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193.527 -607.362 l 193.527 -625.401 m 193.527 -616.381 l S Q 0 g 193.095 612.739 m 191.095 622.784 l 195.095 622.784 l f q 0.9978 0 0 -1.0022 0 0 cm 168.276 -594.733 m 168.276 -565.869 l 153.844 -630.815 m 157.452 -630.815 l 155.648 -632.618 m 155.648 -629.011 l 153.844 -612.774 m 157.452 -612.774 l S Q 1 g 1 G 0 w q 0.9978 0 0 -1.0022 0 0 cm 220.593 -632.619 7.216 21.648 re B* Q 0 G 1.002 w q 0.9978 0 0 -1.0022 0 0 cm 224.201 -632.618 m 227.81 -630.814 l 227.81 -630.814 m 220.593 -627.206 l 220.593 -627.206 m 227.81 -623.598 l 227.81 -623.599 m 220.593 -619.99 l 220.593 -619.99 m 227.81 -616.382 l 227.81 -616.382 m 220.593 -612.774 l 220.594 -612.774 m 224.202 -610.97 l S Q 0 J 0 w q 0.9978 0 0 -1.0022 0 0 cm 171.483 -613.776 m 157.953 -626.805 m S Q BT /F10 1 Tf 12 0 0 12.054 158.1 619.671 Tm 0 g (V)Tj 7 0 0 7.031 164.1 618.164 Tm (be)Tj ET q 0.9978 0 0 -1.0022 0 0 cm 137.006 -604.756 m 124.478 -617.785 m S Q BT 12 0 0 12.054 125.2 610.63 Tm (C)Tj /F19 1 Tf 7 0 0 7.031 132.2 609.124 Tm (\000)Tj ET q 0.9978 0 0 -1.0022 0 0 cm 180.804 -653.465 m 167.775 -667.997 m S Q BT /F10 1 Tf 12 0 0 12.054 168.4 660.955 Tm (C)Tj /F19 1 Tf 7 0 0 7.031 175.4 659.951 Tm (\000)Tj ET q 0.9978 0 0 -1.0022 0 0 cm 103.231 -611.972 m 90.703 -625.001 m S Q BT /F10 1 Tf 12 0 0 12.054 92 617.863 Tm (R)Tj /F19 1 Tf 7 0 0 7.031 98.5 616.356 Tm (\000)Tj ET q 0.9978 0 0 -1.0022 0 0 cm 211.673 -578.898 m 186.617 -591.927 m S Q BT /F10 1 Tf 12 0 0 12.054 187.2 584.715 Tm (g)Tj 7 0 0 7.031 193.2 583.208 Tm (m)Tj 12 0 0 12.054 198.2 584.715 Tm (V)Tj 7 0 0 7.031 204.2 583.208 Tm (be)Tj ET q 0.9978 0 0 -1.0022 0 0 cm 241.139 -611.371 m 229.613 -624.4 m S Q BT 12 0 0 12.054 230.6 617.26 Tm (R)Tj 7 0 0 7.031 237.1 615.753 Tm (o)Tj /F18 1 Tf 12 0 0 12.054 233.9 650.508 Tm (C)Tj -11.567 0 TD (B)Tj 6.45 -7.05 TD (E)Tj /F12 1 Tf 12 0 0 12 306 681 Tm (Hybrid-pi model:)Tj /T2 1 Tf 0 -1.667 TD ( )Tj /F20 1 Tf 0.052 0.5 TD (C)Tj /F11 1 Tf 7 0 1.54 7 314.156 664 Tm (m)Tj 12 0 0 12 322.937 667 Tm (=)Tj /F20 1 Tf 0.797 0 TD (C)Tj 7 0 0 7 340.094 664 Tm (bc)Tj /T2 1 Tf 12 0 0 12 306 644 Tm ( )Tj /F20 1 Tf 0.052 0.5 TD (C)Tj /F11 1 Tf 7 0 1.54 7 314.312 647 Tm (p)Tj 12 0 0 12 322.812 650 Tm (=)Tj /F20 1 Tf 0.797 0 TD (C)Tj 7 0 0 7 339.969 647 Tm (be)Tj /F11 1 Tf 12 0 0 12 350.719 650 Tm (=)Tj /F20 1 Tf 0.797 0 TD (C)Tj /F11 1 Tf 7 0 1.54 7 367.969 646.969 Tm (p)Tj /F21 1 Tf 7 0 0 7 372.656 646.969 Tm (,)Tj /F20 1 Tf 0.33 0 TD (depl)Tj /F11 1 Tf 12 0 0 12 390.875 650 Tm (+)Tj /F20 1 Tf 0.755 0 TD (C)Tj /F11 1 Tf 7 0 1.54 7 407.625 646.969 Tm (p)Tj /F21 1 Tf 7 0 0 7 412.312 646.969 Tm (,)Tj /F20 1 Tf 0.33 0 TD (diff)Tj /T2 1 Tf 12 0 0 12 306 627 Tm ( )Tj /F20 1 Tf 0.052 0.5 TD (C)Tj /F11 1 Tf 7 0 1.54 7 314.312 629.969 Tm (p)Tj /F21 1 Tf 7 0 0 7 319 629.969 Tm (,)Tj /F20 1 Tf 0.33 0 TD (diff)Tj /F11 1 Tf 12 0 0 12 335.937 633 Tm (=)Tj /F20 1 Tf 0.82 0 TD (g)Tj 7 0 0 7 351.656 630 Tm (m)Tj /F11 1 Tf 12 0 2.64 12 357.437 633 Tm (t)Tj /F20 1 Tf 7 0 0 7 364.625 629.969 Tm (f)Tj /T2 1 Tf 12 0 0 12 306 604 Tm ( )Tj /F20 1 Tf 0.229 0.667 TD (f)Tj /F11 1 Tf 7 0 1.54 7 312.094 609 Tm (t)Tj 12 0 0 12 319.844 612 Tm (=)Tj /F20 1 Tf 0.82 0 TD (g)Tj 7 0 0 7 335.562 609 Tm (m)Tj /F21 1 Tf 12 0 0 12 352.5 612 Tm (2)Tj /F11 1 Tf 12 0 2.64 12 359.094 612 Tm (p)Tj /F20 1 Tf 12 0 0 12 370.781 612 Tm (C)Tj /F11 1 Tf 7 0 1.54 7 378.469 609 Tm (p)Tj 12 0 0 12 386.5 612 Tm (+)Tj /F20 1 Tf 0.755 0 TD (C)Tj /F11 1 Tf 7 0 1.54 7 403.094 609 Tm (m)Tj 12 0 0 20.004 366.562 610.281 Tm 3.216 Tc (\(\))Tj 12 0 0 22.332 348.25 609.719 Tm 5.073 Tc (\(\))Tj ET 347.438 624.719 m 341.281 605.469 l 341.781 605.469 l 347.937 624.719 l f BT /T2 1 Tf 12 0 0 12 306 588 Tm 0 Tc ( )Tj /F20 1 Tf 0.076 0.417 TD (g)Tj 7 0 0 7 312.781 590 Tm (m)Tj /F11 1 Tf 12 0 0 12 322.031 593 Tm (=)Tj 12 0 2.64 12 331.5 593 Tm (a)Tj /F20 1 Tf 12 0 0 12 344.5 593 Tm (r)Tj 7 0 0 7 347.781 590 Tm (e)Tj ET 343.344 601.156 m 339.75 589.937 l 340.25 589.937 l 343.844 601.156 l f BT /F11 1 Tf 12 0 0 12 355.031 593 Tm (=)Tj /F20 1 Tf 0.852 0 TD (I)Tj 7 0 0 7 369.281 590 Tm (c)Tj 12 0 0 12 378.688 593 Tm (V)Tj 7 0 0 7 384.844 590 Tm (T)Tj ET 377.75 601.156 m 374.156 589.937 l 374.656 589.937 l 378.25 601.156 l f BT /T2 1 Tf 12 0 0 12 306 571 Tm ( )Tj /F20 1 Tf 0.115 0.417 TD (R)Tj /F11 1 Tf 7 0 1.54 7 314.062 573 Tm (p)Tj 12 0 0 12 322.562 576 Tm (=)Tj 12 0 2.64 12 335.75 576 Tm (b)Tj 12 0 0 12 345.969 576 Tm (+)Tj /F21 1 Tf 0.677 0 TD (1)Tj /F11 1 Tf 12 0 0 15.732 331.875 575.312 Tm 1.966 Tc (\(\))Tj /F20 1 Tf 12 0 0 12 363.5 576 Tm (r)Tj 7 0 0 7 366.781 573 Tm (e)Tj /T2 1 Tf 12 0 0 12 306 555 Tm 0 Tc ( )Tj /F20 1 Tf 0.115 0.417 TD (R)Tj 7 0 0 7 313.937 557 Tm (o)Tj /F11 1 Tf 12 0 0 12 321.562 560 Tm (=)Tj /F20 1 Tf 0.786 0 TD (V)Tj 7 0 0 7 337.687 557 Tm (A)Tj 12 0 0 12 348.875 560 Tm (I)Tj 7 0 0 7 352.906 557 Tm (C)Tj ET 347.156 568.156 m 343.531 556.844 l 344.031 556.844 l 347.656 568.156 l f 2 J 1.004 w q 0.999 0 0 -1.001 0 0 cm 90.594 -523.272 m 242.398 -523.272 l S Q 1 g q 0.999 0 0 -1.001 0 0 cm 188.178 -523.272 30.723 48.795 re B Q q 0.999 0 0 -1.001 0 0 cm 137.581 -523.272 50.602 48.795 re B Q q 0.999 0 0 -1.001 0 0 cm 106.858 -523.272 30.723 48.795 re B Q 1 G q 0.999 0 0 -1.001 0 0 cm 133.966 -507.007 7.229 9.036 re B* Q 0 G q 0.999 0 0 -1.001 0 0 cm 130.352 -505.2 m 144.81 -505.2 l 137.581 -512.429 m 137.581 -505.2 l S Q q -0.999 0 0 -1.001 0 0 cm -137.274 -501.586 m -134.603 -501.586 -132.069 -500.995 -130.352 -499.972 c S Q q 0.999 0 0 -1.001 0 0 cm 137.58 -501.586 m 140.251 -501.586 142.786 -500.995 144.503 -499.972 c 137.581 -501.586 m 137.581 -492.549 l S Q 1 G 0 w q 0.999 0 0 -1.001 0 0 cm 103.244 -510.622 7.229 21.686 re B* Q 0 G 1.004 w q 0.999 0 0 -1.001 0 0 cm 106.858 -510.622 m 110.473 -508.814 l 110.473 -508.814 m 103.244 -505.2 l 103.244 -505.2 m 110.473 -501.586 l 110.473 -501.586 m 103.244 -497.972 l 103.244 -497.972 m 110.473 -494.357 l 110.473 -494.357 m 103.244 -490.743 l 103.244 -490.743 m 106.859 -488.936 l S Q q -0.999 0 0 1.001 0 0 cm -179.135 499.772 m -179.135 494.784 -183.183 490.736 -188.171 490.736 c -193.159 490.736 -197.207 494.784 -197.207 499.772 c -197.207 504.76 -193.159 508.808 -188.171 508.808 c -183.183 508.808 -179.135 504.76 -179.135 499.772 c B Q q -0.999 0 0 1.001 0 0 cm -188.178 487.128 m -188.178 490.742 l -188.178 508.814 m -188.178 512.429 l -188.178 494.357 m -188.178 503.393 l S Q 0 g 187.987 508.93 m 189.993 498.88 l 185.981 498.88 l f q 0.999 0 0 -1.001 0 0 cm 162.882 -474.477 m 162.882 -445.562 l 148.424 -510.622 m 152.039 -510.622 l 150.231 -512.429 m 150.231 -508.815 l 148.424 -492.549 m 152.039 -492.549 l S Q 0 J 0 w q 0.999 0 0 -1.001 0 0 cm 131.557 -484.517 m 119.007 -497.57 m S Q BT /F10 1 Tf 12.036 0 0 12.06 119.889 489.533 Tm (C)Tj /F19 1 Tf 7.021 0 0 7.035 126.91 488.025 Tm (\000)Tj ET q 0.999 0 0 -1.001 0 0 cm 242.801 -484.517 m 229.748 -499.076 m S Q BT /F10 1 Tf 12.036 0 0 12.06 230.518 491.04 Tm (C)Tj /F19 1 Tf 7.021 0 0 7.035 237.539 490.035 Tm (\000)Tj ET q 0.999 0 0 -1.001 0 0 cm 163.585 -527.891 m 152.039 -540.943 m S Q BT /F10 1 Tf 12.036 0 0 12.06 153.389 532.95 Tm (R)Tj 7.021 0 0 7.035 159.908 531.442 Tm (o)Tj /F18 1 Tf 12.036 0 0 12.06 228.913 529.432 Tm (C)Tj -6.317 -6.6 TD (B)Tj -5.1 6.492 TD (E)Tj ET 1 g 1 G 2 J q 0.999 0 0 -1.001 0 0 cm 152.039 -526.886 21.687 7.229 re B Q 0 G 1.004 w q 0.999 0 0 -1.001 0 0 cm 152.039 -523.272 m 153.846 -526.886 l 153.846 -526.886 m 157.461 -519.658 l 157.461 -519.658 m 161.075 -526.886 l 161.075 -526.886 m 164.689 -519.658 l 164.689 -519.658 m 168.303 -526.886 l 168.303 -526.886 m 171.918 -519.658 l 171.918 -519.658 m 173.725 -523.272 l S Q 0 J 0 w q 0.999 0 0 -1.001 0 0 cm 97.621 -493.554 m 90.593 -506.606 m S Q BT /F10 1 Tf 12.036 0 0 12.06 91.504 498.578 Tm 0 g (r)Tj 7.021 0 0 7.035 94.513 497.07 Tm (e)Tj ET 1 g 1 G 2 J 1.004 w q 0.999 0 0 -1.001 0 0 cm 215.291 -503.393 7.229 9.036 re B* Q 0 G q 0.999 0 0 -1.001 0 0 cm 211.677 -501.586 m 226.135 -501.586 l 218.906 -508.814 m 218.906 -501.586 l S Q q -0.999 0 0 -1.001 0 0 cm -218.599 -497.971 m -215.928 -497.971 -213.394 -497.38 -211.677 -496.357 c S Q q 0.999 0 0 -1.001 0 0 cm 218.905 -497.971 m 221.576 -497.971 224.111 -497.38 225.828 -496.357 c 218.906 -497.971 m 218.906 -488.935 l S Q 0 J 0 w q 0.999 0 0 -1.001 0 0 cm 204.548 -459.217 m 179.448 -472.269 m S Q BT 12.036 0 0 12.06 180.269 464.206 Tm 0 g (g)Tj 7.021 0 0 7.035 186.287 462.698 Tm (m)Tj 12.036 0 0 12.06 191.301 464.206 Tm (V)Tj 7.021 0 0 7.035 197.319 462.698 Tm (eb)Tj ET q 0.999 0 0 -1.001 0 0 cm 164.789 -493.554 m 151.235 -506.606 m S Q BT 12.036 0 0 12.06 151.583 498.578 Tm (V)Tj 7.021 0 0 7.035 157.601 497.07 Tm (eb)Tj /F12 1 Tf 12 0 0 12 306 534 Tm ("T"-model)Tj 0 -1 TD (Makes common-base analysis much easier.)Tj T* (Both these models are only approximate,)Tj 0 -1.167 TD (being "good" up to f)Tj 10 0 0 10 404 494 Tm (t)Tj 12 0 0 12 407 496 Tm (. Additionally )Tj /T2 1 Tf 5.833 -0.417 TD ( )Tj /F20 1 Tf 0.115 0.417 TD (R)Tj 7 0 0 7 484.969 492.969 Tm (b)Tj /F21 1 Tf 0.571 0 TD (\251)Tj /F20 1 Tf 0.25 0 TD (b)Tj /F12 1 Tf 12 0 0 12 496 496 Tm ( is)Tj -15.833 -1.167 TD (often an important parasitic \(not discussed)Tj 0 -1 TD (much in 137B.)Tj ET 0.804 w 90 414.8 m 278.279 414.8 l S BT 12 0 0 12 90 416 Tm (Simplification of Emitter Degeneration)Tj 0 -7.167 TD ( )Tj ET 1 g 1 G 2 J 0 w q 0.9986 0 0 -1.0014 0 0 cm 146.018 -395.634 16.275 18.082 re B Q 0 G 1.005 w q 0.9986 0 0 -1.0014 0 0 cm 144.211 -386.593 m 151.444 -386.593 l S Q 1.507 w q 0.9986 0 0 -1.0014 0 0 cm 151.444 -395.635 m 151.444 -377.551 l S Q 1.005 w q 0.9986 0 0 -1.0014 0 0 cm 151.443 -382.976 m 162.293 -377.551 l 162.293 -395.634 m 151.443 -390.209 l 155.06 -381.168 m 158.677 -379.36 l S Q 0 g 162.937 377.651 m 153.067 380.351 l 154.861 383.95 l f q 0.9986 0 0 -1.0014 0 0 cm 162.294 -343.193 m 162.294 -335.959 l 164.102 -332.343 m 160.486 -332.343 l 165.911 -334.152 m 158.677 -334.152 l 167.719 -335.959 m 156.869 -335.959 l 162.294 -377.551 m 162.294 -335.959 l S Q 1 g 1 G 0 w q 0.9986 0 0 -1.0014 0 0 cm 158.677 -368.509 7.233 21.7 re B* Q 0 G 1.005 w q 0.9986 0 0 -1.0014 0 0 cm 162.294 -368.509 m 165.911 -366.7 l 165.911 -366.7 m 158.677 -363.084 l 158.677 -363.084 m 165.911 -359.467 l 165.911 -359.468 m 158.677 -355.851 l 158.677 -355.851 m 165.911 -352.234 l 165.911 -352.234 m 158.677 -348.618 l 158.678 -348.618 m 162.294 -346.809 l 162.294 -395.634 m 162.294 -411.909 l 146.019 -386.593 m 111.661 -386.593 l 169.527 -384.784 m 202.077 -384.784 l S Q 0 g 206.805 385.333 m 196.773 383.321 l 196.773 387.345 l f 1 g 1 G 0 w q 0.9986 0 0 -1.0014 0 0 cm 245.476 -393.826 16.275 18.082 re B Q 0 G 1.005 w q 0.9986 0 0 -1.0014 0 0 cm 243.669 -384.785 m 250.902 -384.785 l S Q 1.507 