Useful Discrete Circuits

Two-transistor feedback current source

Figure 1. Two-transistor current source. Q2 senses the voltage across the sense resistor and steals base drive from Q1 to hold it at one base-emitter drop.

$$I = \frac{V_{BE(Q2)}}{R_S} \approx \frac{0.65\ \text{V}}{R_S}$$

Q1 carries the load current; its base is pulled up through $R_B$. When the drop across $R_S$ reaches Q2's base-emitter turn-on voltage, Q2 conducts and diverts base current from Q1, which limits the emitter current to the value that holds $R_S$ at about 0.65 V. The loop gain is Q2's transconductance times $R_B$, so regulation is good and the output impedance is high.

Design: choose $R_S = 0.65 / I$. Choose $R_B$ so that Q1 has adequate base drive at the maximum load current and Q2's collector current is 0.5 to 2 mA: $R_B \approx (V_{CC} - 2 V_{BE}) / I_{C(Q2)}$. Q1 must be rated for the load current and for the dissipation $V_{CE} \times I$ at the minimum load resistance. Compliance extends from $V_{CE(sat)} + I R_S$ to the transistor's breakdown voltage.

Limits: the reference is a base-emitter junction, so the current has a temperature coefficient of about -0.3 %/°C (2 mV/°C on 650 mV). The absolute value depends on Q2's $V_{BE}$ at its operating current, which varies by ±50 mV between devices, giving ±8 % without trimming. Q1's base current flows through $R_S$ as well, adding $1/\beta$ error. A MOSFET can replace Q1 for high currents; a MOSFET can replace Q2 only with a change in reference voltage to $V_{GS(th)}$, which is far less predictable.

Use: current limiting in linear regulators (this is the current-limit circuit inside classic three-terminal regulators), LED drivers, battery chargers at fixed current, and any load above the compliance of a two-terminal current regulator. Integrated alternative: LM334 for low currents, dedicated LED drivers, or a regulator's built-in limit.

LED-biased current source

Figure 2. Current source with the base biased by a red LED. The LED's forward voltage and temperature coefficient nearly cancel the transistor's base-emitter drop and its coefficient.

$$I = \frac{V_{LED} - V_{BE}}{R_E} \approx \frac{1.8 - 0.65}{R_E} = \frac{1.15\ \text{V}}{R_E}$$

The base is held at the LED's forward voltage, the emitter sits one $V_{BE}$ below it, and $R_E$ converts the difference into current. The circuit has no feedback loop and no stability concern. Its regulation comes from the transistor's output impedance multiplied by the degeneration, which is high enough for bias and LED-drive purposes.

The choice of bias element sets the temperature coefficient. Two silicon diodes in series give a base voltage of two $V_{BE}$ and an emitter voltage of one $V_{BE}$, so the current inherits a -2 mV/°C coefficient on 0.65 V, or -0.3 %/°C, and the cancellation only holds if the diode current density matches the transistor's. A red LED has a forward voltage of 1.7 to 1.9 V with a coefficient of -1.5 to -2 mV/°C. Subtracting the transistor's $V_{BE}$ and its -2 mV/°C leaves 1.15 V with a net coefficient near zero, typically within ±0.5 mV/°C, or ±0.05 %/°C. The LED is also a quieter reference than a low-voltage Zener.

Design: bias the LED at 1 to 5 mA through $R_B$, keep $R_E$ dissipation in mind, and use an LED of a stated color and vendor because the forward voltage differs by 0.3 V or more between types. Compliance is $V_{CC} - 1.15\ \text{V} - V_{CE(sat)}$ minus the load drop.

Use: differential pair tail currents, bias for class-A stages, constant-current LED strings from a raw supply, and anywhere a 1 to 100 mA source is needed with better temperature behavior than a $V_{BE}$ reference. Integrated alternative: a resistor from a regulated rail is the usual replacement; for a genuine current source, the LM334 or a current-output DAC.

JFET current-regulator diode

Figure 3. Self-biased JFET as a two-terminal current regulator. The source resistor sets the current below the saturation current of the device.

$$I_D = I_{DSS}\left(1 - \frac{V_{GS}}{V_P}\right)^2, \qquad V_{GS} = -I_D R_S$$

With the gate tied to the bottom of the source resistor, the JFET's own current develops a negative gate-source voltage across $R_S$, which reduces the current until the two equations agree. With $R_S$ = 0 the current is $I_{DSS}$. The result is a two-terminal current source: connect it in series with the load, and it regulates from about $|V_P| + I_D R_S$ up to the JFET's drain-source rating.

