# How to increase CE amplifier gain to 12?

The gain needs to be increased to 12, currently it is at 10 but I cannot seem to increase this any more. The circuit topology cannot change, but the component values can - except R4, the 56 kΩ resistor.

The input signal is 1 Vpk at 1 kHz. Therefore, I am hoping to achieve a +/- 12 V output. The supply of +/- 15 Vdc is fixed too. The load will be replaced by a class B push-pull amplifier. The quiescent DC voltage at the output should also be +2.4 Vdc.

I have tried to calculate the variables:

Vb = (Vout * R4) / (Vin-Vout) = (2.4 V * 56 k) / (30 V - 2.4 V) = 4869.57 Ω
VE = VB-VBE = 2.4 V-0.6 = 1.8 V
IC = IE = VE/RE = 1.8 V/1 k = 1.8 mA
VCQ = Vcc-IcRc = 30 V-(1.8 mA)(1 k) = 28.2 V

That is what I had tried. I had since had some help which led to the gain of 10, however, I cannot find how that was possible - nor how to increase further without clipping, hence my request for help.

• We won't do your homework for you. You need to demonstrate that you have made a substantial effort to solve this yourself. Show us all of your work, then ask a specific question. Dec 6, 2021 at 20:46
• Steps how to do this: 1) Check the DC voltages and currents. 2) From the NPN's $I_C$ determine what the NPN's $gm$ will be. If you have no clue about $gm$, study: small signal analysis. 3) Draw the small signal equivalent circuit 4) determine an expression for the (voltage) gain. 5) look in the expression what decreases/increases the gain. But really, if you don't know what to do without all this then I think you first need to learn how this circuit actually works. How does it amplify a signal at the input? Dec 6, 2021 at 21:02
• @jonk Yes, this is a teaching excerise. I am a student, however, what is really frustrating is no one can get this circuit to work. I have spent a couple of days on this now and have been left with no real answers.
– Tom
Dec 6, 2021 at 21:05
• Throwing all your KVL and KCL skills at it and calculating the heck out of it means nothing if you do not understand how the circuit operates. By that I mean, suppose the voltage at the base of Q1 increases a little bit, what happens then, think in changes. Forget numbers. I have spent a couple of days on this now Then I sense a serious lack of how you're educated on these type of circuits. I blame your teachers, not you. Dec 6, 2021 at 21:06
• Keep R4 at 56k. Make R3=3k3, R1=15k. For gain of 12 and 30 V supply you don't need a partially by-passed emitter so remove R5 & C3 and connect R2 (1k) straight to negative supply. 56k & 3k3 base resistors bias base to about -13.3 V and so emitter is at -13.3-0.7 = -14 V which gives enough collector negative swing head room. Emitter voltage of 1 V across 1k gives collector current of 1 mA which flowing through 15 k collector resistor biases the collector to about 0 V. Gain equals (R6//R1)/(R2+re) where re=25mV/1mA. So gain is a little over 12 but it will vary with load impedance.
– user173271
Dec 6, 2021 at 22:44

## Schematic

simulate this circuit – Schematic created using CircuitLab

## Sanity Checks

Your output swing is $$\\pm 12\:\text{V}\$$ or $$\24\:\text{V}_\text{PP}\$$. Your power supply rails are $$\\pm 15\:\text{V}\$$ or $$\30\:\text{V}\$$. In addition, your emitter has to swing with the input, so that's $$\\pm 1\:\text{V}\$$ or $$\2\:\text{V}_\text{PP}\$$. Finally, $$\Q_1\$$ cannot be allowed to saturate. So there is a minimum collector-emitter voltage that must be reserved out. Not less than $$\1\:\text{V}\$$, as you don't know what the base-emitter voltage may be here.

So, accounting for all of the above, there's only $$\3\:\text{V}\$$ left over to work with. And that has to be used for the following items:

1. You really do not want the collector current to go to zero. You can't drive the collector right up to the plus rail. So you absolutely must allow some voltage margin for the collector resistor.
2. You really do want some voltage margin for $$\R_{_{\text{E}_2}}\$$ as this sets the quiescent current.
3. The voltage across $$\R_{_{\text{E}_1}}\$$ cannot fall to zero (see #1 above) and will be about $$\\frac1{\mid A_v\mid}\$$ of whatever margin you reserve for #1, above. Or, put another way, #1 will be about $$\\mid A_v\mid\$$ times whatever you reserve here.

I think you can see why things are tight.

But looking at this, I'd say it is doable. If I set aside about $$\500\:\text{mV}\$$ for #2, then this means about $$\200\:\text{mV}\$$ minimum across $$\R_{_{\text{E}_1}}\$$. Sure, the $$\2\:\text{V}_\text{PP}\$$ rides on top of this and that means that there will be quite a %-variation of collector current and therefore some variation of voltage gain due to changes in $$\r_e^{\,'}\$$ (which is also affected by temperature.) But it is livable.

So it passes the basic sanity check.