w q 0.9986 0 0 -1.0014 0 0 cm 250.902 -393.826 m 250.902 -375.743 l S Q 1.005 w q 0.9986 0 0 -1.0014 0 0 cm 250.901 -381.168 m 261.751 -375.743 l 261.751 -393.826 m 250.901 -388.401 l 254.518 -379.36 m 258.135 -377.551 l S Q 0 g 262.253 375.841 m 252.383 378.54 l 254.178 382.139 l f q 0.9986 0 0 -1.0014 0 0 cm 261.752 -341.384 m 261.752 -334.151 l 263.56 -330.534 m 259.944 -330.534 l 265.369 -332.343 m 258.135 -332.343 l 267.177 -334.151 m 256.327 -334.151 l 261.752 -375.743 m 261.752 -334.151 l 261.752 -393.826 m 261.752 -410.101 l 245.477 -384.784 m 211.119 -384.784 l S Q BT /F18 1 Tf 12.038 0 0 12.073 174.301 356.962 Tm (R)Tj 9.029 0 0 9.055 182.995 352.938 Tm (E)Tj /F12 1 Tf 12 0 0 12 306 404 Tm (approximate only; check notes for bounds)Tj 0 -1 TD (on validity)Tj /T2 1 Tf 0 -2 TD ( )Tj /F21 1 Tf 0.318 0.849 TD (\304)Tj /F20 1 Tf -0.266 -0.266 TD (C)Tj /F11 1 Tf 7 0 1.54 7 314.312 372 Tm (p)Tj 12 0 0 12 322.812 375 Tm (=)Tj /F20 1 Tf 0.797 0 TD (C)Tj /F11 1 Tf 7 0 1.54 7 340.062 372 Tm (p)Tj /F20 1 Tf 12 0 0 12 349.875 375 Tm (r)Tj 7 0 0 7 353.156 372 Tm (e)Tj 12 0 0 12 367.375 375 Tm (r)Tj 7 0 0 7 370.656 372 Tm (e)Tj /F11 1 Tf 12 0 0 12 377.437 375 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj 7 0 0 7 394.094 372 Tm (E)Tj /F11 1 Tf 12 0 0 16.596 363.063 374.094 Tm 2.745 Tc (\(\))Tj ET 362.25 385.25 m 357.656 370.937 l 358.156 370.937 l 362.75 385.25 l f BT 12 0 0 18.924 345.562 373.531 Tm 4.534 Tc (\(\))Tj /T2 1 Tf 12 0 0 12 306 347 Tm 0 Tc ( )Tj /F21 1 Tf 0.206 0.62 TD (\304)Tj /F20 1 Tf -0.13 -0.037 TD (g)Tj 7 0 0 7 312.781 351 Tm (m)Tj /F11 1 Tf 12 0 0 12 322.031 354 Tm (=)Tj /F20 1 Tf 0.82 0 TD (g)Tj 7 0 0 7 337.75 351 Tm (m)Tj 12 0 0 12 348.312 354 Tm (r)Tj 7 0 0 7 351.594 351 Tm (e)Tj 12 0 0 12 365.812 354 Tm (r)Tj 7 0 0 7 369.094 351 Tm (e)Tj /F11 1 Tf 12 0 0 12 375.875 354 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj 7 0 0 7 392.531 351 Tm (E)Tj /F11 1 Tf 12 0 0 16.596 361.5 353.094 Tm 2.745 Tc (\(\))Tj ET 360.687 364.25 m 356.094 349.937 l 356.594 349.937 l 361.187 364.25 l f BT 12 0 0 18.924 344 352.531 Tm 4.534 Tc (\(\))Tj 12 0 0 12 409.094 354 Tm (=)Tj 12 0 2.64 12 418.562 354 Tm (a)Tj /F20 1 Tf 12 0 0 12 436.188 354 Tm (r)Tj 7 0 0 7 439.469 351 Tm (e)Tj /F11 1 Tf 12 0 0 12 446.25 354 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj 7 0 0 7 462.906 351 Tm (E)Tj /F11 1 Tf 12 0 0 16.596 431.875 353.094 Tm 2.745 Tc (\(\))Tj ET 431.062 364.25 m 426.469 349.937 l 426.969 349.937 l 431.562 364.25 l f BT /T2 1 Tf 12 0 0 12 306 328 Tm 0 Tc ( )Tj /F21 1 Tf 0.318 0.766 TD (\304)Tj /F20 1 Tf -0.266 -0.266 TD (C)Tj /F11 1 Tf 7 0 1.54 7 314.156 331 Tm (m)Tj 12 0 0 12 322.937 334 Tm (=)Tj /F20 1 Tf 0.797 0 TD (C)Tj /F11 1 Tf 7 0 1.54 7 340.031 331 Tm (m)Tj /T2 1 Tf 12 0 0 12 306 307 Tm ( )Tj /F21 1 Tf 0.302 0.836 TD (\304)Tj /F20 1 Tf -0.187 -0.253 TD (R)Tj /F11 1 Tf 7 0 1.54 7 314.062 311 Tm (p)Tj 12 0 0 12 322.562 314 Tm (=)Tj /F20 1 Tf 0.859 0 TD (R)Tj /F11 1 Tf 7 0 1.54 7 339.562 311 Tm (p)Tj /F20 1 Tf 12 0 0 12 353.344 314 Tm (r)Tj 7 0 0 7 356.625 311 Tm (e)Tj /F11 1 Tf 12 0 0 12 363.406 314 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj 7 0 0 7 380.062 311 Tm (E)Tj /F11 1 Tf 12 0 0 16.596 349.031 313.094 Tm 2.745 Tc (\(\))Tj /F20 1 Tf 12 0 0 12 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103.14 623.781 c 108.12 623.781 112.162 627.831 112.162 632.82 c 112.162 637.809 108.12 641.859 103.14 641.859 c 98.16 641.859 94.118 637.809 94.118 632.82 c B 103.131 620.15 m 103.131 623.766 l 103.131 641.843 m 103.131 645.458 l 103.131 627.382 m 103.131 636.42 l S 0 g 103.131 641.442 m 105.136 631.399 l 101.126 631.399 l f BT 12.029 0 0 12.052 91.504 645.86 Tm (I)Tj 9.022 0 0 9.039 94.846 641.842 Tm (i)Tj ET 1 g 1 G 285.372 638.227 7.217 -9.039 re B* 0 G 281.764 636.42 m 296.199 636.42 l 288.981 643.651 m 288.981 636.42 l S 288.675 632.804 m 286.008 632.804 283.478 632.213 281.763 631.19 c S 288.981 632.804 m 291.648 632.804 294.178 632.213 295.892 631.19 c 288.981 632.804 m 288.981 623.766 l S BT 12.029 0 0 12.052 271.939 642.346 Tm 0 g (C)Tj 9.022 0 0 9.039 280.626 638.329 Tm (L)Tj ET 1 g 1 G 0 w 178.915 658.112 21.652 -7.231 re B 0 G 1.003 w 178.915 654.497 m 180.719 658.112 l 180.72 658.112 m 184.328 650.881 l 184.328 650.881 m 187.937 658.112 l 187.937 658.112 m 191.545 650.881 l 191.545 650.881 m 195.154 658.112 l 195.154 658.112 m 198.763 650.881 l 198.763 650.881 m 200.567 654.497 l S BT 12.029 0 0 12.052 171.096 663.736 Tm 0 g (R)Tj /F19 1 Tf 9.022 0 0 9.039 179.783 659.719 Tm (\000)Tj /T2 1 Tf 12 0 0 12 306 670 Tm ( )Tj /F20 1 Tf 0.042 1.167 TD (V)Tj 7 0 0 7 312.687 681 Tm (out)Tj 12 0 0 12 328.156 684 Tm (V)Tj 7 0 0 7 334.469 681 Tm (gen)Tj /F11 1 Tf 12 0 0 12 348.719 684 Tm (=)Tj ET 327.219 692.156 m 323.187 679.563 l 323.687 679.563 l 327.719 692.156 l f BT /F20 1 Tf 12 0 0 12 360.625 684 Tm (V)Tj 7 0 0 7 366.812 681 Tm (out)Tj 12 0 0 12 382.281 684 Tm (V)Tj 7 0 0 7 388.594 681 Tm (gen)Tj ET 381.344 692.156 m 377.312 679.563 l 377.812 679.563 l 381.844 692.156 l f BT /F11 1 Tf 12 0 0 19.788 356.531 682.312 Tm 3.3 Tc (\(\))Tj /F20 1 Tf 7 0 0 7 404.594 677.969 Tm 0 Tc (MB)Tj /F21 1 Tf 12 0 0 12 427.625 691.469 Tm (1)Tj /F11 1 Tf 0.635 0 TD (+)Tj /F20 1 Tf 0.771 0 TD (s)Tj /F11 1 Tf 12 0 2.64 12 449.156 691.469 Tm (t)Tj /F20 1 Tf 7 0 0 7 455.312 688.469 Tm (zero)Tj /F21 1 Tf 12 0 0 12 417 674.844 Tm (1)Tj /F11 