"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10
"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10
"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10
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Putt<strong>in</strong>g It All Toge<strong>the</strong>r<br />
<strong>10</strong>-22<br />
voltage is multiplied by <strong>10</strong>1 through <strong>the</strong> circuit, but that was previously taken <strong>in</strong>to account<br />
for <strong>the</strong> 78.9 dB signal-to-noise calculation above.<br />
Reduc<strong>in</strong>g <strong>the</strong> value of <strong>the</strong> resistors to decrease <strong>the</strong>ir noise is an option. Chang<strong>in</strong>g <strong>the</strong> voltage<br />
divider resistors from <strong>10</strong>0 kΩ to 1 kΩ while leav<strong>in</strong>g <strong>the</strong> 0.1 µV capacitor <strong>the</strong> same,<br />
changes <strong>the</strong> corner frequency from 32 Hz to 796 Hz, right <strong>in</strong> <strong>the</strong> middle of <strong>the</strong> audio band.<br />
Note:<br />
Resist <strong>the</strong> temptation to make <strong>the</strong> capacitor larger to move <strong>the</strong> p<strong>in</strong>kish effect<br />
below <strong>the</strong> lower limits of human hear<strong>in</strong>g. <strong>The</strong> result<strong>in</strong>g circuit must charge<br />
<strong>the</strong> large capacitor up dur<strong>in</strong>g power up, and down dur<strong>in</strong>g power down. This<br />
may cause unexpected results.<br />
If <strong>the</strong> noise from <strong>the</strong> half-supply generator is critical, <strong>the</strong> best possible solution is to use<br />
a low-noise, low-impedance half-supply source. Remember, however, that its noise will<br />
be multiplied by <strong>10</strong>1 <strong>in</strong> this application.<br />
<strong>The</strong> effect of <strong>the</strong> <strong>10</strong>0-kΩ resistor on <strong>the</strong> <strong>in</strong>vert<strong>in</strong>g <strong>in</strong>put is whitish, and will appear across<br />
<strong>the</strong> entire bandwidth of <strong>the</strong> circuit. Compared to <strong>the</strong> amplifier noise, it is still small, just like<br />
<strong>the</strong> noise from <strong>the</strong> non<strong>in</strong>vert<strong>in</strong>g resistors on <strong>the</strong> <strong>in</strong>put. <strong>The</strong> noise contribution of resistors<br />
will be discounted.<br />
Of much more concern, however, is <strong>the</strong> <strong>10</strong>-MΩ resistor used as <strong>the</strong> feedback resistor. <strong>The</strong><br />
noise associated with it appears as a voltage source at <strong>the</strong> <strong>in</strong>vert<strong>in</strong>g <strong>in</strong>put of <strong>the</strong> op amp,<br />
and, <strong>the</strong>refore, is multiplied by a factor of <strong>10</strong>0 through <strong>the</strong> circuit. From Paragraph <strong>10</strong>.3.2,<br />
<strong>the</strong> noise of a <strong>10</strong>-MΩ resistor is –84.8 dBV, or 57.3 µV. Add<strong>in</strong>g this and <strong>the</strong> <strong>10</strong>0-kΩ resistor<br />
noise to <strong>the</strong> amplifier noise:<br />
ETotalrms 5.73 V2 113.1 V2 126.8 Vrms –77.9 dBV<br />
Signal-to-noise (dB) =<br />
20 log(1V 126.8 V) 20 log(7887) 77.9 dB<br />
(<strong>10</strong>–25)<br />
(<strong>10</strong>–26)<br />
<strong>The</strong> noise contribution from <strong>the</strong> <strong>10</strong>-MΩ resistor subtracts 1 dB from <strong>the</strong> signal-to-noise<br />
ratio. Chang<strong>in</strong>g <strong>the</strong> <strong>10</strong>-MΩ resistor to <strong>10</strong>0 kΩ, and <strong>the</strong> <strong>in</strong>put resistor from <strong>10</strong>0 kΩ to 1 kΩ<br />
preserves <strong>the</strong> overall ga<strong>in</strong> of <strong>the</strong> circuit. <strong>The</strong> redesigned circuit is shown <strong>in</strong> Figure <strong>10</strong>–16:
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