, { "type": "rect", "position": { "x": 231.102, "y": 3193.622 }, "size": { "x": 302.362, "y": 22.677 }, "stroke": { "opacity": 0 }, "text": { "text": "All voltages refer to the same quiet reference (defined lumped victim model)", "align": 1 } } ] }, { "type": "group", "components": [ { "type": "path", "id": "european voltage source", "points": [ { "x": 2250.0, "y": 3163.386 }, { "x": 2250.0, "y": 3050.0 } ], "label": { "value": "V_\\mathrm{Th} = 6\\,\\mathrm{V}" } }, { "type": "wire", "points": [ { "x": 2250.0, "y": 3050.0 }, { "x": 2287.795, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 2287.795, "y": 3050.0 }, { "x": 2363.386, "y": 3050.0 } ], "label": { "value": "Z_\\mathrm{Th} = 500\\,\\Omega" } }, { "type": "wire", "points": [ { "x": 2363.386, "y": 3050.0 }, { "x": 2438.976, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 2438.976, "y": 3050.0 }, { "x": 2438.976, "y": 3163.386 } ], "label": { "value": "Z_\\mathrm{L} = 1\\,\\mathrm{k}\\Omega" } }, { "type": "wire", "points": [ { "x": 2250.0, "y": 3163.386 }, { "x": 2438.976, "y": 3163.386 } ], "directions": [ "--" ] }, { "type": "wire", "points": [ { "x": 2378.504, "y": 3050.0 }, { "x": 2423.858, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "rect", "position": { "x": 2378.504, "y": 3025.433 }, "size": { "x": 45.354, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "$i_\\mathrm{out}$", "align": 1, "fontSize": "normalsize" } }, { "type": "open", "points": [ { "x": 2401.181, "y": 3065.118 }, { "x": 2401.181, "y": 3148.268 } ], "voltage": { "label": "v_\\mathrm{ab}" } }, { "type": "node", "id": "ocirc", "position": { "x": 2401.181, "y": 3050.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 2401.181, "y": 3163.386 } }, { "type": "rect", "position": { "x": 2231.102, "y": 3015.984 }, "size": { "x": 226.772, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "Th\u00e9venin: voltage source + series impedance", "align": 1 } }, { "type": "path", "id": "european current source", "points": [ { "x": 2552.362, "y": 3163.386 }, { "x": 2552.362, "y": 3050.0 } ], "label": { "value": "I_\\mathrm{N} = 12\\,\\mathrm{mA}" } }, { "type": "wire", "points": [ { "x": 2552.362, "y": 3050.0 }, { "x": 2703.543, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 2609.055, "y": 3050.0 }, { "x": 2609.055, "y": 3163.386 } ], "label": { "value": "Z_\\mathrm{N} = 500\\,\\Omega" } }, { "type": "path", "id": "european resistor", "points": [ { "x": 2703.543, "y": 3050.0 }, { "x": 2703.543, "y": 3163.386 } ], "label": { "value": "Z_\\mathrm{L} = 1\\,\\mathrm{k}\\Omega" } }, { "type": "wire", "points": [ { "x": 2552.362, "y": 3163.386 }, { "x": 2703.543, "y": 3163.386 } ], "directions": [ "--" ] }, { "type": "wire", "points": [ { "x": 2643.071, "y": 3050.0 }, { "x": 2688.425, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "rect", "position": { "x": 2643.071, "y": 3025.433 }, "size": { "x": 45.354, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "$i_\\mathrm{out}$", "align": 1, "fontSize": "normalsize" } }, { "type": "open", "points": [ { "x": 2665.748, "y": 3065.118 }, { "x": 2665.748, "y": 3148.268 } ], "voltage": { "label": "v_\\mathrm{ab}" } }, { "type": "node", "id": "ocirc", "position": { "x": 2665.748, "y": 3050.