1 Tf 0.635 0 TD (+)Tj /F20 1 Tf 0.773 0 TD (a)Tj /F21 1 Tf 7 0 0 7 439.156 671.844 Tm (1)Tj /F20 1 Tf 12 0 0 12 442.719 674.844 Tm (s)Tj /F11 1 Tf 0.607 0 TD (+)Tj /F20 1 Tf 0.773 0 TD (a)Tj /F21 1 Tf 7 0 0 7 465.094 671.844 Tm (2)Tj /F20 1 Tf 12 0 0 12 469.219 674.844 Tm (s)Tj /F21 1 Tf 7 0 0 7 474.406 680.187 Tm (2)Tj ET 0 J 0.5 w 417.312 687.094 m 479.719 687.094 l S BT /F12 1 Tf 12 0 0 12 306 655 Tm (given that )Tj /T2 1 Tf 4.25 -0.667 TD ( )Tj /F20 1 Tf 0.128 0.667 TD (A)Tj 7 0 0 7 365.063 652 Tm (vmb)Tj /F11 1 Tf 12 0 0 12 380.875 655 Tm (=)Tj /F20 1 Tf 1.135 0 TD (r)Tj 7 0 0 7 397.781 652 Tm (e)Tj 12 0 0 12 412.438 655 Tm (r)Tj 7 0 0 7 415.719 652 Tm (e)Tj /F11 1 Tf 12 0 0 12 422.5 655 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj 7 0 0 7 439.281 652 Tm (Leq)Tj /F11 1 Tf 12 0 0 19.788 408.125 653.312 Tm 3.263 Tc (\(\))Tj ET 407.313 666.625 m 401.844 649.563 l 402.344 649.563 l 407.813 666.625 l f BT 12 0 0 22.104 390.188 652.781 Tm 5.089 Tc (\(\))Tj /F12 1 Tf 12 0 0 12 460 655 Tm (:)Tj /T2 1 Tf -12.833 -2.917 TD 0 Tc ( )Tj /F20 1 Tf 0.07 0.833 TD (a)Tj /F21 1 Tf 7 0 0 7 312.094 627 Tm (1)Tj /F11 1 Tf 12 0 0 12 319.219 630 Tm (=)Tj /F20 1 Tf 0.797 0 TD (C)Tj /F11 1 Tf 7 0 1.54 7 336.469 627 Tm (p)Tj /F20 1 Tf 12 0 0 12 346.937 630 Tm (R)Tj /F11 1 Tf 7 0 1.54 7 353.625 627 Tm (p)Tj /F20 1 Tf 12 0 0 12 366.625 630 Tm (r)Tj 7 0 0 7 369.906 627 Tm (e)Tj 12 0 0 12 378.344 630 Tm (R)Tj 7 0 0 7 385.312 627 Tm (Leq)Tj /F11 1 Tf 12 0 0 12 399.562 630 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj 7 0 0 7 415.844 627 Tm (i)Tj /F21 1 Tf 12 0 0 12 422.312 630 Tm (1)Tj /F11 1 Tf 0.633 0 TD (-)Tj /F20 1 Tf 0.828 0 TD (A)Tj 7 0 0 7 446.375 627 Tm (vmb)Tj /F11 1 Tf 12 0 0 16.596 419.031 629.094 Tm 3.037 Tc (\(\))Tj ET 0.5 w 376.719 641.625 m 376.719 624.563 l 375.031 641.625 m 375.031 624.563 l S BT 12 0 0 22.104 362.312 627.781 Tm 8.094 Tc (\(\))Tj ET 361.687 643.625 m 361.687 622.563 l 360 643.625 m 360 622.563 l S BT 12 0 0 26.748 341.969 626.656 Tm 10.12 Tc (\(\))Tj /T2 1 Tf 12 0 0 12 306 601 Tm 0 Tc ( )Tj /F11 1 Tf 0.076 0.5 TD (+)Tj /F20 1 Tf 0.589 0 TD (C)Tj /F11 1 Tf 7 0 1.54 7 321.5 604 Tm (m)Tj /F20 1 Tf 12 0 0 12 332.25 607 Tm (R)Tj 7 0 0 7 338.719 604 Tm (i)Tj /F21 1 Tf 12 0 0 12 345.594 607 Tm (transistor input resistance)Tj ET 0.5 w 344.469 616.781 m 344.469 603.406 l 342.781 616.781 m 342.781 603.406 l S BT /F11 1 Tf 12 0 0 17.832 327.281 605.813 Tm 11.414 Tc (\(\))Tj /T2 1 Tf 12 0 0 12 306 580 Tm 0 Tc ( )Tj /F11 1 Tf 0.076 0.583 TD (+)Tj /F20 1 Tf 0.589 0 TD (C)Tj 7 0 0 7 321.937 584 Tm (L)Tj 12 0 0 12 332 587 Tm (R)Tj 7 0 0 7 338.969 584 Tm (Leq)Tj /F21 1 Tf 12 0 0 12 354.375 587 Tm (transistor output resistance)Tj ET 353.25 596.781 m 353.25 583.406 l 351.562 596.781 m 351.562 583.406 l S BT /F11 1 Tf 12 0 0 19.788 327.031 585.312 Tm 12.667 Tc (\(\))Tj /T2 1 Tf 12 0 0 12 306 559 Tm 0 Tc ( )Tj /F20 1 Tf 0.07 0.583 TD (a)Tj /F21 1 Tf 7 0 0 7 312.656 563 Tm (2)Tj /F11 1 Tf 12 0 0 12 320.344 566 Tm (=)Tj /F20 1 Tf 1.19 0 TD (R)Tj 7 0 0 7 341.094 563 Tm (i)Tj /F21 1 Tf 12 0 0 12 347.969 566 Tm (transistor input resistance)Tj ET 346.844 575.781 m 346.844 562.406 l 345.156 575.781 m 345.156 562.406 l S BT /F11 1 Tf 12 0 0 17.832 329.656 564.813 Tm 11.414 Tc (\(\))Tj /F20 1 Tf 12 0 0 12 479.281 566 Tm (R)Tj 7 0 0 7 486.25 563 Tm 0 Tc (Leq)Tj 12 0 0 12 501.5 566 Tm (r)Tj 7 0 0 7 504.781 563 Tm (e)Tj ET 500.531 576.25 m 500.531 561.937 l 498.844 576.25 m 498.844 561.937 l S BT /F11 1 Tf 12 0 0 19.788 474.312 564.313 Tm 2.584 Tc (\(\))Tj /T2 1 Tf 12 0 0 12 306 538 Tm 0 Tc ( )Tj /F11 1 Tf 0.068 0.583 TD (\264)Tj /F20 1 Tf 0.914 0 TD (C)Tj /F11 1 Tf 7 0 1.54 7 325.312 542 Tm (m)Tj /F20 1 Tf 12 0 0 12 330.344 545 Tm (C)Tj /F11 1 Tf 7 0 1.54 7 338.031 542 Tm (p)Tj 12 0 0 12 346.062 545 Tm (+)Tj /F20 1 Tf 0.755 0 TD (C)Tj /F11 1 Tf 7 0 1.54 7 362.656 542 Tm (m)Tj /F20 1 Tf 12 0 0 12 367.687 545 Tm (C)Tj 7 0 0 7 375.656 542 Tm (L)Tj /F11 1 Tf 12 0 0 12 383.281 545 Tm (+)Tj /F20 1 Tf 0.755 0 TD (C)Tj 7 0 0 7 400.312 542 Tm (L)Tj 12 0 0 12 404.656 545 Tm (C)Tj /F11 1 Tf 7 0 1.54 7 412.344 542 Tm (p)Tj 12 0 0 20.004 313.562 543.281 Tm 8.381 Tc (\(\))Tj /T2 1 Tf 12 0 0 12 306 522 Tm 0 Tc ( )Tj /F11 1 Tf 12 0 2.64 12 306.906 527 Tm (t)Tj /F20 1 Tf 7 0 0 7 313.063 524 Tm (zero)Tj /F11 1 Tf 12 0 0 12 329.219 527 Tm (=)Tj /F20 1 Tf 0.82 0 TD (g)Tj 7 0 0 7 344.937 524 Tm (m)Tj 12 0 0 12 356.406 527 Tm (C)Tj /F11 1 Tf 7 0 1.54 7 364.094 524 Tm (p)Tj ET 355.344 535.156 m 351.75 523.875 l 352.25 523.875 l 355.844 535.156 l f 0.804 w 90 493.8 m 430.577 493.8 l S BT /F12 1 Tf 12 0 0 12 90 495 Tm (General Solutions of Problems: Nodal analysis \(Know how to do this!\))Tj 0 -2.083 TD (1\)Write the nodal equations \(sum of the)Tj 0 -1 TD (currents=0\) at each circuit node, and put)Tj T* (the resulting equations in matrix form \(the)Tj T* (Y's being various combinations of g)Tj 10 0 0 10 263.139 432 Tm (m)Tj 12 0 0 12 271 434 Tm ('s,)Tj -15.083 -1 TD (1/R's, and sC's\):)Tj /T2 1 Tf 0 -6.167 TD ( )Tj /F20 1 Tf 0.492 4.964 TD (Y)Tj /F21 1 Tf 7 0 0 7 100.812 404.563 Tm (11)Tj /F20 1 Tf 12 0 0 12 120.25 407.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 125.156 404.563 Tm (12)Tj /F20 1 Tf 12 0 0 12 145.156 407.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 150.063 404.563 Tm (13)Tj /F20 1 Tf 12 0 0 12 169.75 407.