Fundamentals of Microelectronics

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Unformatted text preview: 11.1 V out V in ( j ) = g m parenleftbigg R D bardbl 1 jC L parenrightbigg = g m R D 1 + jC L R D vextendsingle vextendsingle vextendsingle vextendsingle V out V in ( j ) vextendsingle vextendsingle vextendsingle vextendsingle = g m R D radicalBig 1 + ( C L R D ) 2 g m R D radicalBig 1 + ( 1 dB C L R D ) 2 = 0 . 9 g m R D 1 dB = 4 . 84 10 8 rad / s f 1 dB = 1 dB 2 = 77 . 1 MHz 11.3 (a) 3 dB = 1 parenleftBig 1 g m 2 bardbl r 2 parenrightBig C L (b) 3 dB = 1 parenleftBig r 2 + R B 1+ parenrightBig C L 1 parenleftBig 1 g m 2 + R B 1+ parenrightBig C L (c) 3 dB = 1 ( r o 1 bardbl r o 2 ) C L (d) 3 dB = 1 parenleftBig r o 1 bardbl 1 g m 2 bardbl r o 2 parenrightBig C L 11.4 Since all of these circuits are have one pole, all of the Bode plots will look qualitatively identical, with some DC gain at low frequencies that rolls off at 20 dB / dec after hitting the pole at 3 dB . This is shown in the following plot: - 3 dB vextendsingle vextendsingle vextendsingle V out V in ( j ) vextendsingle vextendsingle vextendsingle Slope = 20 dB / dec 20 log | A v | For each circuit, well derive | A v | and 3 dB , from which the Bode plot can be constructed as in the figure. (a) | A v | = g m 1 parenleftbigg 1 g m 2 bardbl r 2 parenrightbigg 3 dB = 1 parenleftBig 1 g m 2 bardbl r 2 parenrightBig C L (b) | A v | = g m 1 parenleftbigg r 2 + R B 1 + parenrightbigg g m 1 parenleftbigg 1 g m 2 + R B 1 + parenrightbigg 3 dB = 1 parenleftBig r 2 + R B 1+ parenrightBig C L 1 parenleftBig 1 g m 2 + R B 1+ parenrightBig C L (c) | A v | = g m 1 ( r o 1 bardbl r o 2 ) 3 dB = 1 ( r o 1 bardbl r o 2 ) C L (d) | A v | = g m 1 parenleftbigg r o 1 bardbl 1 g m 2 bardbl r o 2 parenrightbigg 3 dB = 1 parenleftBig r o 1 bardbl 1 g m 2 bardbl r o 2 parenrightBig C L 11.5 Assuming the transfer function is of the form V out V in ( j...
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This note was uploaded on 05/03/2009 for the course ECSE 2050 taught by Professor Monahella during the Spring '08 term at Rensselaer Polytechnic Institute.

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ch11sol - 11.1 V out V in ( j ) = g m parenleftbigg R D...

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