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 2665.748, "y": 3163.386 } }, { "type": "node", "id": "circ", "position": { "x": 2609.055, "y": 3050.0 } }, { "type": "node", "id": "circ", "position": { "x": 2609.055, "y": 3163.386 } }, { "type": "rect", "position": { "x": 2533.465, "y": 3015.984 }, "size": { "x": 188.976, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "Norton: current source $\\parallel$ impedance", "align": 1 } }, { "type": "rect", "position": { "x": 2231.102, "y": 3193.622 }, "size": { "x": 491.339, "y": 30.236 }, "stroke": { "opacity": 0 }, "text": { "text": "$I_\\mathrm{N} = V_\\mathrm{Th}/Z_\\mathrm{Th}$, $Z_\\mathrm{N} = Z_\\mathrm{Th}$. Both give $v_\\mathrm{ab} = 4$ V and $i_\\mathrm{out} = 4$ mA.", "align": 1 } } ] }, { "type": "group", "components": [ { "type": "node", "id": "ocirc", "position": { "x": 4250.0, "y": 3050.0 } }, { "type": "node", "id": "ocirc", "position": { "x": 4250.0, "y": 3201.181 } }, { "type": "open", "points": [ { "x": 4250.0, "y": 3050.0 }, { "x": 4250.0, "y": 3201.181 } ], "voltage": { "label": "v_\\mathrm{ab}" } }, { "type": "wire", "points": [ { "x": 4250.0, "y": 3050.0 }, { "x": 4287.795, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 4287.795, "y": 3050.0 }, { "x": 4344.488, "y": 3050.0 } ], "label": { "value": "R_\\mathrm{s} = 1\\,\\Omega" } }, { "type": "path", "id": "cute inductor", "points": [ { "x": 4344.488, "y": 3050.0 }, { "x": 4401.181, "y": 3050.0 } ], "label": { "value": "L" } }, { "type": "wire", "points": [ { "x": 4401.181, "y": 3050.0 }, { "x": 4438.976, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "capacitor", "points": [ { "x": 4438.976, "y": 3050.0 }, { "x": 4438.976, "y": 3201.181 } ], "label": { "value": "C" } }, { "type": "wire", "points": [ { "x": 4438.976, "y": 3201.181 }, { "x": 4250.0, "y": 3201.181 } ], "directions": [ "--" ] }, { "type": "wire", "points": [ { "x": 4257.559, "y": 3050.0 }, { "x": 4284.016, "y": 3050.0 } ], "directions": [ "--" ] }, { "type": "rect", "position": { "x": 4248.11, "y": 3025.433 }, "size": { "x": 45.354, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "$i$", "align": 1, "fontSize": "normalsize" } }, { "type": "rect", "position": { "x": 4231.102, "y": 3015.984 }, "size": { "x": 226.772, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "Series RLC: impedance minimum", "align": 1 } }, { "type": "rect", "position": { "x": 4231.102, "y": 3231.417 }, "size": { "x": 226.772, "y": 22.677 }, "stroke": { "opacity": 0 }, "text": { "text": "At $f_0$: $Z_\\mathrm{s} = R_\\mathrm{s} = 1\\,\\Omega$; $Q_\\mathrm{s} = 10$", 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{ "x": 250.0, "y": 7401.181 } ], "directions": [ "--" ] }, { "type": "rect", "position": { "x": 140.394, "y": 7284.016 }, "size": { "x": 75.591, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "short: 0 V", "align": 1, "fontSize": "normalsize" } }, { "type": "rect", "position": { "x": 140.394, "y": 7204.646 }, "size": { "x": 94.488, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "charge: +5 V", "align": 1, "fontSize": "normalsize" } }, { "type": "node", "id": "ground", "position": { "x": 250.0, "y": 7401.181 } }, { "type": "node", "id": "circ", "position": { "x": 325.591, "y": 7250.0 } }, { "type": "node", "id": "circ", "position": { "x": 325.591, "y": 7401.181 } }, { "type": "node", "id": "circ", "position": { "x": 420.079, "y": 7250.0 } }, { "type": "node", "id": "circ", "position": { "x": 420.079, "y": 7401.181 } }, { "type": "node", "id": "circ", "position": { "x": 250.0, "y": 7401.181 } }, { "type": "rect", "position": { "x": 231.102, "y": 7431.417 }, "size": { "x": 415.748, "y": 22.677 }, "stroke": { "opacity": 0 }, "text": { "text": "Charge fully \u2192 short 1 ms \u2192 open and observe. 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the plot uses a local averaged open-loop model", "align": 1 } } ] }, { "type": "group", "components": [ { "type": "path", "id": "european voltage source", "points": [ { "x": 4250.0, "y": 7401.181 }, { "x": 4250.0, "y": 7250.0 } ], "label": { "value": "0 \\to 48\\,\\mathrm{V},\\ 5\\,\\mathrm{ns}" } }, { "type": "wire", "points": [ { "x": 4250.0, "y": 7250.0 }, { "x": 4287.795, "y": 7250.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 4287.795, "y": 7250.0 }, { "x": 4344.488, "y": 7250.0 } ], "label": { "value": "R_\\mathrm{loop} = 0.5\\,\\Omega" } }, { "type": "path", "id": "cute inductor", "points": [ { "x": 4344.488, "y": 7250.0 }, { "x": 4401.181, "y": 7250.0 } ], "label": { "value": "L_\\mathrm{p} = 25.33\\,\\mathrm{nH}" } }, { "type": "wire", "points": [ { "x": 4401.181, "y": 7250.0 }, { "x": 4627.9529999999995, "y": 7250.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "capacitor", "points": [ { "x": 4438.976, "y": 7250.0 }, { "x": 4438.976, "y": 7401.181 } ], "label": { "value": "C_\\mathrm{p} = 400\\,\\mathrm{pF}" } }, { "type": "path", "id": "capacitor", "points": [ { "x": 4533.465, "y": 7250.0 }, { "x": 4533.465, "y": 7401.181 } ], "label": { "value": "C_\\mathrm{test}\\ (\\mathrm{extraction})" } }, { "type": "path", "id": "european resistor", "points": [ { "x": 4627.9529999999995, "y": 7250.0 }, { "x": 4627.9529999999995, "y": 7325.591 } ], "label": { "value": "R_\\mathrm{s} = 8.2\\,\\Omega" } }, { "type": "path", "id": "capacitor", "points": [ { "x": 4627.9529999999995, "y": 7325.591 }, { "x": 4627.9529999999995, "y": 7401.181 } ], "label": { "value": "C_\\mathrm{s} = 1.2\\,\\mathrm{nF}" } }, { "type": "wire", "points": [ { "x": 4250.0, "y": 7401.181 }, { "x": 4627.9529999999995, "y": 7401.181 } ], "directions": [ "--" ] }, { "type": "open", "points": [ { "x": 4416.299, "y": 7265.118 }, { "x": 4416.299, "y": 7386.063 } ], "voltage": { "label": "v_\\mathrm{node}" } }, { "type": "node", "id": "circ", "position": { "x": 4438.976, "y": 7250.0 } }, { "type": "node", "id": "circ", "position": { "x": 4533.465, "y": 7250.0 } }, { "type": "node", "id": "circ", "position": { "x": 4627.9529999999995, "y": 7250.0 } }, { "type": "node", "id": "circ", "position": { "x": 4438.976, "y": 7401.181 } }, { "type": "node", "id": "circ", "position": { "x": 4533.465, "y": 7401.181 } }, { "type": "node", "id": "circ", "position": { "x": 4627.9529999999995, "y": 7401.181 } }, { "type": "rect", "position": { "x": 4231.102, "y": 7215.984 }, "size": { "x": 415.748, "y": 18.898 }, "stroke": { "opacity": 0 }, "text": { "text": "Common fixture; add either the test capacitor (extraction) or the final series RC snubber, not both", "align": 1 } }, { "type": "rect", "position": { "x": 4231.102, "y": 7431.417 }, "size": { "x": 415.748, "y": 22.677 }, "stroke": { "opacity": 0 }, "text": { "text": "Edge-test fixture, not a complete half bridge. The final capacitor blocks DC through $R_\\mathrm{s}$.", "align": 1 } } ] }, { "type": "group", "components": [ { "type": "path", "id": "european voltage source", "points": [ { "x": 6250.0, "y": 7438.976 }, { "x": 6250.0, "y": 7250.0 } ], "label": { "value": "0 \\to 48\\,\\mathrm{V},\\ 5\\,\\mathrm{ns}" } }, { "type": "wire", "points": [ { "x": 6250.0, "y": 7250.0 }, { "x": 6287.795, "y": 7250.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "european resistor", "points": [ { "x": 6287.795, "y": 7250.0 }, { "x": 6344.488, "y": 7250.0 } ], "label": { "value": "0.5\\,\\Omega" } }, { "type": "path", "id": "cute inductor", "points": [ { "x": 6344.488, "y": 7250.0 }, { "x": 6401.181, "y": 7250.0 } ], "label": { "value": "L_\\mathrm{p} = 25.33\\,\\mathrm{nH}" } }, { "type": "wire", "points": [ { "x": 6401.181, "y": 7250.0 }, { "x": 6552.362, "y": 7250.0 } ], "directions": [ "--" ] }, { "type": "path", "id": "capacitor", "points": [ { "x": 6457.874, "y": 7250.0 }, { "x": 6457.874, 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