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 174.656 404.563 Tm (14)Tj /F20 1 Tf 12 0 0 12 95.625 389.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 101.094 386.563 Tm (21)Tj /F20 1 Tf 12 0 0 12 119.969 389.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 125.438 386.563 Tm (22)Tj /F20 1 Tf 12 0 0 12 144.875 389.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 150.344 386.563 Tm (23)Tj /F20 1 Tf 12 0 0 12 169.469 389.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 174.938 386.563 Tm (24)Tj /F20 1 Tf 12 0 0 12 95.656 371.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 101.031 368.563 Tm (31)Tj /F20 1 Tf 12 0 0 12 120 371.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 125.375 368.563 Tm (32)Tj /F20 1 Tf 12 0 0 12 144.906 371.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 150.281 368.563 Tm (33)Tj /F20 1 Tf 12 0 0 12 169.531 371.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 174.906 368.563 Tm (34)Tj /F20 1 Tf 12 0 0 12 95.563 353.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 101.156 350.563 Tm (41)Tj /F20 1 Tf 12 0 0 12 119.906 353.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 125.5 350.563 Tm (42)Tj /F20 1 Tf 12 0 0 12 144.813 353.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 150.406 350.563 Tm (43)Tj /F20 1 Tf 12 0 0 12 169.406 353.563 Tm (Y)Tj /F21 1 Tf 7 0 0 7 175 350.563 Tm (44)Tj /F11 1 Tf 12 0 0 12 91 405.625 Tm (\351)Tj ET q 90 348 184 70 re W n BT 12 0 0 12 91 350.406 Tm (\353)Tj ET Q BT 12 0 0 12 91 394.094 Tm (\352)Tj 0 -0.961 TD (\352)Tj T* (\352)Tj T* (\352)Tj 7.714 3.844 TD (\371)Tj ET q 90 348 184 70 re W n BT 12 0 0 12 183.563 350.406 Tm (\373)Tj ET Q BT 12 0 0 12 183.563 394.094 Tm (\372)Tj 0 -0.961 TD (\372)Tj T* (\372)Tj T* (\372)Tj /F20 1 Tf 1.034 4.003 TD (V)Tj /F21 1 Tf 7 0 0 7 201.594 404.531 Tm (1)Tj /F11 1 Tf 12 0 0 12 208.719 407.531 Tm (=)Tj /F20 1 Tf 0.786 0 TD (V)Tj 7 0 0 7 224.25 404.531 Tm (in)Tj 12 0 0 12 207.969 389.531 Tm (V)Tj /F21 1 Tf 7 0 0 7 214.156 386.531 Tm (2)Tj /F20 1 Tf 12 0 0 12 208.187 371.531 Tm (V)Tj /F21 1 Tf 7 0 0 7 214.281 368.531 Tm (3)Tj /F20 1 Tf 12 0 0 12 193.437 353.531 Tm (V)Tj /F21 1 Tf 7 0 0 7 199.75 350.531 Tm (4)Tj /F11 1 Tf 12 0 0 12 207.406 353.531 Tm (=)Tj /F20 1 Tf 0.786 0 TD (V)Tj 7 0 0 7 223.031 350.531 Tm (out)Tj /F11 1 Tf 12 0 0 12 188.875 405.625 Tm (\351)Tj ET q 90 348 184 70 re W n BT 12 0 0 12 188.875 350.406 Tm (\353)Tj ET Q BT 12 0 0 12 188.875 394.094 Tm (\352)Tj 0 -0.961 TD (\352)Tj T* (\352)Tj T* (\352)Tj 3.745 3.844 TD (\371)Tj ET q 90 348 184 70 re W n BT 12 0 0 12 233.813 350.406 Tm (\373)Tj ET Q BT 12 0 0 12 233.813 394.094 Tm (\372)Tj 0 -0.961 TD (\372)Tj T* (\372)Tj T* (\372)Tj 0.641 1.708 TD (=)Tj /F20 1 Tf 1.273 2.276 TD (I)Tj 7 0 0 7 260.75 404.313 Tm (in)Tj /F21 1 Tf 12 0 0 12 258.75 389.313 Tm (0)Tj 0 -1.5 TD (0)Tj T* (0)Tj /F11 1 Tf -0.609 4.339 TD (\351)Tj 0 -4.56 TD (\353)Tj 0 3.599 TD (\352)Tj 0 -0.961 TD (\352)Tj T* (\352)Tj T* (\352)Tj 1.359 3.844 TD (\371)Tj 0 -4.56 TD (\373)Tj 0 3.599 TD (\372)Tj 0 -0.961 TD (\372)Tj T* (\372)Tj T* (\372)Tj /F12 1 Tf 3.188 9.229 TD (2\) Use Cramer's rule to solve:)Tj /T2 1 Tf 0 -12 TD ( )Tj /F20 1 Tf 0.378 10.786 TD (Y)Tj /F21 1 Tf 7 0 0 7 315.437 452.437 Tm (11)Tj /F20 1 Tf 12 0 0 12 334.875 455.438 Tm (Y)Tj /F21 1 Tf 7 0 0 7 339.781 452.437 Tm (12)Tj /F20 1 Tf 12 0 0 12 359.781 455.438 Tm (Y)Tj /F21 1 Tf 7 0 0 7 364.687 452.437 Tm (13)Tj /F20 1 Tf 12 0 0 12 384.812 455.438 Tm (I)Tj 7 0 0 7 388.781 452.437 Tm (in)Tj 12 0 0 12 310.25 437.437 Tm (Y)Tj /F21 1 Tf 7 0 0 7 315.719 434.438 Tm (21)Tj /F20 1 Tf 12 0 0 12 334.594 437.437 Tm (Y)Tj /F21 1 Tf 7 0 0 7 340.062 434.438 Tm (22)Tj /F20 1 Tf 12 0 0 12 359.5 437.437 Tm (Y)Tj /F21 1 Tf 7 0 0 7 364.969 434.438 Tm (23)Tj 12 0 0 12 386.781 437.437 Tm (0)Tj /F20 1 Tf -6.375 -1.5 TD (Y)Tj /F21 1 Tf 7 0 0 7 315.656 416.437 Tm (31)Tj /F20 1 Tf 12 0 0 12 334.625 419.437 Tm (Y)Tj /F21 1 Tf 7 0 0 7 340 416.437 Tm (32)Tj /F20 1 Tf 12 0 0 12 359.531 419.437 Tm (Y)Tj /F21 1 Tf 7 0 0 7 364.906 416.437 Tm (33)Tj 12 0 0 12 386.781 419.437 Tm (0)Tj /F20 1 Tf -6.383 -1.5 TD (Y)Tj /F21 1 Tf 7 0 0 7 315.781 398.437 Tm (41)Tj /F20 1 Tf 12 0 0 12 334.531 401.438 Tm (Y)Tj /F21 1 Tf 7 0 0 7 340.125 398.437 Tm (42)Tj /F20 1 Tf 12 0 0 12 359.437 401.438 Tm (Y)Tj /F21 1 Tf 7 0 0 7 365.031 398.437 Tm (43)Tj 12 0 0 12 386.781 401.438 Tm (0)Tj ET 0.5 w 309.437 464.594 m 309.437 397.344 l 396.25 464.594 m 396.25 397.344 l S BT /F20 1 Tf 12 0 0 12 309.344 385.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 314.25 382.687 Tm (11)Tj /F20 1 Tf 12 0 0 12 333.687 385.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 338.594 382.687 Tm (12)Tj /F20 1 Tf 12 0 0 12 358.594 385.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 363.5 382.687 Tm (13)Tj /F20 1 Tf 12 0 0 12 383.187 385.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 388.094 382.687 Tm (14)Tj /F20 1 Tf 12 0 0 12 309.062 367.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 314.531 364.687 Tm (21)Tj /F20 1 Tf 12 0 0 12 333.406 367.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 338.875 364.687 Tm (22)Tj /F20 1 Tf 12 0 0 12 358.312 367.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 363.781 364.687 Tm (23)Tj /F20 1 Tf 12 0 0 12 382.906 367.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 388.375 364.687 Tm (24)Tj /F20 1 Tf 12 0 0 12 309.094 349.