Active Components

CTAT Circuit

Q: How does a CTAT circuit combine with a PTAT circuit in a bandgap reference?

The CTAT term is the forward base-emitter voltage V_BE of a diode-connected transistor, which falls by about 2 mV per degree C (roughly minus 1.9 to minus 2.2 mV per degree C near room temperature). The PTAT term is built from the difference in V_BE between two junctions running at different current densities, delta V_BE = (kT/q) times ln(N), which rises with temperature. Slope cancellation requires the total PTAT scaling M times ln(N) to be about 23, since 2 mV per degree C divided by the 0.0862 mV per degree C per unit of ln(N) slope is about 23.2. A typical design uses a current-density ratio N of 8 (ln N about 2.08), so the resistor-set gain M is only about 11. Adding the scaled PTAT to V_BE cancels the positive and negative slopes. The sum settles near the silicon bandgap voltage of about 1.205 V at zero kelvin extrapolation and shows a near-zero first-order temperature coefficient, typically 10 to 50 ppm per degree C over the industrial range.

Q: Why does a base-emitter junction give a CTAT voltage of about minus 2 mV per degree C?

For a fixed collector current, the base-emitter voltage is V_BE = (kT/q) times ln(I_C / I_S). Although the kT/q term rises with temperature, the saturation current I_S grows much faster, roughly as T to the power of 3 to 4 multiplied by an exp(minus Eg/kT) factor. The strong temperature dependence of I_S dominates, so V_BE decreases as temperature climbs. Near 300 K and a typical 1.205 V extrapolated bandgap, the net slope is about minus 2 mV per degree C, which is the defining CTAT behavior. The exact value shifts slightly with bias current and device geometry, so designers measure it during characterization.

Q: What residual error remains after first-order CTAT and PTAT cancellation?

First-order cancellation leaves a curvature, or bow, because V_BE is not perfectly linear with temperature. A standard CTAT plus PTAT bandgap shows a parabolic error of a few millivolts peak to peak, giving roughly 20 to 50 ppm per degree C over minus 40 to plus 125 degrees C. Curvature-corrected designs add a second nonlinear term, such as a temperature-dependent resistor ratio or a squared PTAT current, to flatten the bow and reach 5 to 10 ppm per degree C. In RF bias applications, this residual drift directly shifts amplifier quiescent current, so low-curvature references are chosen when gain and linearity must hold across temperature.

/SEE-tat SUR-kit/ · Complementary To Absolute Temperature

Standing for Complementary To Absolute Temperature, this bias-reference block generates a voltage or current that falls as temperature rises, the opposite slope of a PTAT circuit. The negative coefficient comes from the forward base-emitter voltage of a diode-connected transistor, which drops by roughly −2 mV/°C. Summing a scaled PTAT term with this CTAT term cancels the first-order slope, which is the working principle behind the bandgap reference and the temperature-compensation networks that hold RF amplifier bias points stable from −40 to +125 °C.

Category: Active Components

V_BE Slope: ≈ −2 mV/°C

Tempco (with PTAT): 10 to 50 ppm/°C

How CTAT and PTAT Slopes Cancel

The CTAT term is the quantity that every bandgap reference relies on for its negative temperature slope. In a silicon bipolar junction biased at constant collector current, the base-emitter voltage V_BE behaves as a Complementary To Absolute Temperature source: it sits near 0.65 to 0.70 V at room temperature and decreases by roughly 2 mV for each degree of heating. This slope is remarkably repeatable from device to device because it is anchored to the silicon bandgap energy rather than to process-dependent resistor or capacitor values, which is exactly why it became the foundation of precision references.

On its own, a CTAT voltage drifts too much to serve as a stable reference. The classic solution pairs it with a PTAT voltage, which is generated from the difference in V_BE between two junctions operated at unequal current densities. The PTAT term, ΔV_BE = (kT/q)·ln(N), rises with temperature; its slope is (k/q)·ln(N) ≈ +0.086 mV/°C for every unit of ln(N). To cancel the CTAT slope the total PTAT scaling must satisfy M·ln(N) ≈ 23 (since 2 mV/°C divided by 0.0862 mV/°C ≈ 23.2). A common implementation uses a current-density ratio N of 8, giving ln(N) ≈ 2.08, so the resistor-set gain M is only about 11. Adding the scaled PTAT voltage to the CTAT V_BE makes the +2 mV/°C and −2 mV/°C slopes cancel. The sum lands near 1.205 V, the extrapolated bandgap of silicon, with a near-flat response.

