# Understanding Noise Figures for BJT transistor

I am trying to design a low noise preamplifier with the following part: 2SC3324. This is one of the lowest noise BJTs around I could find and I like to make sure I interpret things correctly. My supply is 5V. The signal I like to amplify is coming from a source with 50 ohm source resistance. My target frequencies are between 1-5KHz. I will be using a common emitter topology with an NPN part. The noise graph is here. I like to achieve the optimum noise given a 5V supply. I can design the bias point and dynamic range using commonly available examples. According to the graph below. 1dB noise figure can be achieved if my source resistance is about 100ohm where the Ic is about 1mA.

The key part I cannot figure out is if I should add another 50 ohm resistance before the coupling capacitor (C1) of the amplifier so that the perceived source resistance become 100ohm.

The other problem is the specification provides Vce of 6V graphs. Using my 5V it will not be possible to achieve this Vce separation. I assume noise will increase when Vce is around 3V. How can I estimate the noise? (Will it be 2x or 20x, I am trying to get a sense).

It's never a good approach to add a resistor in series with the source to get to a point where the device noise figure is better. All you would be doing is increasing the noise form the source so that the device noise is relatively less. The total noise at the output would be increased.

Can't you operate at ~5mA where the device noise is better and it would work well with 50 ohm?

I don't know about how the device noise changes with Vce but you could use a biasing circuit that doesn't lose any of your available supply voltage. For example don't use an emitter resistor but instead use DC feedback from the collector to base. With such low impedances you should be able to do that without adding significant noise in the bias network.

• Could you please show an example schematic of your suggestion? – Ktc Sep 28 '15 at 9:38

No, you can't improve the noise performance by adding source resistance. The trap you're falling into is that the "noise figure" improves because the transistor is adding the same noise to a noisier source! This is specmanship not engineering...

One good way of reading the graph is to focus on the "3dB" curve. The importance of this is that "3dB" means doubling the noise power : in other words this is where the transistor generates the same noise power as the source.

So you can see that the transistor is as noisy as the following resistor (i.e. has an "equivalent noise resistance" (ENR) in each case:

• 100 uA : 120 ohms
• 300 uA : 50 ohms
• 1 mA : 35 ohms
• 3 mA : 25 ohms
• 10 mA : 20 ohms

This is what the transistor does, in terms of voltage noise (thermal noise, Johnson noise). Now compare these "noise resistances" with your noise budget and choose your collector current accordingly.

The upper 3dB curve shows the performance limit in terms of shot noise (current noise, where the statistical fluctuations in current flow develop noise voltage across high resistances. Ignore that curve for now by staying well away from it! Just note that you had a high source impedance, that's the curve you'd be looking at instead)

If you need a lower noise resistance, the way to achieve it is to use a transformer ahead of the input, to transform the transistor's noise resistance to match your budget.

EDIT : earlier version didn't take RMS summation of noise sources into account properly.

For example, if you need a 1dB noise figure at 50 ohms, that would imply 0.1x the noise power, or a noise resistance of sqrt((50 + 50*0.1)^2 - 50^2) = 22.9 ohms. The "3dB" curve suggests this is achievable around 10mA collector current, but the "1dB" curve suggests the target is just missed even at the curve's minimum at 6mA. What happens above 6mA is that the upper curve is starting to converge towards the lower, i.e. current is high enough that shot noise must be added into the budget.

A 1:2 transformer will transform your input voltage up 2x, but transform impedances by N^2 or 4x, so making the source impedance appear to the transistor as 200 ohms, demanding a noise resistance of 4 * 22.9 = 91 ohmsto meet the budget. Or alternatively, translating the transistor's 50 ohm noise impedance (at 300 uA) down to 12.5 ohms at the input, comfortably meeting the budget while saving power. Obviously you also have to budget for the transformer's own winding resistances, and design the transformer accordingly.

Impedance transformation is how vacuum tube triodes, with noise impedances like 300 kilohms, can nevertheless provide low-dB noise figures, even for low impedance ribbon microphones.

So if you cannot afford 10mA collector current, you can use a higher ratio transformer to achieve similar results at lower currents and higher ENR. (Don't take this too far; you'll run into the upper shot noise curve!)

One further note: Vce=6V is probably just a convenient place to measure the noise figures. A lower Vce is unlikely to greatly impact the noise. It will impact dynamic range however, because the amplifier will obviously overload at lower voltages...