[{"data":1,"prerenderedAt":485},["ShallowReactive",2],{"schematic:lm358-inverting-amplifier:en":3},{"schematic":4,"title":19,"shortDescription":22,"proseSource":440,"localizationFallbackIssues":441,"related":442,"confirmations":441},{"schemaVersion":5,"governance":6,"slug":18,"title":19,"cluster":20,"tier":21,"shortDescription":22,"deepTechnicalOverview":23,"theoryOfOperation":24,"keySpecifications":25,"applications":50,"gotchas":55,"formulas":74,"bom":131,"interactiveElements":154,"circuitJson":222,"svg":436,"relatedSchematicSlugs":437,"relatedComponentSlugs":438,"relatedBoardSlugs":439},"1.0",{"publication":7,"verification":10,"provenance":15},{"status":8,"publishedDate":9},"published","2026-11-02",{"status":11,"verifiedDate":9,"verifiedBy":12,"checklist":13},"verified","Gemini (AI documentary, CAD and hardware-localization review against Texas Instruments SLOS068AB; owner publication authorization; no bench, simulation, independent second review or native-speaker claim)",{"schema":14,"technicalFacts":14,"relationships":14,"sources":14},true,{"sourceUrls":16},[17],"https:\u002F\u002Fwww.ti.com\u002Flit\u002Fds\u002Fsymlink\u002Flm358.pdf","lm358-inverting-amplifier","LM358 Inverting Operational Amplifier","analog_sensing","Tier 1","Single-channel inverting amplifier using the Texas Instruments LM358 dual op-amp providing -3.6 V\u002FV closed-loop gain from a ±12 V split supply.","This circuit implements the classic inverting amplifier from Texas Instruments LM358 datasheet SLOS068AB Figure 8-1. Operating from symmetrical ±12 V rails, it provides a closed-loop inverting gain of Av = -RF \u002F RI = -36 kΩ \u002F 10 kΩ = -3.6 V\u002FV. Symmetrical dual supplies allow true bipolar signal amplification (±0.5 V input produces ∓1.8 V output) centered around ground. High open-loop gain forces the inverting terminal into a virtual ground (0 V), while negative feedback establishes high linearity, predictable frequency response up to 152 kHz, and low output impedance.","### 1. Symmetrical split-rail supply\nThe LM358 operational amplifier is powered from symmetrical ±12 V supplies (+12 V connected to pin 8 V+, -12 V connected to pin 4 V-). Symmetrical rails ensure that the internal class-AB output stage can swing undistorted in both positive and negative directions relative to the 0 V circuit ground, enabling clean AC and bipolar DC signal amplification.\n\n### 2. Virtual ground summing junction\nThe non-inverting input (IN+ \u002F pin 3) connects directly to circuit ground (0 V). The op-amp internal differential input stage and high open-loop gain (A_OL ≈ 100 dB) act through the negative feedback loop to drive the differential input voltage V_ID = V+ - V- to virtually zero volts. Consequently, the inverting summing node at pin 2 is maintained at 0 V, forming an ideal virtual ground.\n\n### 3. Inverting gain and feedback current balance\nBecause the LM358 PNP Darlington input transistors draw minimal bias current (I_B ≈ 20 nA typical), signal current arriving from input resistor R1 must flow entirely through feedback resistor R2. Applying Kirchhoff's Current Law at the inverting summing junction gives:\n$$I_{IN} = \\frac{V_{IN} - 0\\text{V}}{R_I} = \\frac{0\\text{V} - V_{OUT}}{R_F}$$\nSolving for output voltage V_OUT yields the ideal inverting amplifier transfer equation:\n$$V_{OUT} = -V_{IN} \\cdot \\frac{R_F}{R_I} = -V_{IN} \\cdot \\frac{36\\text{k}\\Omega}{10\\text{k}\\Omega} = -3.6 \\cdot V_{IN}$$\nAn input signal of ±0.5 V produces an inverted output of ∓1.8 V (180° phase inversion).