Transistors

[Nowhere-Man]

Here's what I learned: Just assuming for some crazy reason you wanted to know the Beta of a transistor and you only have collector current and base current, just divide base value into collector value. The base will be about 20 microamps or around.
So far simple.
If you only have the base and emitter currents, it's the same division but you need to subtract 1 from the total.
That will give the correct Beta.
Example: emitter is 0.004 Amp and base current is 0.000026466. Divide and you get a Beta of 150 (-1). What is useful is you can use the Beta here to get the Alpha 150/151 (about 0.99) and multiplying it by the emitter current will give collector current.
It is pretty useless information in real life but (speaking personally) this helped me understand simpler concepts. It shows emitter current is slightly higher and that the tiny base current is amplified by a known digit.

[Nowhere-Man]

Just think what a blow this was to the Vidor 90 volt 1950's battery portables. They finally got a valve radio that would work on 90 volts, then came a 9 volt alternative. The home based valve sets still had a role but the Vidor sets were rendered pointless. Personally for me the Golden era tranny sets were the chassis mmounted ones. Later I figure the PCB units were destined to become more complicated than the simple, reliable vintage designs. This was the gradual path to the marketing of devices with a limited life-span. I mean my oldest radio is 1947 and it was easily repaired and still tunes in lots of stations..

[Craig]

The design process for a common emitter amplifier is to set the collector voltage to be about half the supply voltage. That gives roughly equal signal swing up and down. Next decide on a collector current - lets chose 1mA and a supply voltage of 9V. So now we have 4.5V and 1mA for the collector resistor Rc = 4.5k. So lets chose the closest common E12 value of 4.7k. Next we have to choose and emitter resistor ( ie between emitter and 0V). This is where you use a rule of thumb - for an amp of that sort, about 1V across the emitter resistor is a good starting point. Since we are talking a silicon transistor with a high beta, the emitter current is very very close to the collector current. So 1V and 1mA Re= 1k for the emitter resistor.

Now we're going to bias the base using a potential divider. We need a base voltage of 1V + the base emitter voltage. This is just a diode voltage drop of about 0.65V, so we need a base voltage of 1.65V. We'll do that with a potential divider. Now this is the *only* time we need beta, and suppose that is a minimum from the spec sheet of 200. For 1mA collector or emitter current, the base current will be 5uA. So we don't have to mess around considering the base current, we'll pass twenty times the base current down the divider - so 100uA. From a 9V supply the total resistance of the divider is 9/50uA = 90k. To calculate the lower resistor Rl we use Ro = V0R/V to get 1.65x90k/9 = 16.5k, and the upper resistor Ru is 90 - 16.5k = 73.5k. So lets round to the nearest values and see where that gets us. Increase them both a bit - so upper resistor Ru = 82k and lower resistor Rl = 18k. That gives a base voltage of 18/(18+82) times 9V = 1.62V - so very close to the design target of 1.65V.

The DC voltage gain is just the ratio of the collector resistor to emitter resistor, or Rc/Re = 4.7 times. Now look what happens if the emitter current increases a bit. If it does so the voltage across the emitter resistor increases a bit. Now since the base voltage is pinned by the potential divider, the increase in emitter current reduces the base emitter voltage, which tends to decrease the emitter current. So this arrangement ensures that the bias conditions are stabilised.

Now this is still a fairly useful amplifier in its own right, with a gain of 4.7. But we want more AC gain than that. So we put a capacitor across the emitter resistor, which shorts the emitter to ground for AC signals. Now the gain equals the collector resistor divided by some other resistor due to the transistor itself. That is given by 26/emitter current (in mA). So for our 1mA design, that resistance is 26 ohms. That means that the voltage gain of our amplifier is 4700/26 = 180, a very useful gain indeed.

There is actually a resonance with valve terminology here. 1/(internal emitter resistor) = gm. In this case 1/26 = 38mA/V. So the gain is gmRc = 38 x 4.7 = 180.

We need to calculate the capacitor value, for which we need to know the lowest frequency we want this amplifier to work at. Suppose that this is an audio amp and we want the low frequency limit to be 10Hz. The calculation is that at 10Hz we want the capacitive reactance to be equal to the emitter resistor. So Re = 1/(2pifCe), or C = 1/(2pifRe) . Putting in the values, Ce ~ 1/(6 x 10 x 1000) = 16uF (since 2pi is about 6). Chose the next largest standard capacitor value of 22uF.

Which completes the design. DC gain of 4.7, AC gain of 180, and an AC frequency response that goes down to 10Hz.

And I only had to use beta once!

[Kalee20]

You did! And if beta changed, it would make very little difference as your potential divider for base bias is passing current which swamps it anyway.

However, I'd say that you haven't calculated input resistance, which is partly directly proportional to beta. The inherent transistor emitter resistance is 26 ohms, beta is 200 so we get 5.2k. This is much lower than the base bias divider, so input resistance is heavily dependent on beta, which could be critical if you are operating from a high-impedance source.