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 314.469 346.687 Tm (31)Tj /F20 1 Tf 12 0 0 12 333.437 349.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 338.812 346.687 Tm (32)Tj /F20 1 Tf 12 0 0 12 358.344 349.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 363.719 346.687 Tm (33)Tj /F20 1 Tf 12 0 0 12 382.969 349.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 388.344 346.687 Tm (34)Tj /F20 1 Tf 12 0 0 12 309 331.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 314.594 328.688 Tm (41)Tj /F20 1 Tf 12 0 0 12 333.344 331.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 338.937 328.688 Tm (42)Tj /F20 1 Tf 12 0 0 12 358.25 331.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 363.844 328.688 Tm (43)Tj /F20 1 Tf 12 0 0 12 382.844 331.687 Tm (Y)Tj /F21 1 Tf 7 0 0 7 388.437 328.688 Tm (44)Tj ET 308.25 394.844 m 308.25 327.594 l 397.469 394.844 m 397.469 327.594 l 307 396.094 m 398.719 396.094 l S BT /F11 1 Tf 12 0 0 12 402.094 393 Tm (=)Tj /F20 1 Tf 0.786 0 TD (V)Tj 7 0 0 7 417.719 390 Tm (out)Tj ET 85 492 1 -1 re f 85 492 1 -1 re f 86 492 215 -1 re f 301 492 1 -1 re f 302 492 215 -1 re f 517 492 1 -1 re f 517 492 1 -1 re f 85 491 1 -177 re f 301 491 1 -177 re f 517 491 1 -177 re f BT /F12 1 Tf 12 0 0 12 90 304 Tm (3\) This comes out as:)Tj /T2 1 Tf 0 -3.083 TD ( )Tj /F20 1 Tf 0.125 1.789 TD (V)Tj 7 0 0 7 97.687 285.469 Tm (out)Tj 12 0 0 12 94.906 271.844 Tm (I)Tj 7 0 0 7 98.875 268.844 Tm (in)Tj ET 0.5 w 91 284.094 m 108.687 284.094 l S BT /F11 1 Tf 12 0 0 12 112.062 281 Tm (=)Tj /F20 1 Tf 0.813 0 TD (ks)Tj 7 0 0 7 132.437 286.344 Tm (m)Tj 12 0 0 12 142.531 288.469 Tm (c)Tj /F21 1 Tf 7 0 0 7 147.719 285.469 Tm (0)Tj /F11 1 Tf 12 0 0 12 154.937 288.469 Tm (+)Tj /F20 1 Tf 0.755 0 TD (c)Tj /F21 1 Tf 7 0 0 7 168.594 285.469 Tm (1)Tj /F20 1 Tf 12 0 0 12 172.156 288.469 Tm (s)Tj /F11 1 Tf 0.607 0 TD (+)Tj /F20 1 Tf 0.755 0 TD (c)Tj /F21 1 Tf 7 0 0 7 193.656 285.469 Tm (2)Tj /F20 1 Tf 12 0 0 12 197.781 288.469 Tm (s)Tj /F21 1 Tf 7 0 0 7 202.969 293.812 Tm (2)Tj /F11 1 Tf 12 0 0 12 208.187 288.469 Tm (+)Tj /T2 1 Tf 0.51 0 TD (L)Tj /F20 1 Tf -6.096 -1.385 TD (d)Tj /F21 1 Tf 7 0 0 7 147.187 268.844 Tm (0)Tj /F11 1 Tf 12 0 0 12 154.406 271.844 Tm (+)Tj /F20 1 Tf 0.773 0 TD (d)Tj /F21 1 Tf 7 0 0 7 169.125 268.844 Tm (1)Tj /F20 1 Tf 12 0 0 12 172.687 271.844 Tm (s)Tj /F11 1 Tf 0.607 0 TD (+)Tj /F20 1 Tf 0.773 0 TD (d)Tj /F21 1 Tf 7 0 0 7 195.25 268.844 Tm (2)Tj /F20 1 Tf 12 0 0 12 199.375 271.844 Tm (s)Tj /F21 1 Tf 7 0 0 7 204.562 277.187 Tm (2)Tj /F11 1 Tf 12 0 0 12 209.781 271.844 Tm (+)Tj /T2 1 Tf 0.51 0 TD (L)Tj ET 140.312 284.094 m 227.531 284.094 l S BT /F12 1 Tf 12 0 0 12 90 258 Tm (,which is divided through to get:)Tj 0 -2 TD (\(if present, m is the number of zeros,)Tj 0 -1 TD (minus the number of poles, in the transfer)Tj T* (function\))Tj 18 7.833 TD (4\))Tj 0 -2.083 TD ( )Tj /T2 1 Tf 0.25 -1.25 TD ( )Tj /F20 1 Tf 0.125 1.872 TD (V)Tj 7 0 0 7 316.687 283.469 Tm (out)Tj 12 0 0 12 313.906 269.844 Tm (I)Tj 7 0 0 7 317.875 266.844 Tm (in)Tj ET 0.5 w 310 282.094 m 327.687 282.094 l S BT /F11 1 Tf 12 0 0 12 331.062 279 Tm (=)Tj /F20 1 Tf 1.349 0.622 TD (V)Tj 7 0 0 7 353.437 283.469 Tm (out)Tj 12 0 0 12 350.656 269.844 Tm (I)Tj 7 0 0 7 354.625 266.844 Tm (in)Tj ET 346.75 282.094 m 364.437 282.094 l S BT /F11 1 Tf 12 0 0 12 340.531 287.312 Tm (\346)Tj 0 -1.503 TD (\350)Tj 0 0.57 TD (\347)Tj 2.023 0.932 TD (\366)Tj 0 -1.503 TD (\370)Tj 0 0.57 TD (\367)Tj /F20 1 Tf 7 0 0 7 371.125 265.187 Tm (mb)Tj 12 0 0 12 381.281 279 Tm (s)Tj 7 0 0 7 386.594 284.344 Tm (m)Tj /F21 1 Tf 12 0 0 12 394.656 286.469 Tm (1)Tj /F11 1 Tf 0.635 0 TD (+)Tj /F20 1 Tf 0.763 0 TD (b)Tj /F21 1 Tf 7 0 0 7 416.312 283.469 Tm (1)Tj /F20 1 Tf 12 0 0 12 419.875 286.469 Tm (s)Tj /F11 1 Tf 0.607 0 TD (+)Tj /F20 1 Tf 0.763 0 TD (b)Tj /F21 1 Tf 7 0 0 7 441.75 283.469 Tm (2)Tj /F20 1 Tf 12 0 0 12 445.875 286.469 Tm (s)Tj /F21 1 Tf 7 0 0 7 451.062 291.812 Tm (2)Tj /F11 1 Tf 12 0 0 12 456.281 286.469 Tm (+)Tj /T2 1 Tf 0.51 0 TD (L)Tj /F21 1 Tf -5.687 -1.385 TD (1)Tj /F11 1 Tf 0.635 0 TD (+)Tj /F20 1 Tf 0.773 0 TD (a)Tj /F21 1 Tf 7 0 0 7 416.312 266.844 Tm (1)Tj /F20 1 Tf 12 0 0 12 419.875 269.844 Tm (s)Tj /F11 1 Tf 0.607 0 TD (+)Tj /F20 1 Tf 0.773 0 TD (a)Tj /F21 1 Tf 7 0 0 7 442.25 266.844 Tm (2)Tj /F20 1 Tf 12 0 0 12 446.375 269.844 Tm (s)Tj /F21 1 Tf 7 0 0 7 451.562 275.187 Tm (2)Tj /F11 1 Tf 12 0 0 12 456.781 269.844 Tm (+)Tj /T2 1 Tf 0.51 0 TD (L)Tj ET 394.469 282.094 m 474.531 282.094 l S BT /F12 1 Tf 12 0 0 12 306 255 Tm (...and the poles and zeroes are found by)Tj 0 -1 TD (factoring the numerator and denominator.)Tj T* (The separated-pole approximation, if)Tj T* (applicable, makes this factoring easy.)Tj ET 85 314 m 86 314 l 86 313 l 85 313 l 85 314 l f 86 314 215 -1 re f 301 314 m 302 314 l 302 313 l 301 313 l 301 314 l f 302 314 215 -1 re f 517 314 m 518 314 l 518 313 l 517 313 l 517 314 l f 85 313 1 -118 re f 301 313 1 -118 re f 517 313 1 -118 re f BT 12 0 0 12 90 185 Tm (5\) To find the )Tj /F13 1 Tf 5.776 0 TD (impulse response)Tj /F12 1 Tf 6.89 0 TD (, do a)Tj -12.667 -1 TD (partial-fraction expansion and then take the)Tj T* (inverse LaPlace transform.)Tj 18 2 TD (6\) To find the sinusiodal frequency)Tj 0 -1.083 TD (response, set )Tj /T2 1 Tf 5.333 -0.333 TD ( )Tj /F20 1 Tf 0.068 0.333 TD (s)Tj /F11 1 Tf 0.646 0 TD (=)Tj /F20 1 Tf 0.935 0 TD (j)Tj /F11 1 Tf 12 0 2.64 12 393.094 172 Tm (w)Tj /F12 1 Tf 12 0 