\n\n### 4. Input impedance and source loading\nAt the inverting terminal, the virtual ground sets the circuit input impedance to exactly the value of the input series resistor:\n$$Z_{IN} = R_I = 10\\text{k}\\Omega$$\nUnlike non-inverting configurations with gigohm input resistance, the inverting amplifier draws a signal current of I_IN = ±0.5 V \u002F 10 kΩ = ±50 µA from the input source. Upstream signal generators must have low internal impedance (\u003C 10 Ω) to avoid gain attenuation errors.\n\n### 5. Dynamic bandwidth and slew rate constraints\nThe LM358 provides a unity-gain bandwidth product (GBW) of 0.7 MHz (700 kHz) and a slew rate of 0.3 V\u002Fµs. With a closed-loop noise gain of A_N = 1 + R_F \u002F R_I = 1 + 3.6 = 4.6 V\u002FV, the small-signal -3 dB bandwidth is:\n$$f_{-3\\text{dB}} \\approx \\frac{GBW}{1 + \\frac{R_F}{R_I}} = \\frac{700\\text{kHz}}{4.6} \\approx 152\\text{ kHz}$$\nFor large output swings (3.6 V peak-to-peak), the full-power bandwidth is constrained by the 0.3 V\u002Fµs slew rate to approximately 26.5 kHz before triangular wave distortion occurs.",[26,29,32,35,38,41,44,47],{"label":27,"value":28},"Closed-Loop Voltage Gain (Av)","-3.6 V\u002FV (-11.13 dB, 180° phase inversion)",{"label":30,"value":31},"Input Resistor (RI \u002F R1)","10 kΩ, 1%, 0.125 W",{"label":33,"value":34},"Feedback Resistor (RF \u002F R2)","36 kΩ, 1%, 0.125 W",{"label":36,"value":37},"Input Signal Range (VI)","±0.5 V nominal (1.0 V p-p)",{"label":39,"value":40},"Output Signal Range (VO)","∓1.8 V nominal (3.6 V p-p)",{"label":42,"value":43},"Power Supply Rails (V+ \u002F V-)","±12 V split supply (operates from ±1.5 V to ±16 V)",{"label":45,"value":46},"Small-Signal Bandwidth (-3 dB)","≈ 152 kHz (GBW = 0.7 MHz, noise gain = 4.6)",{"label":48,"value":49},"Input Impedance (ZIN)","10 kΩ (defined by R1)",[51,52,53,54],"Precision analog signal scaling and mathematical inversion in instrumentation","Audio preamplifier inverting summing stage for active mixers","Sensor interface stage converting bipolar voltage signals for dual-rail ADCs","Foundational laboratory benchmark circuit for operational amplifier education",[56,61,66,70],{"title":57,"trap":58,"solution":59,"severity":60},"Class-AB Crossover Distortion Across Zero Volts","When output current reverses direction across 0 V between sourcing and sinking, the LM358 complementary output stage exhibits a deadband that creates high-frequency crossover spikes on sinusoidal signals.","Connect an external pull-down resistor (2 kΩ to 10 kΩ) from the output (pin 1) to the negative rail (-12 V). This keeps the top NPN transistor sourcing current continuously, forcing class-A operation and eliminating crossover distortion.","critical",{"title":62,"trap":63,"solution":64,"severity":65},"Input Bias Current DC Offset Error","The LM358 input PNP Darlington transistors have an input bias current (IB ≈ 20 nA to 100 nA) flowing out of both inputs. Tying IN+ directly to ground with 0 Ω causes an unequal DC voltage drop across RI || RF (7.83 kΩ), generating an uncompensated output offset.","Insert a bias