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| * The foundation of understanding electric circuits is Ohm's law. | | * The foundation of understanding electric circuits is Ohm's law. |
| [http://tinyurl.com/y579oadd Ohm's Law] | | [http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+10.20027730826997+50+5+43%0Ar+-240+-48+-64+-48+0+1000%0Av+-240+32+-240+-48+0+0+40+5+0+0+0.5%0A370+-64+-48+-64+32+1+0%0Ax+1+34+255+37+4+18+I%5Cs%5Cq%5CsU%5Cs/%5CsR%5Cs%5Cq%5Cs5%5CsV%5Cs/%5Cs1%5CskOhm%5Cs%5Cq%5Cs5%5CsmA%0Ax+-311+-88+330+-85+4+18+This%5Csshows%5Cshow%5Csto%5Cscalculate%5Csthe%5Cscurrent%5Csrunning%5Csthrough%5Csa%5Csresistor%5Csby%5CsOhm's%5Cslaw.%0Ax+-315+101+243+104+4+12+The%5Csvoltage%5Cssource%5Cson%5Csthe%5Csleft%5Cshas%5Cs5V,%5Cswhich%5Csforce%5Csa%5Cscurrent%5Csto%5Csrun%5Csthrough%5Csthe%5Csresistor%5Cswith%5Cs1000%5CsOhms.%0Ax+-317+127+114+130+4+12+%5CsThe%5Csresistor%5Cslimits%5Csthe%5Cscurrent%5Csto%5Cs5%5CsmA%5Cs(milli-Ampleres)%5Csaccording%5Csto%5CsOhm's%5Cslaw.%0Ax+-1+-6+67+-3+4+18+U%5Cs%5Cq%5CsR%5Cs*%5CsI%0Aw+-240+32+-240+48+0%0Aw+-240+48+-64+48+0%0Aw+-64+48+-64+32+0%0Ap+-304+-48+-304+48+1+0%0Aw+-304+48+-240+48+0%0Aw+-304+-48+-240+-48+0%0Ax+-310+-138+-227+-135+4+18+Ohm's%5Cslaw%0Ao+2+64+0+4099+0.0000762939453125+0.00625+0+2+2+3%0A Ohm's Law] |
| | * We can calculate series and parallel resistances with Ohm's law: |
| | [http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+45.7144713268909+50+5+43%0Ax+-483+108+-368+111+4+16+R_tot%5Cs%5Cq%5CsR1%5Cs%5Cp%5CsR2%0Ax+-469+-262+-224+-259+4+18+Series%5Csand%5CsParallel%5CsResistance%0Ax+-483+57+-330+60+4+12+Series%5CsResistances%5Csadd%5Csup!%0Ax+-501+-140+-485+-137+4+12+R1%0Ax+-500+-53+-484+-50+4+12+R2%0Ar+-464+-96+-464+16+0+1000%0Ar+-464+-192+-464+-96+0+1000%0A216+-400+16+-400+-192+0+0.01%0Aw+-400+-192+-464+-192+0%0Aw+-464+16+-400+16+0%0Aw+-96+16+-16+16+0%0Aw+-16+-192+-96+-192+0%0A216+64+16+64+-192+0+0.01%0Ar+-176+-192+-176+16+0+1000%0Ar+-96+-192+-96+16+0+1000%0Ax+-134+-84+-118+-81+4+12+R2%0Ax+-216+-86+-200+-83+4+12+R1%0Ax+-181+55+48+58+4+12+Parallel%5CsResistances%5Cshave%5Csan%5Csinverse%5Cslaw:%0Ax+-177+104+132+107+4+16+1%5Cs/%5CsR_tot%5Cs%5Cq%5Cs1/R1%5Cs%5Cp%5Cs1/R2%5Cs%5Cp%5Cs1/R3%5Cs%5Cp%5Cs...%5Cs%5Cp%5Cs1/R_n%0Aw+-176+-192+-96+-192+0%0Aw+-176+16+-96+16+0%0Ar+-16+-192+-16+16+0+1000%0Aw+-16+-192+64+-192+0%0Aw+-16+16+64+16+0%0Ax+-50+-84+-34+-81+4+12+R2%0A series and parallel resistances] |
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| * A very powerful concept is the voltage divider, it allows us to attenuate (but not amplify!) any voltage in any circuit | | * A very powerful concept is the voltage divider, it allows us to attenuate (but not amplify!) any voltage in any circuit |
| [http://tinyurl.com/yxhsk8sc voltage divider with even resistors] | | [http://tinyurl.com/yxhsk8sc voltage divider with even resistors] |
| * We will use the OpAmp (=operational amplifier) to amplify the small signals from our microphones to usable and less noisy signals before we digitize them in the computer. The opamp (= operational amplifier) is a three port device and its circuit diagram is a triangle. It has a positive and a negative input terminal and an output terminal. The most basic opamp circuit is the "comparator".
