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[http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+10.20027730826997+50+5+43%0Ag+-448+80+-448+96+0%0Av+-448+80+-448+16+0+1+100+1+0+0+0.5%0Ax+-411+-158+-192+-155+4+18+The%5CsNon-Inverting%5CsAmplifier%0Aa+-304+0+-192+0+8+15+-15+1000000+0.6913109108869245+0.691386955087122+100000%0A207+-192+0+-144+0+4+output%0Aw+-192+0+-192+-64+0%0Aw+-304+-64+-304+-16+0%0Ar+-288+-64+-208+-64+0+10000%0Aw+-288+-64+-304+-64+0%0Aw+-208+-64+-192+-64+0%0Ar+-448+-64+-304+-64+0+1000%0Aw+-448+16+-304+16+0%0Ag+-448+-64+-448+-32+0%0Ax+-344+68+-147+71+4+12+Gain%5Cs%5Cq%5Cs1%5Cs%5Cp%5CsR2%5Cs/%5CsR1%5Cs%5Cq%5Cs1%5Cs%5Cp%5Cs10k/1K%5Cs%5Cq%5Cs11%0Ax+-253+-41+-238+-38+4+12+R2%0Ax+-383+-42+-368+-39+4+12+R1%0Ax+-469+11+-439+14+4+14+input%0Ao+1+64+0+4098+5+0.1+0+2+1+3%0Ao+4+64+0+4098+20+0.00009765625+1+2+4+3%0A Non-Inverting Opamp] | [http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+10.20027730826997+50+5+43%0Ag+-448+80+-448+96+0%0Av+-448+80+-448+16+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+0.6913109108869245+0.691386955087122+100000%0A207+-192+0+-144+0+4+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%0Aw+-448+16+-304+16+0%0Ag+-448+-64+-448+-32+0%0Ax+-344+68+-147+71+4+12+Gain%5Cs%5Cq%5Cs1%5Cs%5Cp%5CsR2%5Cs/%5CsR1%5Cs%5Cq%5Cs1%5Cs%5Cp%5Cs10k/1K%5Cs%5Cq%5Cs11%0Ax+-253+-41+-238+-38+4+12+R2%0Ax+-383+-42+-368+-39+4+12+R1%0Ax+-469+11+-439+14+4+14+input%0Ao+1+64+0+4098+5+0.1+0+2+1+3%0Ao+4+64+0+4098+20+0.00009765625+1+2+4+3%0A Non-Inverting Opamp] | ||
* We can use a special configuration of the Opamp together with a capacitor as a simple oscillator. The following simulation is a square wave oscillator. At the positive input terminal, there is a voltage divider, that divides down the output of the opamp in half. Since it is positive feedback, the opamp will drive to the maximum point, which in our case is +-15V. The voltage divider divides this voltage down to half. Depending on whether the output drives high or low, the voltag at the positive input is thus +-7.5V. The capacitor gets constantly charged and discharged from the output of the opamp through the resistor. The voltage at the capacitor on the negative input compares to this threshold voltage and inverts the signal when it exceeds the respective treshold. Since this process is endlessly repeating, the output oscillates. The frequency is dependend on the size of the capacitor and the resistance of the negative feedback resistor. | |||