I'd also like to question the emitter bypass capacitor - for a low-frequency 3db cutoff of 10Hz, you want the capacitor'reactance to equal the emitter internal resistance (26ohms) in parallel with the external 1k, and this gives 628uF, not 16uF!

[Craig]

You did! And if beta changed, it would make very little difference as your potential divider for base bias is passing current which swamps it anyway.

However, I'd say that you haven't calculated input resistance, which is partly directly proportional to beta. The inherent transistor emitter resistance is 26 ohms, beta is 200 so we get 5.2k. This is much lower than the base bias divider, so input resistance is heavily dependent on beta, which could be critical if you are operating from a high-impedance source.

I'd also like to question the emitter bypass capacitor - for a low-frequency 3db cutoff of 10Hz, you want the capacitor'reactance to equal the emitter internal resistance (26ohms)  in parallel with the external 1k, and this gives 628uF, not 16uF!

Well, given the original poster I was trying to keep it simple - but you're right the input R is relatively small . However I thought a treatise on bootstrapping would be a bit OTT in the context of this thread.

You're right about the bypass capacitor though - I must admit I was surprised that it was so small, and just plain forgot it is determined by re and not Re. Of course you can reduce the value considerably by reducing the collector current. At 200uA Ic, re is 130 ohms, and you can get away with 120uF.

The other way around it is to go for a lower gain - say 50 instead of the re calculation that leads to 180 and a monster capacitor. Keep Ic at 1mA. So you split the emitter resistor into a resistor of 4700/50 = 94, subtract 26 ohms re to get a 68 ohm physical resistor, and a bypassed 1k. Then the capacitor is determined by 94 ohms and not 26, which gives 150uF, which is still quite large.

Then go for 200uA (a more common operating point, usually determined by noise), which leads to Rc ~ 22k and Re ~ 4.7k. Go for a gain of 50, giving an unbypassed Re of 440 - re (130 ohms) = 310 ohms, and a bypassed resistor of 4.3k. So the bypass capacitor is now 36uF. Do some rounding and go for 330 ohms and 3.9k with a 47uF capacitor. Gain is then 22k/460 = 48 with a 3dB frequency of ~ 7.5Hz.

[Mark Hennessy]

I'm getting déjà vu here

http://golbornevintageradio.co.uk/forum/...1#pid66491

We didn't get as far as AC analysis there, sadly. And to keep it really simple for the purposes of understanding, I ignored Ib, knowing that 47k and 10k would pass plenty of current.

For AC, when calculating the "full" gain, I go down the gm.RL route, rather than RL/Re. They are mathematically equivalent, it's just that I find it far more intuitive to think of the transistors as a transconductance amplifier with a transconductance of 40 times Ic, which of course comes straight from the Ebers-Moll equation. To consider RL/Re, you really need to think in terms of negative feedback, which is an unnecessary layer for a beginner IMHO. Or you tell them to "just accept it", which many people are uncomfortable with. Teaching is all about the "story" in my experience...

[Nowhere-Man]

There's a lot to learn. I'm sure a few people here will use transistors a lot in design. At the moment, I sometimes revise my basic transistor material, mainly for diversity and a change of theme. Each time, I learn a little more. At the moment I figured I'll revise cathode followers and see how that compares with grounded emitter. With ARRL I am very limited as the 1960 edition I have views transistors as a sort of novelty. Clearly the Hams back then were experimenting with silicon rectifiers. So really alpha and beta was more referenced than fully explained.
I still think valves are simpler but no harm in variety.
I just knocked off work on my boat so will delve deeper later tonight.

[Craig]

I'm getting déjà vu here

http://golbornevintageradio.co.uk/forum/...1#pid66491

Ha ha ha! I honestly did not refer back to your post - and indeed had totally forgotten about it. But interesting that the main resistor values (4k7 and 1k) are exactly the same as my calculation 

[Nowhere-Man]

I now know what the 0.98 figure is in the ARRL semiconductor chapter. They just pulled it out of thin air. The Beta was cited as 50. On an idle day, sat with my dog, I did some research and found some handy lessons online. So, now it's clear. For me a good way was to deduce current values from other figures given. Doing a few sums you can see how the base, emitter and collector currents relate. It's amazing how many sums I had to do to get the idea. Good job my mobile has a calculator.

[Mark Hennessy]

At the moment I figured I'll revise cathode followers and see how that compares with grounded emitter.

It doesn't.

Compare to emitter follower (aka common-collector) instead.

The Art of Electronics - http://wouterjan.deds.nl/The%20Art%20of%...20Hill.pdf - starts out by explaining emitter followers. Page 65 of that PDF. Please forget about ARRL and use this instead. Please. If you're unable to download that and read it at home, then second-hand copies of the first edition can be found for about a tenner: https://www.ebay.co.uk/p/Art-of-Electron...2279589420 - alternatively, if you put a "wanted" request on the forum, someone here might well have a copy going cheap (in return for a promise to stop referring to that damn ARRL book). Another good book is this one: https://www.amazon.co.uk/Intro-Electroni...0521478790 - again, s/h copies of earlier editions can be found cheaply: http://www.ebay.co.uk/itm/A-Practical-In...3021151961