compensation resistor RP = RI || RF ≈ 7.5 kΩ to 8.2 kΩ in series between IN+ (pin 3) and ground to equalize the source resistance seen by both differential inputs.","warning",{"title":67,"trap":68,"solution":69,"severity":65},"Slew Rate Limited Full-Power Bandwidth","With a 0.3 V\u002Fµs slew rate, driving large-amplitude output signals (3.6 V p-p) above 26 kHz causes slew-rate limiting, turning smooth sinusoidal waves into distorted triangular waveforms.","Limit large-amplitude high-frequency signals below 25 kHz. For wider bandwidth applications, substitute a pin-compatible higher-speed op-amp such as the TL072 (13 V\u002Fµs) or OPA2134 (20 V\u002Fµs).",{"title":71,"trap":72,"solution":73,"severity":65},"Source Resistance Alters Closed-Loop Gain","Because circuit input impedance is defined solely by RI (10 kΩ), any internal source impedance R_source of the driving signal generator adds directly to RI, reducing effective circuit gain to -RF \u002F (RI + R_source).","Drive the inverting stage from a low-impedance buffer (\u003C 10 Ω), or calibrate RI by subtracting known source resistance so the combined sum equals 10 kΩ exactly.",[75,98,114],{"name":76,"latexOrText":77,"description":78,"variables":79},"Closed-Loop Inverting Voltage Gain","V_{OUT} = -V_{IN} \\cdot \\frac{R_F}{R_I}","Calculates the inverted output voltage based on the feedback-to-input resistance ratio.",[80,85,89,94],{"symbol":81,"name":82,"typicalValue":83,"unit":84},"V_{OUT}","Amplified output voltage","-1.8","V",{"symbol":86,"name":87,"typicalValue":88,"unit":84},"V_{IN}","Input signal voltage","0.5",{"symbol":90,"name":91,"typicalValue":92,"unit":93},"R_F","Feedback resistor","36","kΩ",{"symbol":95,"name":96,"typicalValue":97,"unit":93},"R_I","Input resistor","10",{"name":99,"latexOrText":100,"description":101,"variables":102},"Small-Signal Closed-Loop Bandwidth","f_{-3\\text{dB}} = \\frac{GBW}{1 + \\frac{R_F}{R_I}}","Calculates the high-frequency -3 dB cutoff based on op-amp gain-bandwidth product and noise gain.",[103,108,112,113],{"symbol":104,"name":105,"typicalValue":106,"unit":107},"f_{-3\\text{dB}}","High-frequency -3 dB cutoff","152.2","kHz",{"symbol":109,"name":110,"typicalValue":111,"unit":107},"GBW","Gain-bandwidth product","700",{"symbol":90,"name":91,"typicalValue":92,"unit":93},{"symbol":95,"name":96,"typicalValue":97,"unit":93},{"name":67,"latexOrText":115,"description":116,"variables":117},"f_{FPBW} = \\frac{SR}{2\\pi \\cdot V_P}","Calculates the maximum frequency achievable at peak output amplitude without slew-rate distortion.",[118,122,127],{"symbol":119,"name":120,"typicalValue":121,"unit":107},"f_{FPBW}","Full-power bandwidth","26.5",{"symbol":123,"name":124,"typicalValue":125,"unit":126},"SR","Op-amp slew rate","0.3","V\u002Fµs",{"symbol":128,"name":129,"typicalValue":130,"unit":84},"V_P","Peak output voltage amplitude","1.8",[132,141,148],{"refDes":133,"componentName":134,"value":135,"package":136,"quantity":137,"componentSlug":138,"role":139,"notes":140},"U1","Dual Operational Amplifier","LM358P","PDIP-8",1,"lm358","Inverting operational amplifier (Channel A used)","Texas Instruments LM358P, SLOS068AB Rev. AB; Pin 1 OUT1, Pin 2 IN1-, Pin 3 IN1+, Pin 4 GND\u002FV-, Pin 8 V+.",{"refDes":142,"componentName":143,"value":144,"package":145,"quantity":137,"role":146,"notes":147},"R1","Input