Design: solve the two equations for $R_S$, or read it from the datasheet's $I_D$ vs $V_{GS}$ curve. The dynamic impedance is $r_{ds}$ multiplied by $(1 + g_m R_S)$, typically 100 kΩ to several MΩ. Noise is low because there is no base current and no reference diode.

Limits: $I_{DSS}$ has a 2:1 to 5:1 spread between devices of one part number, so the absolute current is set by selection or by trimming $R_S$. The compliance floor of 1 to 3 V is higher than a bipolar source's. The drain-source rating of small JFETs is 25 to 40 V, occasionally 60 V. Currents above about 20 mA require a large JFET or a MOSFET version. Temperature coefficient depends on the operating point relative to the JFET's zero-temperature-coefficient current, and can be made small by choosing $R_S$ to sit near it.

Use: two-terminal biasing of LEDs, laser diodes, and Zener references from an unregulated supply; tail currents; pull-ups with constant current for improved slew; and the current-regulator diodes sold as a component (1N5283 through 1N5314 series, J500 series) are exactly this circuit in a two-lead package. Integrated alternative: the packaged current-regulator diode itself, or a three-terminal LM334.

Depletion-mode MOSFET high-voltage current source

Figure 4. Depletion-mode MOSFET as a current source. Same principle as the JFET regulator, at drain-source ratings of hundreds of volts.

A depletion-mode MOSFET conducts at zero gate voltage and turns off with a negative gate-source voltage, like a JFET, but is available with 400 to 1000 V drain ratings and currents from a milliamp to an amp. The self-biased circuit is identical: $R_S$ from source to the lower terminal, gate tied to the bottom of $R_S$. The current is read from the transfer characteristic at $V_{GS} = -I_D R_S$.

Design: the device dissipates $V_{DS} \times I_D$ continuously, so a 10 mA source dropping 300 V dissipates 3 W and needs a heat sink and a check against the safe operating area at that voltage, where thermal instability limits the current well below the package rating. A cascode arrangement, with a low-voltage part setting the current and the depletion device standing off the voltage, improves accuracy and reduces the current setting's dependence on the high-voltage device. Add a gate resistor of a few hundred ohms and keep the source lead short; these devices oscillate at VHF with a capacitive load on the drain.

Limits: the same $I_{DSS}$ spread as JFETs, and a large positive temperature coefficient of $R_{DS(on)}$ that does not affect the current-source operating point but does affect the compliance floor. Devices such as the DN2540 (400 V) and LND150 (500 V, 1 to 3 mA) are the common parts; the class is small, with two or three manufacturers.

Use: start-up bias for offline switching supplies, where a resistor from the bus would dissipate too much; bias and constant-current loads in vacuum tube circuits; high-voltage active loads and pull-ups; current-limited LED strings from rectified mains with appropriate isolation and safety review; and pre-regulators ahead of a linear regulator on a high-voltage input. Integrated alternative: none in the same voltage class at low current; high-voltage LED driver ICs for the lighting case.

Current mirrors are the other discrete current source and belong here for completeness. A diode-connected transistor sets a $V_{BE}$ that a second transistor copies, producing an output current equal to the input current times the area ratio. Emitter degeneration resistors of 50 to 100 mV drop reduce the mismatch from $V_{BE}$ spread between discrete devices to a few percent, and the Wilson or cascode arrangements raise output impedance. With a matched monolithic pair (BCM847, DMMT3904W, or the classic CA3046 array) a discrete mirror reaches 1 % matching.

Base-emitter multiplier

Figure 5. Base-emitter multiplier, also called a rubber diode. The two-terminal voltage is a resistor-ratio multiple of one base-emitter drop.

$$V = V_{BE}\left(1 + \frac{R_1}{R_2}\right), \qquad \frac{dV}{dT} \approx -2\ \text{mV/°C} \times \left(1 + \frac{R_1}{R_2}\right)$$

The transistor holds its base one $V_{BE}$ above the emitter, the divider $R_1$, $R_2$ places the base at a fixed fraction of the collector-emitter voltage, and the collector-emitter voltage settles at the multiple that satisfies both. The circuit is a two-terminal shunt element with a voltage of 1 to 5 $V_{BE}$ and a dynamic impedance of a few ohms, and its temperature coefficient scales with the multiplier.