For RF and microwave front ends, this matters because amplifier quiescent current and gain track the bias reference directly. A drifting CTAT-only bias would let a GaAs or gallium-arsenide stage wander into compression or starve at temperature extremes. A balanced CTAT-plus-PTAT reference keeps the bias point, and therefore the gain, third-order intercept, and noise figure, consistent across the operating range.

Slope and Bandgap Equations

CTAT voltage (base-emitter):
V_BE = (kT/q) × ln(I_C / I_S), dV_BE/dT ≈ −2 mV/°C

PTAT voltage (two junctions):
ΔV_BE = (kT/q) × ln(N), dΔV_BE/dT > 0

Bandgap sum (slope cancellation):
V_REF = V_BE + M × ΔV_BE ≈ 1.205 V (dV_REF/dT ≈ 0)

Where k = Boltzmann constant, q = electron charge, T = absolute temperature (K), I_C = collector current, I_S = saturation current, N = current-density ratio, M = PTAT resistor gain. Slope cancellation requires M·ln(N) ≈ 23; with N = 8 (ln N ≈ 2.08) this gives M ≈ 11. Example: at 300 K, ΔV_BE = (25.85 mV)·ln(8) ≈ 54 mV, so M·ΔV_BE ≈ 11 × 54 mV ≈ 0.59 V; V_REF = 0.62 V + 0.59 V ≈ 1.21 V.

CTAT vs PTAT and the Combined Reference

Property	CTAT Term	PTAT Term	Combined Bandgap
Source	Single V_BE	ΔV_BE of two junctions	V_BE + M·ΔV_BE
Slope vs T	≈ −2 mV/°C	≈ +0.086 mV/°C per ln(N)	≈ 0 (first order)
Room-temp value	0.65 to 0.70 V	50 to 80 mV (pre-gain)	1.20 to 1.25 V
Tempco	−3300 ppm/°C	+3300 ppm/°C	10 to 50 ppm/°C
RF role	Sets negative drift	Sets positive drift	Stable amplifier bias

Common Questions

Frequently Asked Questions

How does a CTAT circuit combine with a PTAT circuit in a bandgap reference?

The CTAT term is the forward V_BE of a diode-connected transistor, falling about −2 mV/°C. The PTAT term, ΔV_BE = (kT/q)·ln(N), rises with temperature. Slope cancellation requires the total PTAT scaling M·ln(N) ≈ 23 (typically a resistor gain M ≈ 11 with a current-density ratio N = 8). Adding the scaled PTAT to V_BE cancels the opposing slopes, so the sum lands near the 1.205 V silicon bandgap with a first-order tempco of roughly 10 to 50 ppm/°C.

Why does a base-emitter junction give a CTAT voltage of about minus 2 mV per degree C?

For fixed collector current, V_BE = (kT/q)·ln(I_C/I_S). The kT/q factor rises with temperature, but the saturation current I_S grows far faster (about T³ to T⁴ times an exp(−E_g/kT) factor), so its dependence dominates and V_BE drops as temperature climbs. Near 300 K the net slope is about −2 mV/°C, the defining CTAT behavior.

What residual error remains after first-order CTAT and PTAT cancellation?

First-order cancellation leaves a parabolic curvature because V_BE is not perfectly linear with temperature. A plain bandgap shows a few millivolts of bow, roughly 20 to 50 ppm/°C over −40 to +125 °C. Curvature-corrected designs add a second nonlinear term to reach 5 to 10 ppm/°C, which directly limits how far an RF amplifier bias point drifts across temperature.

Related Terms

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Temperature-Stable Bias

Bias That Holds Across Temperature

Our millimeter-wave amplifiers and integrated assemblies use bandgap-referenced CTAT/PTAT bias networks to keep gain and linearity flat from −40 to +125 °C. Talk to our engineers about your thermal requirements.

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