[http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+12.050203812241895+54+5+43%0Ag+-240+96+-240+112+0%0Ax+-134+-188+297+-185+4+18+Self-Oscillating%5CsComparator%5Cs(Square%5CsWave%5CsGenerator)%0Aa+-240+0+-128+0+8+15+-15+1000000+6.090293760309295+7.500070481327725+100000%0Aw+-128+0+-96+0+0%0Ag+-304+-16+-304+0+0%0A207+-96+0+-48+0+4+output%0Ac+-304+-16+-240+-16+0+1.0000000000000001e-7+-6.090293760309295%0Ar+-240+48+-240+96+0+100000%0Ar+-240+48+-128+48+0+100000%0Aw+-240+16+-240+48+2%0Aw+-128+0+-128+48+0%0Ar+-240+-64+-128+-64+0+100000%0Aw+-128+-64+-128+0+0%0Aw+-240+-64+-240+-16+2%0Ao+9+64+0+4098+10+0.00009765625+0+2+9+3%0Ao+13+64+0+4098+10+0.00078125+1+2+13+3%0A Square Wave Generator] | [http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+12.050203812241895+54+5+43%0Ag+-240+96+-240+112+0%0Ax+-134+-188+297+-185+4+18+Self-Oscillating%5CsComparator%5Cs(Square%5CsWave%5CsGenerator)%0Aa+-240+0+-128+0+8+15+-15+1000000+6.090293760309295+7.500070481327725+100000%0Aw+-128+0+-96+0+0%0Ag+-304+-16+-304+0+0%0A207+-96+0+-48+0+4+output%0Ac+-304+-16+-240+-16+0+1.0000000000000001e-7+-6.090293760309295%0Ar+-240+48+-240+96+0+100000%0Ar+-240+48+-128+48+0+100000%0Aw+-240+16+-240+48+2%0Aw+-128+0+-128+48+0%0Ar+-240+-64+-128+-64+0+100000%0Aw+-128+-64+-128+0+0%0Aw+-240+-64+-240+-16+2%0Ao+9+64+0+4098+10+0.00009765625+0+2+9+3%0Ao+13+64+0+4098+10+0.00078125+1+2+13+3%0A Square Wave Generator] | ||
* To shape the spectrum of our oscillators we will use a lowpass filter. The simplest form of a lowpass filter is the passive lowpass filter. You can view this lowpass filter as an elaborated voltage divider: the capacitor has a frequency dependent resistance (which we call an impedance). This impedance is very high for static voltages (DC) and low frequencies. The impedance goes down the higher the frequency is at its input. The higher the frequency, the lower the impedance at the capacitor and the lower will be the voltage at the capacitor. This will effectively filter out high frequencies and leave lower frequencies in the signal. | |||
[http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+12.050203812241895+54+5+43%0Ag+-192+-64+-192+-48+0%0Ax+-196+-216+-12+-213+4+18+Passive%5CsLowpass%5CsFilter%0Aw+-192+-128+-160+-128+0%0A207+-160+-128+-112+-128+4+output%0Ac+-192+-128+-192+-64+0+1.0000000000000001e-7+0.6852026285128602%0Ar+-192+-128+-288+-128+0+1000%0AR+-288+-128+-336+-128+0+1+1591.5+1+0+0+0.5%0Ax+-13+-92+91+-89+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*R*C)%0Ax+-14+-67+180+-64+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*10%5E3%5CsOhm*10%5E-7%5CsF)%0Ax+-14+-40+156+-37+4+14+f%5Cs%5Cq%5Cs10%5E4%5Cs/%5Cs(2*pi)%5Cq10000/%5Cs2pi%0Ax+-14+-12+69+-9+4+14+f%5Cs%5Cq%5Cs1591,5%5CsHz%0Ax+-13+-130+293+-127+4+14+Calculation%5Csof%5Csfilter%5Cscutoff%5Cspoint%5Cs(-3dB%5CsFrequency)%0Ao+3+4+0+4106+1.25+0.00009765625+0+2+3+3%0A Passive Lowpass Filter] | |||
* The passive low pass filter has the same disadvantage as the voltage divider: the output cannot be loaded without changing its characteristics. To prevent this, we can just put a buffer at the output of the low pass filter. | |||
[http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+12.050203812241895+54+5+43%0Ag+-256+32+-256+48+0%0Ax+-164+-202+66+-199+4+18+Simple%5CsActive%5CsLowpass%5CsFilter%0Aw+-256+-32+-224+-32+0%0A207+-112+-48+-64+-48+4+output%0Ac+-256+-32+-256+32+0+1.0000000000000001e-7+0.41109475569201465%0Ar+-256+-32+-352+-32+0+1000%0AR+-352+-32+-400+-32+0+1+1591.5+1+0+0+0.5%0Ax+-13+-92+91+-89+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*R*C)%0Ax+-14+-67+180+-64+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*10%5E3%5CsOhm*10%5E-7%5CsF)%0Ax+-14+-40+156+-37+4+14+f%5Cs%5Cq%5Cs10%5E4%5Cs/%5Cs(2*pi)%5Cq10000/%5Cs2pi%0Ax+-14+-12+69+-9+4+14+f%5Cs%5Cq%5Cs1591,5%5CsHz%0Ax+-13+-130+293+-127+4+14+Calculation%5Csof%5Csfilter%5Cscutoff%5Cspoint%5Cs(-3dB%5CsFrequency)%0Aw+-224+-112+-224+-64+0%0Aw+-112+-112+-224+-112+0%0Aw+-112+-48+-112+-112+0%0Aa+-224+-48+-112+-48+8+15+-15+1000000+0.4110906447855668+0.41109475569201465+100000%0Ao+3+4+0+4106+1.25+0.00009765625+0+2+3+3%0A Simple Active Lowpass Filter] | |||
* Still, since the resistance of our source adds to our first resistor, the cutoff point will change, when the resistance of the source changes. To mitigate this we can change the topologie of our filter like so: | |||
[http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+12.050203812241895+54+5+43%0Ax+-164+-202+6+-199+4+18+Active%5CsLowpass%5CsFilter%0A207+-128+0+-80+0+4+output%0Ac+-128+-112+-240+-112+0+1.0000000000000001e-7+-0.06865131933234453%0Ar+-128+-64+-240+-64+0+1000%0AR+-336+-64+-384+-64+0+1+1591.5+1+0+0+0.5%0Ax+-13+-92+99+-89+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*R2*C)%0Ax+-14+-67+180+-64+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*10%5E3%5CsOhm*10%5E-7%5CsF)%0Ax+-14+-40+156+-37+4+14+f%5Cs%5Cq%5Cs10%5E4%5Cs/%5Cs(2*pi)%5Cq10000/%5Cs2pi%0Ax+-14+-12+69+-9+4+14+f%5Cs%5Cq%5Cs1591,5%5CsHz%0Ax+-13+-130+293+-127+4+14+Calculation%5Csof%5Csfilter%5Cscutoff%5Cspoint%5Cs(-3dB%5CsFrequency)%0Aw+-240+-64+-240+-16+0%0Aw+-128+0+-128+-64+0%0Aa+-240+0+-128+0+8+15+-15+1000000+6.865063282601628e-7+0+100000%0Aw+-240+-112+-240+-64+0%0Ar+-240+-64+-336+-64+0+1000%0Ag+-240+16+-240+32+0%0Aw+-128+-112+-128+-64+0%0Ax+-298+-40+-280+-37+4+14+R1%0Ax+-194+-40+-176+-37+4+14+R2%0Ax+-14+42+81+45+4+14+-R2/R1%5Cs...%5CsGain%0Ax+-14+95+226+98+4+14+R2%5Cs...%5CsSets%5Cscutoff%5Csfrequency%5Cs(and%5Csgain)%0Ax+-14+69+83+72+4+14+R1%5Cs...%5CsSets%5Csgain%0Ao+1+4+0+4106+1.25+0.00009765625+0+2+1+3%0A Active Low Pass Filter] | |||