Design: set $R_2$ so the divider current is at least ten times the base current. Make $R_1$ adjustable for trimming. A capacitor across the whole element lowers its AC impedance. Bias current through the element of 1 to 10 mA.

The scaled temperature coefficient is the reason to use it. Mounted on the same heat sink as a class-AB output pair, the multiplier's voltage falls with temperature at the same rate as the output transistors' combined $V_{BE}$, which holds the quiescent current constant and prevents thermal runaway. Every discrete audio power amplifier uses it for this purpose.

Use: class-AB bias spreader, low-cost shunt reference at odd voltages, and level shifts of a few volts. Integrated alternative: the TL431 for a precise adjustable shunt reference without the temperature coefficient; nothing integrated replaces the thermal tracking function.

Discrete bandgap reference (Brokaw cell)

Figure 6. Brokaw bandgap cell with a discrete transistor pair and an op-amp. The op-amp forces equal collector currents; the difference in base-emitter voltages, which is proportional to absolute temperature, appears across the first resistor.

$$\Delta V_{BE} = \frac{kT}{q} \ln N, \qquad V_{REF} = V_{BE(Q2)} + 2\,\frac{R_2}{R_1}\,\Delta V_{BE}$$

Two transistors run at the same collector current, enforced by the op-amp through the equal collector resistors. Q1 has $N$ times the emitter area of Q2 (or, with a discrete matched pair of equal area, runs at $1/N$ of the current through unequal collector resistors, which changes the factor 2 to $1 + I_2/I_1$). Its base-emitter voltage is lower by $\Delta V_{BE} = (kT/q) \ln N$, and that difference appears across $R_1$, setting a current proportional to absolute temperature. Both emitter currents flow through $R_2$, producing a PTAT voltage of $2 (R_2/R_1) \Delta V_{BE}$. Adding Q2's $V_{BE}$, which falls with temperature at about -2 mV/°C, gives a sum whose temperature coefficient is zero when the PTAT term is about 0.6 V, and the total is then about 1.23 V, the bandgap voltage of silicon extrapolated to 0 K.

Design: with $N$ = 8, $\Delta V_{BE}$ is 53.7 mV at 300 K, so $R_2/R_1 \approx 5.9$ makes the PTAT term 0.63 V. Trim $R_2$ for minimum temperature coefficient, not for the exact output voltage; the two adjustments are the same one. Use a monolithic matched pair (DMMT3904W, BCM847DS, or a transistor array) so that the two $V_{BE}$ values track. The cell has a second stable state at zero current; a start-up resistor from the supply to the output ensures it leaves it. Bypass the output.

Limits: with a discrete matched pair, 20 to 50 ppm/°C is achievable after trimming, against 3 to 10 ppm/°C for a trimmed integrated reference. Noise and long-term drift are also worse than an IC. The circuit is nevertheless the one to know: every integrated bandgap reference, every regulator's internal reference, and the reference inside most ADCs is a variant of it, and its equation explains why reference outputs are 1.2 V and 2.5 V.

Use: understanding; references at temperatures or in environments where integrated references are unavailable or unqualified; and a demonstration that a reference can be built from parts on hand. Integrated alternative: any bandgap reference (LM4040, REF30xx, ADR4xx family), which is better on every axis except the two above.

Shunt reference with a follower, and the LED as a reference

Figure 7. Zener or LED shunt reference buffered by an emitter follower.

$$V_{OUT} = V_Z - V_{BE}$$

The shunt element is biased through $R_B$ and the follower supplies load current without disturbing it. Output impedance is roughly the shunt element's dynamic resistance divided by the transistor's current gain, plus the follower's $1/g_m$. The output has the follower's -2 mV/°C added to whatever the shunt element does.

Choice of shunt element:

• Zener diodes between 5.1 and 6.2 V have a temperature coefficient near zero, because below about 5 V the Zener mechanism dominates with a negative coefficient and above 6 V avalanche dominates with a positive one. A 5.6 V diode at its rated current has a coefficient of a few mV/°C at most. Zeners below 5 V are noisy and soft-kneed; above 7 V they have a coefficient of +2 to +5 mV/°C, which can be cancelled with a series forward diode. Bias at the datasheet test current for the specified voltage.
• A red LED is a 1.7 to 1.9 V reference with -1.5 to -2 mV/°C, low noise, and a sharp knee at low current, making it useful as a bias reference for current sources (Figure 2) and for low-voltage circuits where a Zener has no usable knee. The forward voltage varies by color, vendor, and lot, so it is a stable reference, not an accurate one.
• Two or three forward diodes in series give 1.3 to 2 V with -2 mV/°C per diode and the lowest cost.

