Datasheet MAT02 (Analog Devices) - 9

MAT02
Figure 6. Multifunction Converter Collector current range is the key design decision. The inher-
MULTIFUNCTION CONVERTER
ently low rBE of the MAT02 allows the use of a relatively high The multifunction converter circuit provides an accurate means collector current. For input scaling of ± 10 V full-scale and using of squaring, square rooting, and raising ratios to arbitrary pow- a 10 V reference, we have a collector-current range for I1 and I2 ers. The excellent log conformity of the MAT02 allows a wide of: range of exponents. The general transfer function is:  –10 10  10 10 m +  I V  Z  R R C  ≤ ≤ +  R R  (13) V (15) 1 2 1 2 O = VY V   X Practical values for R1 and R2 would range from 50 kΩ to V 100 kΩ. Choosing an R X, VY, and VZ are input voltages and the exponent “m” has a 1 of 82 kΩ and R2 of 62 kΩ provides a practical range of approximately 0.2 to 5. Inputs V collector current range of approximately 39 µA to 283 µA. An X and VY are often taken from a fixed reference voltage. With a REF01 pro- RO of 108 kΩ will then make the output scale factor 1/10 and viding a precision 10 V to both V V X and VY, the transfer function O = VXVY/10. The output, as well as both inputs, are scaled for ± would simplify to: 10 V full scale. Linear error for this circuit is substantially improved by the m V   Z small correction voltage applied to the base of Q1 as shown in VO = 10 (16) 10   Figure 5. Assuming an equal bulk emitter resistance for each
OBSOLETE
MAT02 transistor, then the error is nulled if: As with the multiplier/divider circuits, assume that the transistor (I pairs have excellent matching and are at the same temperature. 1 + I2 – I3 – IO) rBE + ρVO = 0 The In ISA/ISB will then be zero. In the circuit of Figure 6, the The currents are known from the previous discussion, and the voltage drops across the base-emitter junctions of Q1 provide: relationship needed is simply: RB IZ r V = kT In (17) BE A V R + B KRA q IX O = VO (14) RO IZ is VZ/R1 and IX is VX/R1. Similarly, the relationship for Q2 is: The output voltage is attenuated by a factor of rBE/RO and ap- plied to the base of Q1 to cancel the summation of voltage drops RB = kT IO due to r V A In (18) BEIC terms. This will make In (I1 I2/I3 IO) more nearly R + q I B 1 – K ( )RA Y zero which will thereby make I O = I1 I2/I3 a more accurate rela- tionship. Linearity of better than 0.1% is readily achievable with IO is VO/RO and IY is VY/R1. These equations for Q1 and Q2 can this circuit if the MAT02 pairs are carefully kept at the same then be combined. temperature. R + B KRA I I In Z = In O R + 1 – K ( )R I (19) X IY B A REV. E –9–