That said, I'd like to see $$\C_{_\text{E}}\$$ set very large, so as to keep variations of the voltage across $$\R_{_{\text{E}_2}}\$$ from causing trouble, given how tight things are. A few millivolts of variation are tolerable here. But things are very tight. So getting sloppy is a recipe for trouble. Making $$\C_{_\text{E}}\$$ large mitigates this worry of mine.

## Design

I'm going to set off $$\500\:\text{mV}\$$ for $$\R_{_{\text{E}_2}}\$$, so there's only $$\2.5\:\text{V}\$$ left now for $$\R_{_\text{C}}\$$'s minimum voltage margin plus the minimum voltage margin for $$\R_{_{\text{E}_1}}\$$. Since those are related to each other by the voltage gain, $$\A_v\$$, it's all in a single package. Without accounting for $$\r_e^{\,'}\$$ in this mess, this means $$\\frac{2.5\:\text{V}}{\mid A_v\mid +1}\approx 190\:\text{mV}\$$ for $$\R_{_{\text{E}_1}}\$$'s minimum and about $$\2.31\:\text{V}\$$ for $$\R_{_{\text{C}}}\$$'s minimum.

From this, I find:

\begin{align*} V_{_{\text{C}_\text{Q}}}&=+15\:\text{V}-2.31\:\text{V}-12\:\text{V}&=690\:\text{mV} \\\\ V_{_{\text{E}_\text{Q}}}&=-15\:\text{V}+500\:\text{mV}+190\:\text{mV}+1\:\text{V}&=-13.31\:\text{V} \end{align*}

There's no quiescent current specification, no THD specification, no temperature stability specification, etc... so I can pretty much pick any quiescent current I want.

Standard values for resistors may be a problem if you are supposed to nail the voltage gain, exactly. But I suspect that's not a problem. (It better not be, because BJTs vary a lot, temperature varies, and this stage is going to have a varying voltage gain anyway because of the very wide swings and practically no voltage margins to work with.) So we can get close to the right voltage gain and just be happy.

So let's just pick $$\R_{_{\text{C}}}=4.7\:\text{k}\Omega\$$ as a starting point. (Have to start somewhere.) Since we need to drop a quiescent $$\2.31\:\text{V}+12\:\text{V}=14.31\:\text{V}\$$, we find $$\I_{_{\text{C}_\text{Q}}}=\frac{14.31\:\text{V}}{4.7\:\text{k}\Omega}\approx 3\:\text{mA}\$$.

I don't know what the BJT $$\\beta\$$ is (the emitter current will be slightly more), but we can estimate $$\R_{_{\text{E}_1}}=\frac{190\:\text{mV}+1\:\text{V}}{3\:\text{mA}}\approx 390\:\Omega\$$. Convenient.

And now $$\R_{_{\text{E}_2}}=\frac{500\:\text{mV}}{3\:\text{mA}}\approx 165\:\Omega\$$. We need to pick something standard. Either way, this will mess with the reserved $$\500\:\text{mV}\$$. But that's okay. Because things are so tight, let's use a smaller resistor value here, $$\R_{_{\text{E}_2}}=150\:\Omega\$$, and recalculate that we'll drop about $$\450\:\text{mV}\$$, plus a little because the emitter current is a little higher. Call it $$\460\:\text{mV}\$$.

Guessing about $$\700\:\text{mV}\$$ for the base-emitter voltage, this means the base voltage for $$\Q_1\$$ is $$\-15\:\text{V}+460\:\text{mV}+1.19\:\text{V}+700\:\text{mV}=-12.65\:\text{V}\$$.

A stiff divider will have about 10% of the collector current, or $$\300\:\mu\text{A}\$$, in $$\R_{_{\text{B}_2}}\$$. So $$\R_{_{\text{B}_2}}=\frac{-12.65\:\text{V}-\left(-15\:\text{V}\right)}{300\:\mu\text{A}}\approx 7.83\:\text{k}\Omega\$$. Since you have a low-impedance signal generator driving this, I'm going to round the resistor value down to $$\R_{_{\text{B}_2}}=7.5\:\text{k}\Omega\$$ and re-calculate $$\\frac{-12.65\:\text{V}-\left(-15\:\text{V}\right)}{7.5\:\text{k}\Omega}\approx 313\:\mu\text{A}\$$ as the current.

Since the base current will be no worse than $$\\frac1{100}\$$th of the collector current, the required current for $$\R_{_{\text{B}_1}}\$$ is $$\313\:\mu\text{A}+30\:\mu\text{A}=343\:\mu\text{A}\$$. So $$\R_{_{\text{B}_1}}=\frac{15\:\text{V}-\left(-12.65\:\text{V}\right)}{343\:\mu\text{A}}\approx 80.6\:\text{k}\Omega\$$. Also not a standard value. Since we know the base current might be (probably is) less than estimated, we can raise the value so that $$\R_{_{\text{B}_1}}=82\:\text{k}\Omega\$$.