Use: bias points, comparator thresholds, and supplies for small circuits where 5 % accuracy is adequate and the load is a few milliamps. Integrated alternative: the TL431 adjustable shunt reference, which costs about the same as a Zener and gives 1 % accuracy with 50 ppm/°C; or a fixed-voltage LDO.

Capacitance multiplier

Figure 8. Capacitance multiplier. The transistor presents the base filter's low ripple to the load and supplies the load current from the raw input.

An RC low-pass at the base of an emitter follower filters the ripple, and the follower reproduces the filtered base voltage at the emitter while delivering the load current from the collector. The load sees the base capacitor multiplied by the transistor's current gain, and the ripple attenuation is that of the RC filter at the ripple frequency:

$$\text{attenuation} \approx \frac{f_{ripple}}{f_c}, \qquad f_c = \frac{1}{2\pi R_1 C_1}$$

With $R_1$ = 1 kΩ and $C_1$ = 100 µF, $f_c$ is 1.6 Hz and 120 Hz ripple is attenuated by about 75 times, or 37 dB. The load sees the equivalent of 100 µF × β, or about 10 mF, from a 100 µF part. The output voltage is $V_{IN} - V_{BE} - I_{load} R_1 / \beta$; at 100 mA and β of 100 the drop is about 1.65 V, dissipated in the transistor.

Limits: it is a filter, not a regulator. The output follows the input's average value, so it removes ripple and noise but not variation in the DC level. The drop and the dissipation are set by $R_1 / \beta$ times the load current, so a Darlington or a MOSFET (with $R_1$ increased and the gate threshold accepted as the drop) reduces it. At start-up the base capacitor charges through $R_1$ over several time constants, during which the transistor sees the full input voltage and the load current: check the safe operating area for that interval. The transistor's output impedance is $1/g_m + R_1/\beta$, low enough for most loads.

Use: quiet supplies for op-amps, oscillators, preamps, and ADC references from a switching converter's output; class-A stages where a regulator's noise is worse than its ripple rejection; and anywhere a large electrolytic would be replaced by a small one and a transistor. Integrated alternative: a low-noise LDO with high power-supply rejection, which also regulates; the multiplier wins when the drop must be under 0.5 V at high current or the supply is above the LDO's rating.

Charge-pump negative rail from a logic pin

Figure 9. Negative supply from a square wave: a diode-capacitor inverter driven by a microcontroller PWM output.

$$V_{OUT} \approx -(V_{DD} - 2 V_F), \qquad R_{OUT} \approx \frac{1}{f\, C_1}, \qquad V_{ripple} \approx \frac{I_{load}}{f\, C_2}$$

When the pin is high, $C_1$ charges through D1 to $V_{DD} - V_F$ with its right end at ground. When the pin goes low, the right end of $C_1$ is driven to $-(V_{DD} - V_F)$, and D2 conducts to transfer charge to $C_2$, leaving the output at about $-(V_{DD} - 2 V_F)$. With Schottky diodes at 0.3 V and a 5 V pin, the output is about -4.4 V. At 100 kHz with $C_1$ = 1 µF the output impedance is about 10 Ω, and with $C_2$ = 10 µF a 10 mA load produces about 10 mV of ripple.

Limits: the current comes from the logic pin, so the load is limited to the pin's rating, typically 5 to 20 mA including the charging peaks. A logic buffer, a paralleled pair of pins, or a small gate driver raises it. The output is unregulated and drops with load; add a small LDO or a Zener if the value matters. The switching edges are a noise source; keep the loop small. Reversing the diodes and referencing them to $V_{DD}$ turns the same parts into a doubler that gives about $2 V_{DD} - 2 V_F$.

Use: a negative rail of a few milliamps so that an op-amp can swing to and through 0 V; bias for an LCD; gate drive for a P-channel switch; a bipolar supply for a single-supply board. Integrated alternative: a charge-pump IC (ICL7660, LM2776, TPS60400) with regulated output and no pin loading; the discrete version costs nothing when a PWM pin is free.

