5320 EEE Bipolar Analog IC Design
Analysis of Biasing Circuits
Lecture 6
In previous lectures, weve considered what biasing is, why it is important, and what some of the key issues are in bias design. Now lets consider how to find the operating point of a circuit, given its schematic. Well probably need some simplified models for the transistors as well. Analyzing a circuit to find its operating point is usually harder than designing a circuit to have a desired operating point. When you design a circuit, you already know what you want it do, and its just a matter of setting things up so this happens. When you start an analysis, especially of an unknown circuit, you generally dont know what its supposed to do, and finding out what it does can be like solving a puzzle. Often its tricky to know how to start; after that, it usually gets easier. Following are some tips on how to get started; youll need to practice solving some circuits to get better at it. In the process of learning to analyze these puzzling circuits, you should get insights that make you better at designing bias circiuts. Well also see how a circuit simulation programs tries to find operating points computers find this difficult, too. Biasing Circuit Analyis: Getting Started The main reason biasing analysis is tricky is that you dont really know what operating region the transistors are in, so you have to guess. Assuming its an analog circuit, you can start by guessing that the transistors are active. If you have ideal current sources and current mirrors, then you can assume theyre working as designed and solve for mirror outputs currents according to transistor area ratios. Real circuits wont have ideal currents sources. For well-designed BJT circuits, you can then assume that the VBEs are about 0.7 V. Look for a loops of VBEs, voltage sources, and resistors, and write a Kirchoff voltage loop equation in the form
! ( VSource VBE ) ! ( VSource 0.7V) = , that uses our VBE ! 0.7 V assumption to find the R R voltage across some resistor R to get a reference current I. (Many biasing circuits will have negative feedback. There should be some go around the feedback loop, in the opposite direction from the feedback signal flow, solving for voltages and currents as go around the loop. Eventually, youll come back to where you started, with estimates for the collector currents and the VCEs for all transistors.) I=
Now you need to see whether your assumptions were valid. Are all VCEs > VCEsat? Are all base currents really negligible? Are all VCEs << VA? Does VBE = 0.7 V give accurate enough current estimates? If not, youll to have go aound the circuit again and iterate using your more precise estimates to make more precise estimates. If the circuit was well-designed in the first place, you should not need this extra iteration step. If you do, the circuit is probably going to be very dependent on the details of transistor operation and therefore the bias design will not be robust. To quickly check whether the transistors are active, verify that all VCEs are > VCEsat ! ~0.2 V. If you can estimate a typical value for the saturation current IS, you could plug into VBE = Vt ln( I C / I S ) and get a more precise estimate for each of the VBEs. Then you coluld see whether your estimate of initial reference current was accurate, and if not, you could now repeat the whole process. Now we come to three of most important insights for the whole course:
EEE 5320 Bipolar Analog IC Design
Lecture 6
1. We should end the process of trying to get increasing precision as soon as we possibly can increasing precision is probably not really meaningful anyway, due to modeling uncertainty, and more importantly, because it will probably not add to our insight. 2. Simulation programs have to follow a very very similar iterative process to find operating points. This iterative process is not guaranteed to converge in general, but in well-designed circuits it usually doesnt. 3. However, one nice things about negative feedback is that it can allow the result to be relatively insensitive to modeling assumptions. FET circuits may have loops of voltage sources, VGSs and resistors. FET bias circuits tend to be harder to analyze than BJT circuits, because VGS depends more strongly on current than VBE does. Because of this, bias currents in FET circuits tend to be more device-dependent. In summary, Use simple models and assume a region of operation Start from loops of voltage sources, VBEs and resistors. Iterate if needed: I =
! ( VSource VBE ) ! ( VSource 0.7V) = R R
!! " #! !
VBE = Vt ln( I C / I S )
Feedback should be negative If so, the above iteration should converge quickly. The above analysis assumes that the biasing is properly designed so that all the transistors are active. What if those conditions arent true? If the analysis just described leads to inconsistencies, then one or more of your assumptions must be incorrect. Probably one or more transistor is a different operation region than you thought. Now, we can respond in two ways. One is to redesign the bias circuit so that the circuit works that way we wants. Hopefully the analysis to this point provides some guidance as to how to improve the design.