0 12 404 172 Tm (.)Tj ET 85 195 m 86 195 l 86 194 l 85 194 l 85 195 l f 86 195 215 -1 re f 301 195 m 302 195 l 302 194 l 301 194 l 301 195 l f 302 195 215 -1 re f 517 195 m 518 195 l 518 194 l 517 194 l 517 195 l f 85 194 1 -38 re f 85 156 m 86 156 l 86 155 l 85 155 l 85 156 l f 85 156 m 86 156 l 86 155 l 85 155 l 85 156 l f 86 156 215 -1 re f 301 194 1 -38 re f 301 156 m 302 156 l 302 155 l 301 155 l 301 156 l f 302 156 215 -1 re f 517 194 1 -38 re f 517 156 m 518 156 l 518 155 l 517 155 l 517 156 l f 517 156 m 518 156 l 518 155 l 517 155 l 517 156 l f endstream endobj 16 0 obj << /ProcSet [/PDF /Text ] /Font << /F11 5 0 R /F12 6 0 R /F13 17 0 R /F18 7 0 R /F19 8 0 R /F20 9 0 R /F21 10 0 R /T2 11 0 R >> /ExtGState << /GS1 12 0 R >> >> endobj 19 0 obj << /Length 18475 >> stream BT /F12 1 Tf 12 0 0 12 168 747 Tm 0 g /GS1 gs 0 Tc 0 Tw (ECE137B: High-Frequency Amplifier Crib Sheet, Page 3)Tj ET 0 G 0 J 0 j 0.804 w 10 M []0 d 1 i 90 691.8 m 372.973 691.8 l S BT 12 0 0 12 90 693 Tm (General Solutions of Problems: Method of Time Constants)Tj ET 1 g 2 J 1.002 w q 0.9985 0 0 -1.0015 0 0 cm 159.14 -579.298 70.306 48.673 re B Q q 0.9985 0 0 -1.0015 0 0 cm 215.024 -635.182 70.306 48.673 re B Q q 0.9985 0 0 -1.0015 0 0 cm 162.745 -671.236 70.306 48.673 re B Q q 0.9985 0 0 -1.0015 0 0 cm 97.847 -635.182 70.306 48.673 re B Q 2.003 w q 0.9985 0 0 -1.0015 0 0 cm 141.113 -651.406 113.571 86.53 re B Q BT /F18 1 Tf 12 0 0 12.036 148.799 627.114 Tm 0 g (Circuit without)Tj 0 -1.042 TD (Capacitors or)Tj T* (Inductors)Tj ET 1 g 1 G 1.002 w q 0.9985 0 0 -1.0015 0 0 cm 94.242 -617.155 7.211 9.014 re B* Q 0 G q 0.9985 0 0 -1.0015 0 0 cm 90.637 -615.352 m 105.058 -615.352 l 97.847 -622.563 m 97.847 -615.352 l S Q q -0.9985 0 0 -1.0015 0 0 cm -97.541 -611.747 m -94.877 -611.747 -92.349 -611.157 -90.636 -610.137 c S Q q 0.9985 0 0 -1.0015 0 0 cm 97.847 -611.747 m 100.511 -611.747 103.039 -611.157 104.752 -610.137 c 97.847 -611.747 m 97.847 -602.733 l S Q 1 G 0 w q 0.9985 0 0 -1.0015 0 0 cm 191.589 -678.447 14.422 14.422 re B Q 0 G 1.002 w q 0.9985 0 0 -1.0015 0 0 cm 196.997 -678.447 m 196.997 -664.025 l S Q q 0.9985 0 0 1.0015 0 0 cm 202.152 664.026 m 201.168 665.738 200.602 668.219 200.602 670.829 c S Q q 0.9985 0 0 -1.0015 0 0 cm 187.983 -671.236 m 196.997 -671.236 l 200.602 -671.236 m 209.616 -671.236 l 202.152 -678.447 m 201.168 -676.735 200.602 -674.253 200.602 -671.644 c S Q 1 G q 0.9985 0 0 -1.0015 0 0 cm 281.725 -617.155 7.211 9.014 re B* Q 0 G q 0.9985 0 0 -1.0015 0 0 cm 278.119 -615.352 m 292.541 -615.352 l 285.33 -622.563 m 285.33 -615.352 l S Q q -0.9985 0 0 -1.0015 0 0 cm -285.024 -611.747 m -282.36 -611.747 -279.832 -611.157 -278.119 -610.137 c S Q q 0.9985 0 0 -1.0015 0 0 cm 285.329 -611.747 m 287.994 -611.747 290.522 -611.157 292.235 -610.137 c 285.33 -611.747 m 285.33 -602.733 l S Q 1 G 0 w q 0.9985 0 0 -1.0015 0 0 cm 186.181 -537.835 14.422 14.422 re B Q 0 G 1.002 w q 0.9985 0 0 -1.0015 0 0 cm 191.589 -537.835 m 191.589 -523.413 l S Q q 0.9985 0 0 1.0015 0 0 cm 196.744 523.414 m 195.76 525.126 195.194 527.607 195.194 530.217 c S Q q 0.9985 0 0 -1.0015 0 0 cm 182.575 -530.624 m 191.589 -530.624 l 195.194 -530.624 m 204.208 -530.624 l 196.744 -537.835 m 195.76 -536.123 195.194 -533.641 195.194 -531.032 c S Q BT 7 0 0 7.021 109.499 622.399 Tm 0 g (port 1)Tj 10.029 4.629 TD (port 2)Tj -0.257 -14.143 TD (port 4)Tj 12 0 0 12.036 104.099 600.233 Tm (C)Tj /F19 1 Tf 9 0 0 9.027 112.766 596.221 Tm (1)Tj /F18 1 Tf 12 0 0 12.036 204.9 677.866 Tm (C)Tj /F19 1 Tf 9 0 0 9.027 213.566 673.854 Tm (2)Tj /F18 1 Tf 12 0 0 12.036 266.3 596.622 Tm (C)Tj /F19 1 Tf 9 0 0 9.027 274.966 592.61 Tm (3)Tj /F18 1 Tf 12 0 0 12.036 205.1 540.653 Tm (C)Tj /F19 1 Tf 9 0 0 9.027 213.766 536.641 Tm (4)Tj ET 1 g 0.8 w 382.8 598.009 56.218 -38.826 re B 427.486 642.588 56.218 -38.826 re B 385.683 671.348 56.218 -38.826 re B 333.789 642.588 56.218 -38.826 re B 1.6 w 368.385 655.53 90.814 -69.025 re B BT /F18 1 Tf 9.61 0 0 9.587 374.711 635.398 Tm 0 g (Circuit without)Tj 0 -1.042 TD (Capacitors or)Tj T* (Inductors)Tj 5.606 0 0 5.592 343.239 631.643 Tm (port 1)Tj 10.029 4.629 TD (port 2)Tj 10.8 -3.601 TD (port 3)Tj -11.057 -10.542 TD (port 4)Tj ET 1 g 1 G 0.8 w 319.374 635.394 24.505 -23.008 re B 473.614 635.394 24.505 -23.008 re B 397.215 567.807 24.505 -23.008 re B BT 9.61 0 0 9.587 307.201 622.771 Tm 0 g (R)Tj 7.207 0 0 7.19 314.141 625.967 Tm (2)Tj 0.556 -0.778 TD (11)Tj ET 0 G 330.906 625.328 m 349.645 625.328 l S 353.649 625.328 m 345.641 623.73 l 345.641 626.926 l f 1 g 1 G 398.656 688.601 24.505 -23.008 re B 0 g 308 615 22 19 re f BT /F12 1 Tf 7.2 0 0 7.164 313.328 650.113 Tm (R)Tj 0.695 -0.558 TD (11)Tj 0 0.976 TD (0)Tj ET 85 690 1 -1 re f 85 690 1 -1 re f 86 690 215 -1 re f 301 690 1 -1 re f 302 690 215 -1 re f 517 690 1 -1 re f 517 690 1 -1 re f 85 689 1 -166 re f 301 689 1 -166 re f 517 689 1 -166 re f 1 g 0 G 0.861 w q 0.9979 0 0 -1.0021 0 0 cm 172.729 -429.497 60.422 41.83 re B Q q 0.9979 0 0 -1.0021 0 0 cm 220.757 -477.525 60.422 41.83 re B Q q 0.9979 0 0 -1.0021 0 0 cm 175.828 -508.51 60.422 41.83 re B Q q 0.9979 0 0 -1.0021 0 0 cm 120.054 -477.525 60.422 41.83 re B Q 1.721 w q 0.9979 0 0 -1.0021 0 0 cm 157.236 -491.468 97.604 74.365 re B Q BT /F18 1 Tf 10.307 0 0 10.35 163.695 471.187 Tm 0 g (Circuit without)Tj 0 -1.042 TD (Capacitors or)Tj T* (Inductors)Tj 6.012 0 0 6.037 129.94 466.702 Tm (port 1)Tj 10.029 4.629 TD (port 2)Tj 10.8 -3.601 TD (port 3)Tj -11.057 -10.542 TD (port 4)Tj ET 1 g 1 G 0.861 w q 0.9979 0 0 -1.0021 0 0 cm 104.561 -469.775 26.338 24.788 re B Q q 0.9979 0 0 -1.0021 0 0 cm 270.334 -469.775 26.338 24.788 re B Q q 0.9979 0 0 -1.0021 0 0 cm 188.222 -396.959 26.338 24.788 re B Q BT 10.307 0 0 10.35 91.288 457.125 Tm 0 g (R)Tj 7.73 0 0 7.762 98.732 460.575 Tm (2)Tj 0.556 -0.778 TD (11)Tj ET 0 G q 0.9979 0 0 -1.0021 0 0 cm 116.955 -458.93 m 137.096 -458.93 l S Q 141.106 459.885 m 132.517 458.16 l 132.517 461.61 l f BT /T2 1 Tf 12 0 0 12 306 482 Tm ( )Tj /F20 1 Tf 0.167 2.039 TD (V)Tj 7 0 0 7 314.188 503.469 Tm (out)Tj 12 0 0 12 307.5 489.844 Tm (V)Tj 7 0 0 7 313.812 486.844 Tm (gen)Tj ET 0 J 0.5 w 307 502.094 m 325.687 502.094 l S BT /F11 1 Tf 12 0 0 12 329.062 499 Tm (=)Tj /F20 1 Tf 1.391 0.622 TD (V)Tj 7 0 0 7 351.937 503.469 Tm (out)Tj 12 0 0 12 345.25 489.844 Tm (V)Tj 7 0 0 7 351.562 486.844 Tm (gen)Tj ET 344.75 502.094 m 363.437 502.094 l S BT /F11 1 Tf 12 0 0 12 338.531 508.687 Tm (\346)Tj 0 -1.732 TD (\350)Tj 0 0.57 TD (\347)Tj 2.107 1.161 TD (\366)Tj 0 -1.732 TD (\370)Tj 0 0.57 TD (\367)Tj /F20 1 Tf 7 0 0 7 370.125 483.812 Tm (mb)Tj /F21 1 Tf 12 0 0 12 381.656 506.469 Tm (1)Tj /F11 1 Tf 0.635 0 TD (+)Tj /F20 1 Tf 0.763 0 TD (b)Tj /F21 1 Tf 7 0 0 7 403.312 503.469 Tm (1)Tj /F20 1 Tf 12 0 0 12 406.875 506.469 Tm (s)Tj /F11 1 Tf 0.607 0 TD (+)Tj /F20 1 Tf 0.763 0 TD (b)Tj /F21 1 Tf 7 0 0 7 428.75 503.469 Tm (2)Tj /F20 1 Tf 12 0 0 12 432.875 506.469 Tm (s)Tj /F21 1 Tf 7 0 0 7 438.063 511.812 Tm (2)Tj /F11 1 Tf 12 0 0 12 443.281 506.469 Tm (+)Tj /T2 1 Tf 0.51 0 TD (L)Tj /F21 1 Tf -5.688 -1.385 TD (1)Tj /F11 1 Tf 0.635 0 TD (+)Tj /F20 1 Tf 0.773 0 TD (a)Tj /F21 1 Tf 7 0 0 7 403.312 486.844 Tm (1)Tj /F20 1 Tf 12 0 0 12 406.875 489.844 Tm (s)Tj /F11 1 Tf 0.607 0 TD (+)Tj /F20 1 Tf 0.773 0 TD (a)Tj /F21 1 Tf 7 0 0 7 429.25 486.844 Tm (2)Tj /F20 1 Tf 12 0 0 12 433.375 489.844 Tm (s)Tj /F21 1 Tf 7 0 0 7 438.562 495.188 Tm (2)Tj /F11 1 Tf 12 0 0 12 443.781 489.844 Tm (+)Tj /T2 1 Tf 0.51 0 TD (L)Tj ET 381.469 502.094 m 461.531 502.094 l S BT 12 0 0 12 306 452 Tm ( )Tj /F20 1 Tf 0.07 0.417 TD (a)Tj /F21 1 Tf 7 0 0 7 312.094 454 Tm (1)Tj /F11 1 Tf 12 0 0 12 319.219 457 Tm (=)Tj /F20 1 Tf 0.859 0 TD (R)Tj /F21 1 Tf 7 0 0 7 335.531 454 Tm (11)Tj 0.232 1.192 TD (0)Tj /F20 1 Tf 12 0 0 12 342.406 457 Tm (C)Tj /F21 1 Tf 7 0 0 7 349.406 454 Tm (1)Tj /F11 1 Tf 12 0 0 12 356.062 457 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj /F21 1 Tf 7 0 0 7 372.438 454 Tm (22)Tj 0.152 1.192 TD (0)Tj /F20 1 Tf 12 0 0 12 379.875 457 Tm (C)Tj /F21 1 Tf 7 0 0 7 387.438 454 Tm (2)Tj /F11 1 Tf 12 0 0 12 394.656 457 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj /F21 1 Tf 7 0 0 7 410.937 454 Tm (33)Tj 0.165 1.192 TD (0)Tj /F20 1 Tf 12 0 0 12 418.062 457 Tm (C)Tj /F21 1 Tf 7 0 0 7 425.531 454 Tm (3)Tj /F11 1 Tf 12 0 0 12 432.437 457 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj /F21 1 Tf 7 0 0 7 448.937 454 Tm (44)Tj 0.134 1.192 TD (0)Tj /F20 1 Tf 12 0 0 12 456.344 457 Tm (C)Tj /F21 1 Tf 7 0 0 7 464.031 454 Tm (4)Tj /T2 1 Tf 12 0 0 12 306 422 Tm ( )Tj /F20 1 Tf 0.07 0.417 TD (a)Tj /F21 1 Tf 7 0 0 7 312.656 424 Tm (2)Tj /F11 1 Tf 12 0 0 12 320.344 427 Tm (=)Tj /F20 1 Tf 0.859 0 TD (R)Tj /F21 1 Tf 7 0 0 7 336.656 424 Tm (11)Tj 0.232 1.192 TD (0)Tj /F20 1 Tf 12 0 0 12 344.281 427 Tm (R)Tj /F21 1 Tf 7 0 0 7 350.844 424 Tm (22)Tj 0.067 1.192 TD (1)Tj /F20 1 Tf 12 0 0 12 358.281 427 Tm (C)Tj /F21 1 Tf 7 0 0 7 365.281 424 Tm (1)Tj /F20 1 Tf 12 0 0 12 368.656 427 Tm (C)Tj /F21 1 Tf 7 0 0 7 376.219 424 Tm (2)Tj /F11 1 Tf 12 0 0 12 383.437 427 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj /F21 1 Tf 7 0 0 7 399.25 424 Tm (11)Tj 0.232 1.192 TD (0)Tj /F20 1 Tf 12 0 0 12 406.875 427 Tm (R)Tj /F21 1 Tf 7 0 0 7 413.344 424 Tm (33)Tj 0.08 1.192 TD (1)Tj /F20 1 Tf 12 0 0 12 420.469 427 Tm (C)Tj /F21 1 Tf 7 0 0 7 427.469 424 Tm (1)Tj /F20 1 Tf 12 0 0 12 430.844 427 Tm (C)Tj /F21 1 Tf 7 0 0 7 438.312 424 Tm (3)Tj /F11 1 Tf 12 0 0 12 445.219 427 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj /F21 1 Tf 7 0 0 7 461.031 424 Tm (11)Tj 0.232 1.192 TD (0)Tj /F20 1 Tf 12 0 0 12 468.656 427 Tm (R)Tj /F21 1 Tf 7 0 0 7 475.344 424 Tm (44)Tj 0.049 1.192 TD (1)Tj /F20 1 Tf 12 0 0 12 482.75 427 Tm (C)Tj /F21 1 Tf 7 0 0 7 489.75 424 Tm (1)Tj /F20 1 Tf 12 0 0 12 493.125 427 Tm (C)Tj /F21 1 Tf 7 0 0 7 500.812 424 Tm (4)Tj /T2 1 Tf 12 0 0 12 306 404 Tm ( )Tj /F11 1 Tf 0.076 0.417 TD (+)Tj /F20 1 Tf 0.651 0 TD (R)Tj /F21 1 Tf 7 0 0 7 321.281 406 Tm (22)Tj 0.152 1.192 TD (0)Tj /F20 1 Tf 12 0 0 12 329.469 409 Tm (R)Tj /F21 1 Tf 7 0 0 7 335.937 406 Tm (33)Tj 0.161 1.192 TD (2)Tj /F20 1 Tf 12 0 0 12 343.062 409 Tm (C)Tj /F21 1 Tf 7 0 0 7 350.625 406 Tm (2)Tj /F20 1 Tf 12 0 0 12 354.562 409 Tm (C)Tj /F21 1 Tf 7 0 0 7 362.031 406 Tm (3)Tj /F11 1 Tf 12 0 0 12 368.937 409 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj /F21 1 Tf 7 0 0 7 385.312 406 Tm (22)Tj 0.152 1.192 TD (0)Tj /F20 1 Tf 12 0 0 12 393.5 409 Tm (R)Tj /F21 1 Tf 7 0 0 7 400.187 406 Tm (44)Tj 0.129 1.192 TD (2)Tj /F20 1 Tf 12 0 0 12 407.594 409 Tm (C)Tj /F21 1 Tf 7 0 0 7 415.156 406 Tm (2)Tj /F20 1 Tf 12 0 0 12 419.094 409 Tm (C)Tj /F21 1 Tf 7 0 0 7 426.781 406 Tm (4)Tj /F11 1 Tf 12 0 0 12 433.969 409 Tm (+)Tj /F20 1 Tf 0.818 0 TD (R)Tj /F21 1 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