Gyrator (simulated inductor)

Figure 10. Gyrator. The op-amp and RC network present the impedance of an inductor at the input terminal, with one end grounded.

$$L_{eq} = R_1 R_2 C_1, \qquad Q_{max} \approx \frac{1}{2}\sqrt{\frac{R_1}{R_2}}, \qquad R_{series} = R_2$$

The op-amp buffers the voltage across $R_1$ (the voltage at the node after $C_1$) and feeds it back through the small resistor $R_2$ to the input. At low frequency $C_1$ blocks, the buffered voltage equals the input, and no current flows through $R_2$: high impedance. At high frequency $C_1$ passes, the buffered voltage is small, and the input current through $R_2$ is large: low impedance. That is the impedance of an inductor. With $R_1$ = 100 kΩ, $R_2$ = 100 Ω, and $C_1$ = 100 nF, $L_{eq}$ is 1 H with about 100 Ω of series resistance and a maximum Q near 16.

Limits: one end of the inductor is ground. The circuit stores no magnetic energy and can carry no DC beyond what the op-amp sources through $R_2$, so it is a small-signal filter element only, not a power component. The op-amp's gain-bandwidth limits it to audio and low ultrasonic frequencies. Q is bounded by the resistor ratio, and the op-amp's input bias current through $R_1$ sets a DC offset.

Use: notch and band-pass filters at mains and audio frequencies without wound inductors; graphic equalizer sections; bass boost and hum filters; telephone and audio line interfaces. Integrated alternative: switched-capacitor filter ICs, or a DSP; the gyrator wins for single-frequency analog filters in a circuit that has an op-amp to spare.

Bootstrapped emitter follower

Figure 11. Bootstrapped emitter follower. The bias resistor's lower end is driven with the output signal so that almost no signal current flows through it.

$$Z_{IN} \approx \frac{R_1}{1 - A_V} \parallel Z_{in(Q1)}, \qquad A_V = \frac{R_E}{R_E + r_e} \approx 0.98\ \text{to}\ 0.995$$

An emitter follower's input impedance is high, but the bias resistors that set its base voltage are in parallel with it and dominate. Bootstrapping drives the lower end of $R_1$ from the emitter through $C_B$, so that both ends of $R_1$ move with the signal and almost no signal current flows through it. The effective value of $R_1$ is multiplied by $1/(1 - A_V)$, 50 to 200 times, and a 1 MΩ resistor presents 50 to 200 MΩ. The stray capacitance at the base is bootstrapped by the same factor, which is why the technique is used for high-impedance probes.

Design: $R_2$ and $R_3$ set the DC base voltage through $R_1$, so their values are not multiplied and do not need to be large. $C_B$ must be a short circuit at the lowest frequency of interest relative to $R_2 \parallel R_3$: $C_B \geq 10 / (2\pi f_{low} (R_2 \parallel R_3))$. $C_{in}$ with the bootstrapped input impedance sets the input high-pass corner, and can be small. A JFET or a Darlington in place of Q1 raises $Z_{in(Q1)}$ so that the bootstrapped resistor remains the dominant term.

Limits: the multiplication factor depends on the follower's gain, which depends on load. The circuit can oscillate with a capacitive source because the bootstrap is positive feedback at high frequency; a small resistor in series with the base damps it. The input impedance returns to $R_1$ below the bootstrap capacitor's corner.

Use: piezoelectric pickups and contact microphones, condenser capsules, electrometer-style probes, and any source above 1 MΩ. Integrated alternative: a CMOS or JFET-input op-amp follower with a 10 MΩ to 1 GΩ bias resistor, which achieves the same input impedance directly; the discrete bootstrap survives where the op-amp's supply or input range does not, and the same trick applied to an op-amp's bias resistor extends its impedance further.

High-side current sense with an op-amp and a PNP

Figure 12. High-side current monitor. The op-amp forces the shunt voltage across the first resistor, and the PNP delivers the resulting current to a ground-referenced load resistor.

$$V_{OUT} = I_{load}\, R_{SENSE}\, \frac{R_2}{R_1}$$

The op-amp's inputs sit across the shunt at the supply rail. It drives the PNP's base until the voltage across $R_1$ equals the shunt voltage, so the PNP's emitter current is $I_{load} R_{SENSE} / R_1$. That current flows out of the collector into $R_2$ at ground, producing a ground-referenced output proportional to the load current. The common-mode voltage of the measurement is at the rail, but the output is at ground, and the only components that see the rail voltage are the op-amp's inputs and the PNP's collector-base junction.

