Bandgap voltage reference Based on lecture of Paul Brokaw in 1989 Why voltage reference? 1) 2) Reference in LDO feedback 3) Analog multiplier 4) And more… Zener vs. Bandgap • • • • predictable reverse voltage. fairly constant over temperature. very constant over time. very low noise. • relatively high variances in initial voltage. • lack flexibility: require high supply voltages, and offer relatively few output voltages. • Easy to implement on silicon. • Accurate initial voltage and low temperature drift. • More flexibility, lower supply voltages needed. BJT πΌπΆ = πΌπ (π ππ΅πΈ/ππ −1) ≈ πΌπ π ππ΅πΈ/ππ ππ ππ = ≈ 26ππ @ π = 300πΎ π πΌπ = πΌ0 exp(−ππΊ0 /ππ ) I0 – process and geometry depended current. Also depends on temperature. VG0 – bandgap voltage: about 1.25V in silicon Current mirror The two transistors are identical: is1 = is2 Current mirror 4:1 mirror operates all transistors at the same current density Current mirror Voltage driven current source VBE is controlled by V1 source, it’s not ~0.7V as in the current mirror. For small values of V1 where currents are relatively small, the voltage across R1 will be small and will hardly interfere with Vbe of Q1, so the collector currents will stay very nearly in the ratio eight to one. At 450mV the eight to one ratio is only starting to be reduced by the difference in the two Vbes resulting from ~15 nA in R1. Voltage driven current source While the current in Q2 can rise exponentially with V1, the rise of current in Q1 will be asymptotic to a linear slope defined by R1. This means that as V1 rises, the ratio of collector currents falls until it is below one. In the figure this happens as V1 crosses ~720mV in a room temperature simulation. In order to more accurately set and maintain this crossover voltage an opamp may be used to adjust Vbe2 to the value that makes the collector currents equal. Using a feedback loop While the feedback makes the two collector currents equal it does not answer the question of what value the currents actually have. However, it should be apparent that the common value for the currents is closely approximated by the current in R1, which itself is determined by the difference between Q1 Vbe and Q2 Vbe. βVBE ππ΅πΈ1 π ππ πΌπΆ1 π΄1 πΌπ π΄1 ππ΅πΈ1π−ππ΅πΈ2 π ≈ = π π π΅πΈ2 πΌπΆ2 π΄2 π π΄2 πΌπ π π βππ΅πΈ = ππ΅πΈ1 − ππ΅πΈ2 ππ πΌπΆ1 π΄2 = ππ β π πΌπΆ2 π΄1 ππ π΄2 = ππ π π΄1 This is the voltage across R1! Called also PTAT: proportional to absolute temperature VBE vs. Temperature Called also CTAT: complementary to absolute temperature PTAT and CTAT Implementation Different output voltages There is an error due to base currents in R5, with no corresponding current in R6. Can often be neglected, if R5 and R6 are small enough. Another error is due to the VBE curvature vs. temperature. CTAT curvature