Series Resistor","10kΩ","Axial \u002F 0805","Input signal scaling and impedance definition","10 kΩ, 1%, 0.125 W metal film resistor. Sets input impedance to 10 kΩ.",{"refDes":149,"componentName":150,"value":151,"package":145,"quantity":137,"role":152,"notes":153},"R2","Feedback Resistor","36kΩ","Closed-loop negative feedback","36 kΩ, 1%, 0.125 W metal film resistor. Establishes closed-loop gain of -3.6 V\u002FV.",{"U1A":155,"R1":166,"R2":175,"P1":181,"P2":189,"P_VCC":196,"P_VEE":205,"GND1":213},{"refDes":156,"name":157,"value":135,"role":158,"description":159,"componentSlug":138,"footprint":136,"specs":160},"U1A","Texas Instruments LM358P Dual Op-Amp (Channel A)","Inverting Operational Amplifier","Inverting amplifier stage operating from ±12 V split rails. Drives negative feedback loop to maintain virtual ground at pin 2 and deliver scaled inverted output at pin 1.",{"Supply Voltage":161,"Gain-Bandwidth Product":162,"Slew Rate":163,"Input Bias Current":164,"Quiescent Current":165},"±12 V (±1.5 V to ±16 V)","0.7 MHz typ","0.3 V\u002Fµs typ","20 nA typ","350 µA\u002Fchannel typ",{"refDes":142,"name":167,"value":144,"role":168,"description":169,"footprint":145,"specs":170},"Input Series Resistor (RI)","Input Signal Scaling and Summing","Converts input voltage VI into input current I_IN = VI \u002F 10 kΩ. Defines circuit input impedance Z_IN = 10 kΩ.",{"Resistance":171,"Tolerance":172,"Power Rating":173,"Temperature Coefficient":174},"10 kΩ","1%","0.125 W","±50 ppm\u002F°C",{"refDes":149,"name":176,"value":151,"role":177,"description":178,"footprint":145,"specs":179},"Feedback Resistor (RF)","Closed-Loop Negative Feedback","Establishes negative feedback loop from output (pin 1) to inverting input (pin 2). Sets closed-loop voltage gain magnitude to |Av| = 36 kΩ \u002F 10 kΩ = 3.6 V\u002FV.",{"Resistance":180,"Tolerance":172,"Power Rating":173,"Temperature Coefficient":174},"36 kΩ",{"refDes":182,"name":183,"value":184,"role":185,"description":186,"footprint":187,"specs":188},"P1","Input Signal Port","VIN","Bipolar AC\u002FDC Input Signal","Input terminal receiving nominal ±0.5 V signal relative to circuit ground.","Through-hole Test Point",{"Signal Range":37},{"refDes":190,"name":191,"value":192,"role":193,"description":194,"footprint":187,"specs":195},"P2","Inverted Output Port","VOUT","Amplified Inverted Output Signal","Output terminal delivering nominal ∓1.8 V signal (180° phase shifted) to subsequent stages or load.",{"Signal Range":40},{"refDes":197,"name":198,"value":199,"role":200,"description":201,"footprint":202,"specs":203},"P_VCC","Positive Supply Port","+12V","Positive Power Rail Connection","Supplies +12 V to op-amp pin 8 (V+). Requires 100 nF bypass capacitor to ground.","Power Terminal",{"Nominal Voltage":204},"+12 V DC",{"refDes":206,"name":207,"value":208,"role":209,"description":210,"footprint":202,"specs":211},"P_VEE","Negative Supply Port","-12V","Negative Power Rail Connection","Supplies -12 V to op-amp pin 4 (V-). Requires 100 nF bypass capacitor to ground.",{"Nominal Voltage":212},"-12 V DC",{"refDes":214,"name":215,"value":216,"role":217,"description":218,"footprint":219,"specs":220},"GND1","Circuit Ground Port","GND","Reference Ground for Non-Inverting Input","Ties non-inverting input (pin 3) directly to 0 V system