Design: with $R_{SENSE}$ = 10 mΩ, $R_1$ = 100 Ω, and $R_2$ = 4.99 kΩ, the gain is 49.9 and a 10 A load produces 4.99 V. The op-amp is powered from the rail and its input common-mode range must include the positive supply, which excludes many general-purpose parts; a rail-to-rail-input op-amp, or a bipolar part whose input range reaches the positive rail, is required. The PNP's base current subtracts from the emitter current, adding an error of $1/\beta$; a P-channel MOSFET in its place removes it. The op-amp's offset divided by the full-scale shunt voltage is the dominant error at low current: 100 µV of offset on a 100 mV full scale is 0.1 %.

Limits: accuracy of 1 % is achievable with 0.1 % resistors and a low-offset op-amp; bandwidth is set by the op-amp and is usually tens of kHz. For rails above the op-amp's supply rating, a local supply for the op-amp is derived from the rail with a Zener and a resistor, and the PNP's collector-base rating must exceed the rail.

Use: current monitoring on rails above 80 V, where integrated current-sense amplifiers are not available; bidirectional or unusual gain requirements; and boards that already carry an op-amp. Integrated alternative: current-sense amplifiers (INA180, INA240, INA290) with fixed gains, 0.5 % accuracy, and common-mode ranges to about 110 V, which are better below that voltage.

Transistor as a temperature sensor

Figure 13. Diode-connected transistor as a temperature sensor, driven at two currents from two GPIO pins through different resistors. The difference in the two readings is proportional to absolute temperature.

A diode-connected transistor's base-emitter voltage has two useful properties. Its absolute value falls at about -2 mV/°C, which gives a sensor that needs one calibration point and then holds ±2 °C. Its change between two currents is independent of the device:

$$\Delta V_{BE} = \frac{kT}{q} \ln \frac{I_A}{I_B}, \qquad T = \frac{q\, \Delta V_{BE}}{k \ln (I_A / I_B)}$$

With a current ratio of 10, $\Delta V_{BE}$ is 198 µV per kelvin, or 59.5 mV at 300 K. The measurement needs no calibration, and it is how every remote-diode temperature sensor IC works, with a discrete 2N3904 or MMBT3904 as the standard remote sensing element.

Design: drive two GPIO pins in turn, each through a resistor, and read the ADC after each. The ratio of currents is the ratio of resistors, corrected for the small difference in $V_{BE}$ between the two readings (about 2 %, which shifts the ratio slightly and is corrected in software from the measured voltages). Keep the current below 1 mA so self-heating stays under 1 mW. The resolution requirement is the difficulty: 198 µV/K needs an ADC LSB well below 100 µV for 0.5 K resolution, which means a 16-bit converter, or a 12-bit converter with an instrumentation amplifier at a gain of 20, or oversampling. Series resistance in the transistor's base and emitter adds an error of $r_S \times \Delta I$; at 0.5 Ω and a 300 µA current difference this is 150 µV, or about 0.75 K, which is why sensor ICs use a three-current method to cancel it.

Use: temperature of a board, a heat sink, or a die where a transistor is the smallest and cheapest sensing element that fits, and any existing transistor in a circuit whose $V_{BE}$ can be read. Integrated alternative: remote-diode sensor ICs (TMP451, LM95xx, MAX6642) that perform this measurement with 1 °C accuracy, and local sensors (TMP117, Si7051) for 0.1 °C.

LED as a photodiode

Figure 14. LED operated as a photodiode into a transimpedance amplifier. Response is confined to wavelengths at and below the LED's emission color.

An LED is a PN junction with a bandgap set by its emission color, and it generates photocurrent from light with photon energy above that bandgap, which means wavelengths at or shorter than its emission wavelength. A green LED responds to green and blue but not red; a red LED responds to red and everything shorter. The photocurrent is nanoamps to microamps in room light, and the transimpedance amplifier of the op-amp cheat sheet converts it with a feedback resistor of 1 to 10 MΩ. The LED's capacitance of 10 to 50 pF and the amplifier's input capacitance set the feedback capacitor for stability.

A microcontroller can read an LED with no amplifier: drive the LED reverse-biased from two pins to charge its junction capacitance, switch the cathode pin to a high-impedance input, and time how long the photocurrent takes to discharge the capacitance to the input's logic threshold. The time is inversely proportional to light intensity, from milliseconds in bright light to seconds in the dark. The same LED can emit and sense alternately, which gives a proximity or reflectance sensor from one part.