The final circuit is:

simulate this circuit

Now, I honestly have no idea if I've made some gross mistake above, except to try it out in LTspice. Hopefully, it either will confirm my hopes or else it will help me find a mistake in my above work product.

Also, all of the above adjustments to find standard resistor values have also changed some of my earlier assumptions. And it is tight in here. Real tight. There's not a lot of wiggle room for adjustments. So even if I got things right, when you build this thing I'd still expect the need for some minor, final tweaks to deal with vagaries of BJTs and resistor tolerances and the ambient temperature. There just is NOT enough headroom in order to make a design that is bullet-proof against temperature and part variations. Can't be done with so little headroom.

My last caveat is that I expect the voltage gain to be a little below expectations because I didn't account for $$\r_e^{\,'}\$$, which is about $$\9\:\Omega\$$. If you find that the gain isn't to your liking, feel free to lower the value of $$\R_{_{\text{E}_1}}\$$ by about that much.

Let's see.

Looks like $$\\mid A_v\!\mid\, \approx 11\$$. Close. Plus, it worked without exhibiting any clipping. And it did this without me making any gross mistakes, either. Kind of "just worked."

You can set the emitter capacitor back to a smaller value, if you want. That will allow a larger swing there. But the ripple was only a couple of millivolts (I checked) with that large capacitor I used. Putting it back to your value will mean maybe $$\80\:\text{mV}\$$ of peak to peak ripple. But I don't think anyone will care that much about the consequences of it. The output will still look okay on a scope.

When you get to building one of these, just get things up and see what you have. Check the collector voltage signal, directly. If it is clipping on the bottom then you are saturating the BJT (pushing up against the emitter too tightly) and you can open things up a bit by increasing the value of $$\R_{_{\text{E}_2}}\$$ (because that will lower the quiescent current.) If things are clipping on the top, then do the opposite. You can use this resistor to move your collector curve up or down, that way. (Please note that I'm not talking about the output across the $$\100\:\text{k}\Omega\$$ load resistor. I'm actually talking about the signal variations at the collector of $$\Q_1\$$. Keep that straight!)

• Thank you so much for the help! It’s really appreciated that you’ve done so much. This has really given me some extra understanding of the circuit, which I have not been as clear previously
– Tom
Dec 7, 2021 at 11:21
• @Tom You interacted well, here, which suggests you want to know more. That's a good and worthy trait. And thanks very much for letting me know it helped. Makes it all worth the time! Best wishes and be sure to help others when you find a moment and someone else interested. Pass it on.
– jonk
Dec 7, 2021 at 14:27
• Guessing about 700mV for the base-emitter voltage, this means the base voltage for 𝑄1 is −15V+460mV+1.19V+700mV=−12.65V. - Please can you clarify where the 1.19V has come from? Maybe it is very simple, but I should ask rather than guess.
– Tom
Dec 7, 2021 at 14:53
• @Tom It comes from the 190 mV minimum plus the 1 V peak signal value. The emitter resistor (1) will go from 190 mV across it to 2.190 V across it. The quiescent point is halfway between the two.
– jonk
Dec 7, 2021 at 14:58
• Thank you very much. I understand that now. Again, much appreciated!
– Tom
Dec 7, 2021 at 14:59

How to increase CE amplifier gain to 12 in five steps

First, identify essential components of your design and make sure you understand their purpose.

1. NPN transistor. This is an amplifying device.
2. Resistor R1 connecting the transistor collector to VCC. The transistor operates as the current/voltage controlled current source, the resistor transforms the current generated to an output voltage.
3. Two resistors and a capacitor connecting the emitter to VEE. The prototypical CE requires no such components as the emitter is connected to the network common for both input and output ports.
4. The input signal source and network (a signal voltage source, a coupling capacitor, voltage divider resistors).
5. The output RC network.

With a clear understanding of CE amplifier working principles, you can try and solve your problem in five steps, alternating calculations and simulation runs.

To cut a long story short, I show here the circuit with adjusted component parameters. The two simulation plots are the emitter junction voltage drop V(base)-V(em) and the emitter current Ie(Q1). The ranges where V(base)-V(em) plunges well below 600mV are responsible for a noticeable signal distortion. For those interested in how one can arrive at these adjusted component parameters, see the first version of my answer. Notice that the R3 resistor in that earlier version was selected to be 3.6K. The value 3.9K gives a much better linearity, with a THD coefficient < 1.5%.

The FFT plot of an output voltage shows the signal distortion in numbers.

The second harmonics is -40dB, not too bad for that simple amplifier. The distortion is so weak that it is hardly noticeable in visual comparison and is only detectable with the overlay of Vin and Vout. Notice also that the gain is actually 12.6, better than the target 12.

Naturally, the amplifier becomes better when it amplifies a small signal (the source is a 100mV sine wave).

The THD value decreases to 0.06%, and the FFT plot looks like:

The second harmonic is less then -60dB.

Still, the merit of this design is very questionable, because the quality parameters are very sensitive to component values. You cannot build a precise CE amplifier with a gain of 12 and an output swing of 12V with +15V/-15V supply.