ground, establishing virtual ground reference at inverting input.","Ground Point",{"Potential":221},"0 V",{"schemaVersion":223,"id":18,"meta":224,"components":230,"nets":289,"junctions":334,"netLabels":343,"wires":344},"1.5",{"title":19,"locale":225,"grid":226,"source":227},"en",20,{"type":228,"ref":229,"url":17},"datasheet","Texas Instruments SLOS068AB (Rev. AB, Oct 2024), Figure 8-1 \"Application Schematic\". Inverting amplifier with gain Av = -3.6 V\u002FV (RI = 10 kΩ, RF = 36 kΩ, ±12 V split supply, VI = ±0.5 V, VO = ∓1.8 V).",[231,239,248,255,261,268,275,282],{"id":232,"symbolId":233,"refDes":182,"position":234,"rotation":237,"properties":238},"comp-p-in","port.input",{"x":235,"y":236},80,220,0,{"value":184},{"id":240,"symbolId":241,"refDes":142,"position":242,"rotation":237,"properties":244},"comp-r1","resistor.iec",{"x":243,"y":236},200,{"value":144,"tolerance":172,"powerRating":245,"package":145,"mpn":246,"manufacturer":247},"0.125W","MFR-25FRF52-10K","Yageo",{"id":249,"symbolId":241,"refDes":149,"position":250,"rotation":237,"properties":253},"comp-r2",{"x":251,"y":252},400,40,{"value":151,"tolerance":172,"powerRating":245,"package":145,"mpn":254,"manufacturer":247},"MFR-25FRF52-36K",{"id":256,"symbolId":257,"refDes":156,"position":258,"rotation":237,"properties":259},"comp-u1","opamp.inverting",{"x":251,"y":236},{"value":135,"package":136,"mpn":135,"manufacturer":260},"Texas 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2.0 V to 36.0 V)","Supply Voltage (VCC)","mixed","LM393 Precision Voltage Comparator with Hysteresis","Texas Instruments LM393 dual differential comparator in a non-inverting Schmitt trigger configuration with 48.5 mV positive feedback hysteresis, 2.5 V reference threshold, and open-collector output.",9,4,"lm393 precision voltage comparator with hysteresis\ntexas instruments lm393 dual differential comparator in a non-inverting schmitt trigger configuration with 48.5 mv positive feedback hysteresis, 2.5 v reference threshold, and open-collector output.\nlm393 precision voltage comparator with hysteresis\ntexas instruments lm393 dual differential comparator in a non-inverting schmitt trigger configuration with 48.5 mv positive feedback hysteresis, 2.5 v reference threshold, and open-collector output.\nlm393 precision voltage comparator with hysteresis\ntexas instruments lm393 dual differential comparator in a non-inverting schmitt trigger configuration with 48.5 mv positive feedback hysteresis, 2.5 v reference threshold, and open-collector output.\nanalog_sensing\ndual differential comparator\nlm393p\nu1\nreference divider upper resistor\n10kω\nr1\nreference divider lower resistor\n10kω\nr2\ninput series isolation resistor\n10kω\nr3\npositive feedback hysteresis resistor\n1mω\nr4\nopen-collector pull-up resistor\n4.7kω\nr5\nsupply bypass decoupling capacitor\n100nf\nc1\nanalog input port\nvin\np_vin\ncomparator output port\nvout\np_vout",{"slug":458,"cluster":459,"tier":21,"supplyVoltage":460,"voltageSpecification":463,"signalDomain":466,"breadboardFriendly":14,"title":467,"shortDescription":468,"bomCount":469,"formulaCount":455,"search":470},"2n2222-relay-driver-flyback-protection","microcontroller_interfaces",[461,446,462],"3.3v","12v",{"kind":448,"value":464,"label":465},"+12.0 V DC nominal (+10.8 V to +13.2 V operating