Limits: sensitivity is one to two orders of magnitude below a photodiode of the same area, the spectral response is uncalibrated, and the packages are not designed for optical repeatability. Use it for presence, relative level, and color discrimination, not photometry.

Use: ambient light sensing, color discrimination with an LED matched to the color of interest, cheap reflectance and turbidity sensing, and bidirectional emit-and-sense elements in arrays. Integrated alternative: a photodiode, an ambient light sensor IC with digital output, or a color sensor IC; the LED wins when it is already on the board.

Copper as a resistance thermometer

Figure 15. Copper trace or winding read as an RTD, ratiometrically against a reference resistor with Kelvin connections.

$$R(T) = R_0 \left[1 + \alpha (T - T_0)\right], \qquad \alpha_{Cu} = 0.00393\ /\text{°C}$$

Copper's resistance rises 0.393 % per degree, close to platinum's 0.385 %, and copper is already present as PCB traces, motor windings, transformer windings, and cables. A serpentine trace of 1 oz copper, 0.15 mm wide, has about 3.2 Ω per meter; five meters of it gives 16 Ω and 63 mΩ per degree. With 10 mA excitation the signal is 0.63 mV per degree, which a 16-bit or a delta-sigma converter resolves to 0.1 °C. Reading the copper resistance and a reference resistor in series with the same current makes the measurement ratiometric: the excitation current cancels, and only the reference resistor's tolerance and drift remain.

Design: four-wire (Kelvin) connections so that lead resistance is excluded; excitation low enough that self-heating is negligible (10 mA into 16 Ω is 1.6 mW, spread over the trace area); a reference resistor of 0.1 % and 25 ppm/°C; and a differential ADC or a multiplexed single-ended one reading both drops. For motor and transformer windings, the winding resistance is measured with a small DC test current during a pause in operation, or computed from the drive's known voltage and current, and gives the average winding temperature that no surface sensor can.

Limits: absolute accuracy is poor because trace thickness varies by ±10 % between boards, so the sensor is calibrated at one temperature and used for changes. Thermoelectric voltages at the junctions between copper and other metals add microvolts per degree of gradient, which matters at the 63 µV/°C signal level of a 1 mA excitation; use 10 mA or reverse the excitation and average. The measurement is the average over the trace, not a point.

Use: average temperature of a board region, a heat sink, or a winding; over-temperature protection in motors, solenoids, and transformers without an embedded sensor; and combined heater-sensor traces for small temperature-controlled zones. Integrated alternative: a thermistor or a silicon sensor at a point; the copper measurement is used because the copper is already where the temperature is wanted.

NTC thermistor linearization

Figure 16. NTC thermistor with a parallel resistor chosen to make the combination linear around a chosen temperature, in a divider to the ADC.

$$R_P = R_T(T_m)\,\frac{B - 2 T_m}{B + 2 T_m}$$

A thermistor's resistance is exponential in temperature, with sensitivity that falls rapidly at the hot end. A resistor in parallel with it, chosen by the formula above ($T_m$ in kelvin, $B$ the thermistor's beta constant), places an inflection point of the combined resistance at $T_m$ and makes it nearly linear on either side. For a 10 kΩ thermistor with $B$ = 3950 K and $T_m$ = 25 °C (298 K), $R_P$ is 7.38 kΩ, and the combination is linear within about 1 °C over ±25 °C around $T_m$. Placing the combination in a divider with a series resistor equal to its value at $T_m$ gives maximum sensitivity there and an output that is linear enough to feed a comparator, a meter, or an ADC lookup with equal steps.

Design: read $B$ from the datasheet for the temperature range of interest, because it is itself temperature-dependent. Keep the thermistor's dissipation under 0.1 mW; the dissipation constant in still air is 1 to 2 mW per degree of self-heating. Use a ratiometric reference for the divider so that reference drift cancels.

Limits: the linearization is an approximation valid over a limited span, and the parallel resistor reduces sensitivity. With a microcontroller, the parallel resistor is unnecessary: read the divider, compute the thermistor resistance, and apply the Steinhart-Hart equation or a table, which is accurate over the full range. The linearization trick is for analog-only readouts, comparators with a fixed threshold, and cases where the ADC's resolution must be spread evenly over the range.

