basic: BJT biasing and small signal model - Page 1
Forum section: electronics / beginners

author: ealex
author_rank: Frequent Contributor
timestamp: December 03, 2015, 01:38:50 pm
content: HelloI'm trying to understand some basic BJT amplifier circuits and design methods.I'm using for reference the following documents:1.http://www.seas.upenn.edu/~ese319/Lecture_Notes/Lec_6_BJTSmSig1_13.pdf2.http://users.ece.gatech.edu/~alan/ECE3040/Lectures/Lecture20-BJT%20Small%20Signal%20Model.pdfI want to design a basic RF amplifier - RC coupled, etc. and i will be using BFG198:http://www.nxp.com/documents/data_sheet/BFG198.pdfas the active device.The biasing point is chosen form the datasheet : Vce = 8V, Ic = 50mAThe schematic and biasing point is shown in the following picture:Lc is chosen big enough so it behaves as an open circuit at RF.Rc and Rb are chosen as described in the picture, to ensure the chosen biasing point - no E24 values for this exercise.This picture represents the small signal model and small signals parameters of the transistor.I skipped ro (r out ) as i can't find a way to calculate it, and in most examples it's missingYou can see the equivalent small signal circuit with the active device replaced with the PI modelThe value of interest is Vout - output voltage variation against Vs - input voltage variationThis image shows the small signal circuit simplified and some intermediary values.This images shows the calculated circuit gain Av = vo/vs with actual values.I've used the formula gain = 20 log( vo/vs ) = ~33dBI've skipped all internal capacitance, etc - so this circuit will work only at low frequencies.Does it look correct ? Is there something i missed in determining Av ?also - how can i embed attached images ?EDIT: embed images

author: alterbaron
author_rank: Contributor
timestamp: December 03, 2015, 06:54:25 pm
content: Your analysis looks good!However, you wouldn't want to use this sort of biasing scheme in the real world, for a few reasons:Transistor beta is a very poorly defined parameter, and varies a lot between individual transistors. Look at thedatasheet of the popular 2n3904 NPN transistorfor example. Beta can vary anywhere between 30 and 300, depending on bias current and your individual transistor.What would happen if your beta was 45 instead of 90? Well, assume that around the same amount of current (0.6mA) flows into the base. Ic = B*Ib = 45*(0.6mA) = 27mA. This sets the quiescent output voltage at 12-27mA*20kohm = 2.16V, quite far off of the 8V target!Another consideration:Beta has a strong temperature dependence, as seen in this figure from a 2n3904 datasheet:In your case, even small variations in temperature will translate to significant shifts in your bias point! (Do some calculations to see what I mean.)And remember also that each shift in bias point corresponds to a shift in gain.Finally, due to the sensitivity of your bias point (and the large impedance of the bias resistor relative to the impedance seen looking into the base of your transistor), even very small input signals will modulate the bias point -- and thereby the gain -- of your amplifier. For instance, if you send in a 1mVpeak signal, Vbe will swing up and down with 1mV amplitude. A 1mV increase in Vbe causes a change of about 2mA in Ic, which changes your gm by 4%. Therefore, your gain changes by +- 4% for a 1mVpeak input signal. This means your amplifier will be very nonlinear. You can expect significant distortion with this biasing scheme.The solution is to use a biasing scheme that remains stable for variations in beta, and is stiff, i.e. the bias point should not depend on the input signal. A good start is to introduce a resistor between the emitter of your transistor and ground -- a technique known as emitter degeneration.

author: ealex
author_rank: Frequent Contributor
timestamp: December 04, 2015, 06:00:44 am
content: thanks for the info and confirming that i understood the math behind those thingsthere is a nice pdf about biasing made by a HAM :http://www.qsl.net/va3iul/Bias/Bias_Circuits_for_RF_Devices.pdfthere are some interesting / active biasing circuits in that PDF - i will look over it.also, once i get the parts i will use one of those rf transistors to make some tests on a piece of raw pcb - with different biasing schemes, etc.

author: alterbaron
author_rank: Contributor
timestamp: December 04, 2015, 08:29:21 pm
content: Thanks for the link, looks like a good read!

author: LvW
author_rank: Frequent Contributor
timestamp: December 05, 2015, 09:32:32 am
content: Quote from: alterbaron on December 03, 2015, 06:54:25 pmYes - but realize that such an emitter resistor RE drastically will reduce the voltage gain - unless you place a (sufficiently large) capacitor across RE.In fact, emitter degeneration is nothing else than negative feedback (current-controlled voltage feedback).

author: ealex
author_rank: Frequent Contributor
timestamp: December 10, 2015, 02:55:33 pm
content: Took a break from C and as an extra exercise I've tried designing a "proper" amplifier : emitter resistor and proper base divider with ~ low impedance.The emitter resistor is bypassed with an appropriate bias cap.The collector is connected to Vcc via an appropriate inductor.Image 1 shows the schematic and design parameters:Ic / Vce , etc where kept at the datasheet specified points - 50mA and 8VDetermining the base bias resistors seems difficult:Image 2 shows the equivalent and the 2 equations / 3 variables system that results from itTo solve it i've imposed a divider current 10x the base one.The resulting values and E24 series one are shown in picture 3Figure 4 shows the recalculated bias point with E24 resistors - close to the specified oneWith that bias point gm is 2.053, rpi = 43.838 => Av is 45.7604 - approx. 33.209dB of gainNext step is to change beta to 70 with the already determined resistors.The bias point changes to what is shown in image 5:Under those condition gm becomes 2.008 and rpi = 34.860.Av is 39.68923 - approx 31.94dB of gainThe gain variation between a beta of 90 and a beta of 70 is 1.269dBIs there any better way to design the base bias resistors ?