range)","Relay Supply Voltage (VLOAD)","digital","2N2222 \u002F 2N2222A NPN BJT Relay Driver with 1N4007 Flyback Clamping Diode","Discrete NPN bipolar junction transistor low-side relay driver circuit with 1N4007 flyback suppression diode, base saturation drive, and supply decoupling for 3.3V\u002F5V MCU control.",7,"2n2222 \u002F 2n2222a npn bjt relay driver with 1n4007 flyback clamping diode\ndiscrete npn bipolar junction transistor low-side relay driver circuit with 1n4007 flyback suppression diode, base saturation drive, and supply decoupling for 3.3v\u002F5v mcu control.\n2n2222 \u002F 2n2222a npn bjt relay driver with 1n4007 flyback clamping diode\ndiscrete npn bipolar junction transistor low-side relay driver circuit with 1n4007 flyback suppression diode, base saturation drive, and supply decoupling for 3.3v\u002F5v mcu control.\n2n2222 \u002F 2n2222a npn bjt relay driver with 1n4007 flyback clamping diode\ndiscrete npn bipolar junction transistor low-side relay driver circuit with 1n4007 flyback suppression diode, base saturation drive, and supply decoupling for 3.3v\u002F5v mcu control.\nmicrocontroller_interfaces\nnpn general purpose bipolar transistor\n2n2222a\nq1\ngeneral purpose rectifier \u002F clamp diode\n1n4007\nd1\nsubminiature spdt signal \u002F power relay\ng5v-1-dc12\nk1\nbase current-limiting resistor 1 kω\n1kω\nr1\nbase pull-down bleeder resistor 10 kω\n10kω\nr2\nhigh-frequency ceramic decoupling mlcc\n100nf 50v\nc1\nbulk aluminum electrolytic decoupling\n47µf 25v\nc2",{"slug":472,"cluster":473,"tier":21,"supplyVoltage":474,"voltageSpecification":475,"signalDomain":478,"breadboardFriendly":479,"title":480,"shortDescription":481,"bomCount":482,"formulaCount":483,"search":484},"bjt-astable-multivibrator-led-flasher","timing_oscillators",[446],{"kind":448,"value":476,"label":477},"5.0 V DC nominal design assumption for educational demonstration. Requires sufficient headroom above the blue LED forward voltage (~3.3 V typ) to bias collector and base resistors; reverse base-emitter transients must remain within the transistor's absolute maximum rating (VEBO = 6.0 V for 2N3904BU).","Nominal Operating Supply Voltage","analog",false,"BJT Astable Multivibrator & Dual LED Flasher","Discrete two-transistor cross-coupled relaxation oscillator driving alternating LEDs without an integrated circuit.",10,3,"bjt astable multivibrator led flasher\ndiscrete two-transistor cross-coupled relaxation oscillator driving alternating leds without an integrated circuit.\nbjt astable multivibrator & dual led flasher\ndiscrete two-transistor cross-coupled relaxation oscillator driving alternating leds without an integrated circuit.\nbjt astable multivibrator led flasher\ndiscrete two-transistor cross-coupled relaxation oscillator driving alternating leds without an integrated circuit.\ntiming_oscillators\nnpn bipolar junction transistor\n2n3904bu\nq1\nnpn bipolar junction transistor\n2n3904bu\nq2\ncarbon film resistor 1\u002F4w\n1kω\nr1\ncarbon film resistor 1\u002F4w\n47kω\nr2\ncarbon film resistor 1\u002F4w\n47kω\nr3\ncarbon film resistor 1\u002F4w\n1kω\nr4\nnonpolar x7r multilayer ceramic capacitor\n10µf\nc1\nnonpolar x7r multilayer ceramic capacitor\n10µf\nc2\nstandard 5mm red indicator led\nred\nd1\nstandard 5mm blue indicator led\nblue\nd2",1793836431935]