Use: over-temperature thresholds, analog temperature meters, and fan control with an analog controller. Integrated alternative: a silicon temperature sensor with linear output (TMP235, LM35) at about the same cost as the thermistor plus resistors; the thermistor wins on size, on operation above 150 °C, and on response time.

Piezo disc with a charge amplifier

Figure 17. Piezoelectric disc into a charge amplifier. The output depends on the feedback capacitor, not on the disc's or cable's capacitance.

$$V_{OUT} = -\frac{Q}{C_f}, \qquad f_{low} = \frac{1}{2\pi R_f C_f}$$

A piezoelectric element produces charge proportional to strain. Read with a voltage amplifier, the signal is $Q / (C_{piezo} + C_{cable} + C_{in})$ and depends on every capacitance in the path. The charge amplifier holds the element at a virtual ground so that its charge is transferred entirely into $C_f$, and the output is $Q / C_f$ regardless of the element or cable. $R_f$ provides the DC path for the op-amp's bias current and sets the low-frequency corner: with $C_f$ = 1 nF and $R_f$ = 100 MΩ, 1.6 Hz. The op-amp must have a bias current whose product with $R_f$ is an acceptable offset, which means a CMOS or JFET input part.

Design: $R_S$ limits the current into the op-amp's protection diodes when the element is struck; a 27 mm buzzer disc produces tens of volts open-circuit from a sharp tap. Add clamp diodes to the rails for anything that may be hit. For a knock or tap detector where amplitude accuracy does not matter, a 1 MΩ resistor across the element, clamp diodes, and a comparator are sufficient. For measurement, calibrate the element's charge sensitivity with a known force, because buzzer discs are not specified for it.

Limits: leakage across $R_f$ on a humid board lowers the effective resistance and raises the low-frequency corner; a guard ring around the inverting input node prevents it. Pyroelectric output from temperature changes appears as a slow drift below the corner. The disc's resonance (a few kHz for a 27 mm disc) colors the response.

Use: vibration and shock sensing, engine knock detection, contact microphones, tap and impact detection on enclosures, and force measurement at low cost. Integrated alternative: MEMS accelerometers for vibration with calibrated sensitivity; the piezo disc wins on cost, bandwidth to ultrasonic frequencies, and operation at temperatures beyond a MEMS part.

Wien bridge oscillator with JFET amplitude control

Figure 18. Wien bridge oscillator. The RC network sets frequency, the negative feedback sets gain, and the JFET adjusts the gain to hold the amplitude at the level where the loop gain is exactly one.

$$f = \frac{1}{2\pi R C}, \qquad \text{required gain} = 1 + \frac{R_f}{R_g + r_{DS}} = 3$$

The series and parallel RC arms form a band-pass network with a gain of 1/3 and zero phase shift at $f$, so an amplifier with a gain of exactly 3 sustains oscillation. Gain above 3 grows the amplitude until the amplifier clips; gain below 3 lets it decay. The control loop holds the gain at 3: the diode and capacitor form a negative peak detector on the output, the resulting negative voltage on the JFET gate raises its channel resistance, and the gain falls as amplitude rises. The amplitude settles at the value where the loop gain is one. The original version used an incandescent lamp's positive temperature coefficient in the $R_g$ position; the JFET does the same job with a controllable time constant.

Design: use the same value of $R$ and $C$ in both arms, 1 % C0G capacitors, and an op-amp with gain-bandwidth at least 100 times $f$ and slew rate adequate for the output amplitude. Keep the signal across the JFET below 100 mV so that its channel resistance stays linear; make $R_g$ about ten times the JFET's on-resistance and set the output amplitude with the detector ratio. The AGC time constant $R_{agc} C_{agc}$ must be long relative to the oscillation period, or the amplitude modulates itself at the AGC rate, and short enough for reasonable start-up. Feeding half the JFET's drain-source voltage back to its gate through two equal resistors cancels its second-harmonic distortion.

Limits: frequency is fixed by the components; tuning requires a dual potentiometer or switched capacitors. Distortion of 0.01 to 0.1 % is straightforward; below 0.001 % requires care with the JFET and the op-amp. Frequency stability depends on the capacitors' temperature coefficient.

Use: a low-distortion sine source for testing amplifiers, ADCs, DACs, and filters at fixed frequencies; audio test tones; excitation for bridges and LVDTs. Integrated alternative: direct digital synthesis for frequency agility and precision, with distortion and noise set by the DAC and its filter; the Wien bridge wins for the lowest distortion at a single frequency, which is why THD analyzers still use it.