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| [http://tinyurl.com/yxrdh8gx opamp as a comparator]
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| * the opamp's output can also directly follow one of its input voltages, but providing more current. This is the basis building block of opamp based amplifiers and is called "voltage follower" or "buffer".
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| [http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+10.20027730826997+50+5+43%0Ag+-384+-48+-384+-32+0%0Av+-384+-48+-384+-128+0+1+100+5+0+0+0.5%0Ag+-272+-48+-272+-32+0%0Ax+-496+-235+-330+-232+4+18+The%5CsSource%5CsFollower%0Ax+-506+33+181+36+4+12+Once%5Csyou%5Csapply%5Csa%5Csfeedback%5Cspath%5Csfrom%5Csthe%5Csopamp's%5Csoutput%5Csto%5Csthe%5Csnegative%5Csinput,%5Csthe%5Csoutput%5Csvoltage%5Csdirectly%5Csfollws%5Csthe%5Csinput%5Csvoltage.%0Ax+-506+57+-440+60+4+12+Why%5Csis%5Csthat?%0Ax+-506+82+-3+85+4+12+When%5Csthe%5Cssinwave%5Csof%5Csthe%5Cspositive%5Csinput%5Csgoes%5Csup,%5Csthe%5Csoutput%5Cswill%5Csalso%5Csgo%5Csup%5Cs(with%5Csvery%5Cshigh%5Csgain).%0Ax+-509+109+299+112+4+12+%5CsBut%5Cssince%5Csthis%5Cshigh%5Csgain%5Cssignal%5Csis%5Csreflected%5Csback%5Csto%5Csthe%5Csnegative%5Csinput%5Csit%5Cswill%5Cscounteract%5Cson%5Csthe%5Csoutput,%5Csforcing%5Csthe%5Csoutput%5Cseven%5Csmore%5Csto%5Csthe%5Csminus%5Csdirection.%5Cs%0Aa+-384+-144+-272+-144+8+15+-15+1000000+2.8621324318134485+2.8621610531377666+100000%0Ap+-272+-144+-272+-48+1+0%0Aw+-272+-144+-240+-144+0%0A207+-240+-144+-192+-144+0+output%0A207+-384+-128+-416+-128+0+input%0Aw+-272+-144+-272+-208+0%0Aw+-272+-208+-384+-208+0%0Aw+-384+-208+-384+-160+0%0Ax+-508+134+367+137+4+12+However,%5Csfeedback%5Csis%5Csan%5Csendless%5Csprocess%5Csand%5Csas%5Cssuch%5Csthe%5Csforce%5Csto%5Csthe%5Csminus%5Csdirection%5Cswill%5Csbe%5Csreflected%5Csback%5Csto%5Csthe%5Csinput%5Csagain,%5Csforcing%5Csthe%5Csoutput%5Csto%5Csbe%5Cspositive%5Csagain.%0Ax+-510+164+175+167+4+12+All%5Csthose%5Cspositive%5Csand%5Csnegative%5Csforces%5Cswill%5Csmagically%5Cssum%5Csup%5Csin%5Csevery%5Csmoment%5Csin%5Cstime,%5Csforcing%5Csthe%5Csoutput%5Csto%5Csexactly%5Csfollow%5Csthe%5Csinput!%0Ax+-510+195+87+198+4+12+This%5Cscircuit%5Csis%5Csalso%5Cscalled%5Csa%5Cs%22buffer%22%5Cssince%5Csit%5Cscan%5Csbe%5Csused%5Csto%5Csrepeat%5Csa%5Csweak%5Cssignal.%5CsMeaning%5Csamplifiying%5Csthe%5Cscurrent,%5Cs%0Ax+-511+222+-63+225+4+12+since%5Csthe%5Csopamp%5Cscan%5Csprovide%5Csmore%5Cscurrent%5Csat%5Csthe%5Csouput%5Csthen%5Csis%5Csavailable%5Csat%5Csits%5Csinputs.%0Ao+9+64+0+4098+20+0.1+0+3+1+0+1+3%0A stabilized opamp as a source follower]
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| * once you provide a voltage divider circuit in the feedback loop of an voltage follower, you are able to control the gain of the output port. This means the voltage of the output can be a scaled version of the input, either attenuating or amplifying the input voltage. Depending on whether the voltage divider is applied on the positive or negative input, the output is an inverted or non-inverted version of the input voltage. The two basic building blocks are shown below.
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| [http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+10.20027730826997+50+5+43%0Ag+-304+16+-304+32+0%0Av+-448+16+-448+-64+0+1+100+1+0+0+0.5%0Ax+-411+-158+-231+-155+4+18+The%5CsInverting%5CsAmplifier%0Aa+-304+0+-192+0+8+15+-15+1000000+0.00009213554917863564+0+100000%0Aw+-192+0+-160+0+0%0A207+-160+0+-112+0+0+output%0Aw+-192+0+-192+-64+0%0Aw+-304+-64+-304+-16+0%0Ar+-288+-64+-208+-64+0+10000%0Aw+-288+-64+-304+-64+0%0Aw+-208+-64+-192+-64+0%0Ar+-448+-64+-304+-64+0+1000%0Ag+-448+16+-448+32+0%0Ax+-365+72+-208+75+4+12+Gain%5Cs%5Cq%5CsR2%5Cs/%5CsR1%5Cs%5Cq%5Cs10k/1K%5Cs%5Cq%5Cs10%0Ao+1+64+0+4098+5+0.1+0+2+1+3%0Ao+5+64+0+4099+10+0.00009765625+1+2+5+3%0A Inverting Opamp]
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| [http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+10.20027730826997+50+5+43%0Ag+-448+112+-448+128+0%0Av+-448+112+-448+32+0+1+100+1+0+0+0.5%0Ax+-411+-158+-192+-155+4+18+The%5CsNon-Inverting%5CsAmplifier%0Aa+-304+0+-192+0+8+15+-15+1000000+0.1842741783321202+0.18429444849173673+100000%0Aw+-192+0+-160+0+0%0A207+-160+0+-112+0+0+output%0Aw+-192+0+-192+-64+0%0Aw+-304+-64+-304+-16+0%0Aw+-448+32+-448+16+0%0Ar+-288+-64+-208+-64+0+10000%0Aw+-288+-64+-304+-64+0%0Aw+-208+-64+-192+-64+0%0Ar+-448+-64+-304+-64+0+1000%0Aw+-448+16+-304+16+0%0Ag+-448+-64+-448+-32+0%0Ax+-365+72+-168+75+4+12+Gain%5Cs%5Cq%5Cs1%5Cs%5Cp%5CsR2%5Cs/%5CsR1%5Cs%5Cq%5Cs1%5Cs%5Cp%5Cs10k/1K%5Cs%5Cq%5Cs11%0Ao+1+64+0+4098+5+0.1+0+2+1+3%0Ao+5+64+0+4099+20+0.00009765625+1+2+5+3%0A Non-Inverting Opamp]
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