* Unfortunately we can't set the cutoff frequency independently of the gain of our filter with just one resistor (e.g. a potentiometer). With another filter topology, the "bridged T low pass filter", we can tune the filter without changing its gain. To get a bridged T filter, we exchange the capacitor in the feedback loop with two capacitors in series and add a resistor. | |||
[http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+12.050203812241895+54+5+43%0Ax+-167+-245+39+-242+4+18+Bridged%5CsT%5CsLow%5CsPass%5CsFilter%0A207+-112+0+-80+0+4+output%0Ac+-176+-192+-240+-192+0+1.0000000000000001e-7+0.07208828582967249%0Ar+-112+-64+-240+-64+0+1000%0AR+-320+-64+-368+-64+0+6+1591+1+0+0+0.5%0Ax+-20+-133+185+-130+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*sqrt(R1*R2*C1*C2)))%0Ax+-21+-108+173+-105+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*10%5E3%5CsOhm*10%5E-7%5CsF)%0Ax+-21+-81+149+-78+4+14+f%5Cs%5Cq%5Cs10%5E4%5Cs/%5Cs(2*pi)%5Cq10000/%5Cs2pi%0Ax+-21+-53+62+-50+4+14+f%5Cs%5Cq%5Cs1591,5%5CsHz%0Ax+-20+-171+170+-168+4+14+Calculation%5Csof%5Csfilter%5Cscutoff%5Cspoint%0Aw+-240+-64+-240+-16+0%0Aw+-112+0+-112+-64+0%0Aa+-240+0+-112+0+8+15+-15+1000000+8.53353504561735e-8+0+100000%0Aw+-240+-192+-240+-64+0%0Aw+-112+-192+-112+-64+0%0Ax+-181+-37+-163+-34+4+14+R1%0Ax+-210+-152+-192+-149+4+14+R2%0Ax+-14+42+81+45+4+14+-R2/R1%5Cs...%5CsGain%0Ax+-14+95+157+98+4+14+R2%5Cs...%5CsSets%5Cscutoff%5Csfrequency%0Ax+-14+69+83+72+4+14+R3%5Cs...%5CsSets%5Csgain%0Ac+-112+-192+-176+-192+0+1.0000000000000001e-7+-0.08062190621064029%0Ar+-320+-64+-240+-64+0+1000%0Ag+-240+16+-240+48+0%0Ar+-176+-192+-176+-128+0+1000%0Ag+-176+-128+-176+-112+0%0Ax+-291+-36+-273+-33+4+14+R3%0Ax+-13+123+276+126+4+14+R1%5Cs...%5CsThe%5Csbigger%5CsR1,%5Csthe%5Csmore%5CsQ%5Cs(resonance)%0Ao+1+4+0+5128+2.5+0.00009765625+0+2+1+3%0A Bridged T Low Pass Filter] | |||
* modifiying the capacitor and resistor values, we can use a 100k potentiometer to have a variable cutoff frequency filter | |||
[http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+12.050203812241895+54+5+43%0Ax+-167+-245+39+-242+4+18+Bridged%5CsT%5CsLow%5CsPass%5CsFilter%0A207+-112+0+-80+0+4+output%0Ac+-176+-192+-240+-192+0+2e-9+0.09900202645250962%0Ar+-112+-64+-240+-64+0+100000%0AR+-320+-64+-368+-64+0+6+1591+1+0+0+0.5%0Ax+-20+-133+183+-130+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*sqrt(R1*R2*C1*C2)))%0Ax+-21+-108+173+-105+4+14+f%5Cs%5Cq%5Cs1%5Cs/%5Cs(2*pi*10%5E3%5CsOhm*10%5E-7%5CsF)%0Ax+-21+-81+147+-78+4+14+f%5Cs%5Cq%5Cs10%5E4%5Cs/%5Cs(2*pi)%5Cq10000/%5Cs2pi%0Ax+-21+-53+62+-50+4+14+f%5Cs%5Cq%5Cs1591,5%5CsHz%0Ax+-20+-171+167+-168+4+14+Calculation%5Csof%5Csfilter%5Cscutoff%5Cspoint%0Aw+-240+-64+-240+-16+0%0Aw+-112+0+-112+-64+0%0Aa+-240+0+-112+0+8+15+-15+1000000+-0.000002138187387850065+0+100000%0Aw+-240+-192+-240+-64+0%0Aw+-112+-192+-112+-64+0%0Ax+-181+-37+-164+-34+4+14+R1%0Ax+-210+-152+-193+-149+4+14+R2%0Ax+-14+42+79+45+4+14+-R3/R1%5Cs...