7.8.2 Temperature Independent Reference Generators

Chapter 7.8.2 Temperature Independent Reference Generators

Radio Frequency Integrated Circuit Design Second Edition Book
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Radio Frequency Integrated Circuit Design Second Edition Book

  • 224 LNA Design =D» -D�constant2 mV/ CcBEivT (7.140) 0.5%/ CTβD » +D� (7.141)A typical temperature range might be 0° to 85°C. Thus for a constant voltage bias, if the current is 1 mA at 20°C, then (7.139) predicts it will change to about 0.2 mA at 0°C and about 71 mA at 85°C, taking into account only the temperature dependence of vBE and vT. Thus, the current changes by more than 300 times over this temperature range. This illustrates why constant current biasing (for example, with the current mirrors, discussed in Section 7.8) is used. If both transistors in the current mirror are at the same temperature, then output current is roughly indepen-dent of temperature. 7.8.2  Temperature Independent Reference GeneratorsAll RF circuits require bias currents, and these currents must be generated some-how. Bias circuits should produce a current or voltage that as much as possible is insensitive to supply and process variations. As well, these references should have some well defined behavior over temperature. This behavior can often be adjusted to help compensate for circuit variation with temperature [1, 11, 12]. Since circuit performance in a silicon process is affected by temperature, supply voltage, and process variations, it is sometimes possible to find dependencies that cancel one another. Most of these types of circuits make use of bipolar transistors, even in an all CMOS process. Typically all CMOS processes include a very slow lateral PNP transistor for the purpose of building bias references. To start the design, consider the bipolar base emitter voltage characteristic de-scribed by =ln CBESkTIVqI (7.142)This expression seems to show that base-emitter voltage is directly proportional to temperature; however, IS has a large temperature dependence as well. An expres-sion for VBE as a function of temperature is [13, 14] æö×æö=-+++ç÷ç÷èøèø2.31lnlnOCBEBGBEOOOCOTTkTTkTIVVVTTqTqI (7.143)where TO is the reference temperature, VBEO is the base-emitter voltage at the reference temperature, and VBG is the bandgap voltage of silicon (approximately 1.206V). Even though it may not be immediately obvious from this expression, VBE will actually decrease for a constant collector current with increasing temperature. Thus, if the collector current is assumed to be constant, then the derivative of VBE with respect to temperature is: