Photoresistor

A photoresistor, also called a light-dependent resistor or LDR, is a two-terminal component whose resistance changes with incident light. A common photoconductive implementation uses an illuminated semiconductor between contacts; an external circuit converts its resistance change into a voltage or current signal. A manufacturer’s CdS datasheet explicitly identifies these names and describes resistance decreasing with visible illumination.^[ref]

The photoconductor mechanism is a change in conductivity through generated mobile carriers. A photoresistor’s resistance is consequently not a calibrated unit of optical power by itself. Material, wavelength distribution, temperature, illumination history and the measuring circuit help determine the observed response.

For an original illustrative model over a limited range, let $R(P)=R_0(P/P_0{)}^{-\gamma }$ with $\gamma >0$, fixed spectrum and geometry. Choose $R_0=20\mathrm{k\Omega }$ and $\gamma =0.7$. Four times the reference optical input gives $R\approx 7.579\mathrm{k\Omega }$, rather than one quarter of the original resistance. This stipulated power law illustrates a nonlinear response, not a fitted specification for the cited part.

In a divider with supply $V_s$ and fixed resistor $R_L$, measuring across $R_L$ givesAt $V_s=3.3\mathrm{V}$ and $R_L=10\mathrm{k\Omega }$, the model output rises from $1.10\mathrm{V}$ at $P_0$ to about $1.877\mathrm{V}$ at $4P_0$. The logarithmic sensitivity is greatest when $R(P)=R_L$, where it is $\gamma V_s/4$. Choosing a resistor therefore selects an operating region; it does not remove the material’s response law.

The electrical input must also be characterized. The divider seen at its output has Thevenin resistance $R(P)\parallel R_L$. A finite-input-resistance voltmeter or an analog-to-digital converter with a switched input can change the reading. Self-heating depends on the detector’s actual voltage and resistance, while photoconductor response time can make a rapidly sampled value differ from its settled value.

Photoresistor spectral calibration is essential when interpreting an illumination reading. Lux is photometrically weighted, so equal illuminance from different spectra need not produce equal absorption or equal resistance. The cited manufacturer specifies source conditions for light-resistance measurements, a waiting time for dark resistance and light-adaptation preconditioning before its tests.^[ref] Those conditions describe what was tested; they should not be silently omitted from a comparison.

A proposed characterization uses a stable monitored light source, fixed detector position and a controlled spectrum, stepping illumination in both directions and recording the settled resistance and transient. Measure actual bias and temperature, then test the intended readout separately. A component can work well as a light/dark threshold sensor while requiring substantially more characterization to estimate optical power quantitatively.

Photoresistor spectral calibration determines how a photoresistor's electrical reading depends on the illumination spectrum under specified geometry, background, temperature, bias and adaptation history. A resistance-versus-lux curve measured with one lamp is not automatically valid for another spectrum. The manufacturer's primary CdS datasheet specifies a $2854\mathrm{K}$ source for its light-resistance tests and preconditions cells with light before electrical measurements.^[ref]

The distinction is between irradiance and illuminance. With spectral irradiance $E_{\lambda }(\lambda )$, illuminance is approximatelywhere $V$ is the photopic luminous efficiency function. The detector weights wavelengths according to its own physical response, which need not be proportional to $V$. NIST's detector-based photometric realization measures that spectral response, rather than assuming an arbitrary detector reproduces the photometric weighting.^[ref]

For a locally linear small-signal model about a fixed operating state, writeHere $s_G$ is the differential spectral responsivity of electrical conductance, including the stated illumination geometry. It is not automatically a global, illumination-independent material constant. A background-dependent photoresistor spectral response requires rechecking this derivative when the operating point changes.

An original two-band example makes the mismatch quantitative. Stipulate relative photometric weights $V_a=0.8$, $V_b=0.2$ and equal detector generation weights $s_a=s_b$ for two narrow bands. Equal illuminance requires four times as much irradiance in band $b$, so its detector-weighted generation is four times greater. If, over this illustrative range, $R\propto g^{-0.7}$, the resistance ratio is $R_b/R_a=4^{-0.7}\approx 0.379$. These weights and exponent are stipulated, not measured specifications or tabulated values for named wavelengths. Equal lux can produce substantially unequal resistance.

A proposed spectral characterization uses narrow-band sources or a monochromator, a reference detector to measure incident irradiance, fixed beam geometry and controlled detector temperature. Record resistance or conductance after a defined settling time at several background levels. A separate calibrated photometer can establish illuminance; it cannot by itself establish the photoresistor's spectral weighting. Keep electrical loading and self-heating fixed while changing the source.

For a broadband transfer, characterize the reference and test spectra and test whether the measured spectral-response model predicts their relative readings. Existing spectral mismatch correction methods address the analogous transfer problem for photometers, but a nonlinear photoresistor first needs a justified operating-point model.^[ref] The result is a calibration valid for stated conditions, not a universal conversion from resistance to optical power.

A background-dependent photoresistor spectral response is the differential change of a photoresistor's output with wavelength-specific illumination, evaluated at a stated background state. It can depend on illumination level, spectral composition, bias, temperature and prior adaptation. The primary CdS datasheet specifies light-adaptation preconditioning before electrical tests, demonstrating that a measurement condition includes more than the instantaneous lux value.^[ref]

Let the steady electrical conductance be a functional $G=\mathcal{F}[E_{\lambda }]$ of incident spectral irradiance. About a background $E_{\lambda ,0}$, define the local response byThis derivative concerns small changes after specifying the operating state. A finite change or rapid modulation needs further nonlinear or dynamic characterization. Photoresistor spectral calibration establishes the required optical and electrical conditions.

An original separable model makes a useful distinction. Suppose $g=\int a(\lambda )E_{\lambda }(\lambda )d\lambda$ and $G=G_d+\kappa g^{\gamma }$, with positive $g,\kappa ,\gamma$. ThenThe amplitude changes with background, but the normalized spectral shape remains $a(\lambda )$. With $\gamma =0.7$, quadrupling $g_0$ multiplies the absolute differential response by $4^{-0.3}\approx 0.6598$. For a small one-percent generation increment, the leading fractional conductance change above the dark contribution is $0.7\%$; the exact model gives $(1.01{)}^{0.7}-1\approx 0.69895\%$.

A change in spectral shape requires more than that single separable nonlinearity. For an illustrative two-band response in dimensionless input coordinates, letThe derivatives are $\partial G/\partial E_a=1/(2\sqrt{E_a})$ and $\partial G/\partial E_b=1$. Changing the first-band background from $E_a=1$ to $4$ changes their ratio from $1/2$ to $1/4$. This toy model shows how relative spectral sensitivity can change; it is not measured behavior of a named component. Separable and nonseparable photoresistor spectral-response models should consequently be distinguished in a calibration analysis.

Resistance readout adds another operating-point factor: since $R=1/G$, $\delta R=-\delta G/G_0^2$. A resistance-divider output has yet another derivative. Comparing raw electrical slopes without converting to the same output variable can imitate a change in material response. Likewise, equal illuminance need not mean equal detector excitation, because the photopic luminous efficiency function supplies a different spectral weighting.^[ref]

A proposed apparatus combines a stable background source with a weak wavelength-selectable probe beam, a monitored reference detector and a fixed illumination geometry. At each background, measure the output derivative while decreasing probe amplitude to test the small-signal regime, then repeat after the prescribed settling or adaptation period. Normalize spectra only after retaining their absolute scale. This separates a changing overall gain from a changing spectral shape and from readout loading; it does not assume that a curve measured at one background transfers to every illumination condition.