%5CsGain%0Ax+-14+95+154+98+4+14+R2%5Cs...%5CsSets%5Cscutoff%5Csfrequency%0Ax+-14+69+81+72+4+14+R3%5Cs...%5CsSets%5Csgain%0Ac+-112+-192+-176+-192+0+2e-9+0.11481885051988475%0Ar+-320+-64+-240+-64+0+100000%0Ag+-240+16+-240+48+0%0Ag+-176+-128+-176+-112+0%0Ax+-291+-36+-274+-33+4+14+R3%0Ax+-13+123+269+126+4+14+R1%5Cs...%5CsThe%5Csbigger%5CsR1,%5Csthe%5Csmore%5CsQ%5Cs(resonance)%0A174+-176+-192+-176+-128+1+100000+0.33170000000000005+Cutoff%0Aw+-160+-160+-128+-160+0%0Aw+-128+-160+-128+-128+0%0Aw+-128+-128+-176+-128+0%0Ao+1+4+0+5128+2.5+0.00009765625+0+2+1+3%0A Variable Cutoff Active Filter] | |||
[http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+9.001713130052181+54+5+43%0Ax+-132+-156+68+-153+4+18+Triangle%5Cs/%5CsSaw%5CsGenerator%0Aa+-240+0+-128+0+8+15+-15+1000000+0+3.6818713027031436+100000%0Ag+16+32+16+64+0%0A207+128+16+176+16+4+output%0Ac+16+-64+128+-64+0+1e-8+0.5101696765160468%0Ar+-240+48+-240+128+0+100000%0Ar+-240+48+-128+48+0+270000%0Aw+-240+16+-240+48+2%0Aw+-128+0+-128+48+0%0Ar+-64+0+16+0+0+100000%0Ad+-80+-64+-128+-64+2+default%0Aa+16+16+128+16+8+15+-15+1000000+0.000005101645748702981+0+100000%0Aw+16+-64+16+0+0%0Aw+128+-64+128+16+0%0Aw+128+16+128+128+0%0Aw+128+128+-240+128+0%0Ag+-240+-16+-288+-16+0%0Ag+-64+64+-64+80+0%0Ar+-64+0+-64+64+0+50000%0Ar+-128+0+-64+0+0+50000%0Aw+-128+-64+-128+0+0%0Ar+-80+-64+-32+-64+0+1000%0As+-32+-64+16+-64+0+1+false%0Ax+-21+-87+5+-84+4+8+triangle%0Ax+-16+-44+-3+-41+4+8+saw%0Ao+7+8+0+4098+20+0.00009765625+0+2+7+3%0Ao+8+8+0+4106+20+0.1+1+2+8+3%0Ao+3+8+0+4106+20+0.1+2+2+3+3%0A Trianlge / Saw Generator] | [http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+9.001713130052181+54+5+43%0Ax+-132+-156+68+-153+4+18+Triangle%5Cs/%5CsSaw%5CsGenerator%0Aa+-240+0+-128+0+8+15+-15+1000000+0+3.6818713027031436+100000%0Ag+16+32+16+64+0%0A207+128+16+176+16+4+output%0Ac+16+-64+128+-64+0+1e-8+0.5101696765160468%0Ar+-240+48+-240+128+0+100000%0Ar+-240+48+-128+48+0+270000%0Aw+-240+16+-240+48+2%0Aw+-128+0+-128+48+0%0Ar+-64+0+16+0+0+100000%0Ad+-80+-64+-128+-64+2+default%0Aa+16+16+128+16+8+15+-15+1000000+0.000005101645748702981+0+100000%0Aw+16+-64+16+0+0%0Aw+128+-64+128+16+0%0Aw+128+16+128+128+0%0Aw+128+128+-240+128+0%0Ag+-240+-16+-288+-16+0%0Ag+-64+64+-64+80+0%0Ar+-64+0+-64+64+0+50000%0Ar+-128+0+-64+0+0+50000%0Aw+-128+-64+-128+0+0%0Ar+-80+-64+-32+-64+0+1000%0As+-32+-64+16+-64+0+1+false%0Ax+-21+-87+5+-84+4+8+triangle%0Ax+-16+-44+-3+-41+4+8+saw%0Ao+7+8+0+4098+20+0.00009765625+0+2+7+3%0Ao+8+8+0+4106+20+0.1+1+2+8+3%0Ao+3+8+0+4106+20+0.1+2+2+3+3%0A Trianlge / Saw Generator] | ||
Line 32: | Line 54: | ||
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Oscillators, Filter and Gate] | |||
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