I originally starting working on this device about the same time as the Sky65116 power amplifier. The idea was that I should put a PA on the transmitter, and a low-noise amplifier (LNA) on the receiver. In this post, I'll discuss the why and how of LNAs, as well as the construction and evaluation of the Sky65047 400MHz to 3GHz LNA board shown below. I've had these boards sitting on the bench for quite some time, and I finally got all the random-value passives that I needed gathered and the equipment necessary to measure it. Finished LNA

## Low noise amplifier — why?

The goal of any receiver is to increase the strength of a desired signal from the antenna to a useful level. Often, the point is driving a speaker. If we ignore selectivity, and some receivers do this to an extent, every receiver is simply an amplifier.

I'll discuss AM radio as an example because there's a more direct connection between the input radio power level and the audio power level. Let's assume that the station we're listening to is producing -70dBm of power at your antenna. It's irrelevant for the discussion, but for the purposes of illustration, that means that the peak to peak voltage is less than 200 uV, or .0002 volts (assuming 50 ohms)! Then, let's assume that we want 1 watt out of a speaker, or 30dBm. This means that the receiver needs a total of 100 dB of system gain.

While I'm sure there are amplifiers that are capable of this much gain, it's unlikely that it's going to be appropriate for this application. It is much more common to have a chain of amplifiers. Even though I said you could sometimes ignore selectivity, we still want to amplify only the desired signal. It is the goal of our amplification chain, therefore, to preferentially amplify the desired signal and not the noise. The ability of an amplifier to do this is defined as the Noise Figure or Noise Factor (NF). These are equivalent, but noise figure is in dB.

The total noise figure of a receiver is dominated by the first amplifier in the chain. This is the reason that we develop specialized now-noise amplifiers. If you spend the time, energy and money on a LNA it will pay off by lowering the noise figure of the entire receiver. On the other hand, if you take a crappy amp and put it in front of a good receiver, you're likely to reduce its performance. This is formalized by Friis' equation: $$F_{total} = F_1 + \frac{F_2-1}{G_1} + \frac{F_3-1}{G_1G_2} + \frac{F_4-1}{G_1G_2G_3} + ... + \frac{F_n-1}{G_1G2...G_{n-1}}$$

The $$F$$ terms are the noise figure of the subscripted amplifier stage, and the $$G$$ term is the gain of the stage. You can see the the noise figure of any given stage is divided by the product of the gain of every prior stage. Therefore, a good LNA has low noise, and high gain. A simpler way to express this relationship, especially if you're considering adding an LNA to an existing receiver is this other version: $$F_{new} = F_{lna} + \frac{F_{old}-1}{G_{lna}}$$

## Low noise amplifier — how?

I'm not going to explain how to make a low noise amplifier, at least not at any substantial level, because I don't know. I'm not actually an electrical engineer, and I'm certainly not designing silicon. If I want an LNA, I'm going to digi-key like every other mortal. However, I will discuss how I selected this chip, designed the PCB and evaluated its performance.

I begin any project like this in basically the same way: I go to Digi-key and start parametrically searching. In this case I'm looking for a 400MHz amplifier, so I selected all the devices that were in stock, in small quantities, that cover the frequency I want. That left me with on 13 pages of results! Ok, next, I decide that I'm only interested in amplifiers with a noise figure less than 1dB. Good, now we're down to 15 results. I can actually think about these choices now. If I'm being honest, I sort by price next. If I wanted to do the best job, I'd sort by gain. Sorting by gain, the top two choices are $12 and$20 each, with gain values of 24 and 22 dB respectively. In contrast, the one I picked is $0.56 and 15.7 dB of gain. I like my way better. 😉 I should say that if you need the best LNA, it don't matter how much it costs. And, in this case, you're probably not shopping at digi-key. Of course, before I hit "buy," I read the data sheet. First and foremost, I'm looking for a relatively simply evaluation circuit. I'm the RF engineering equivalent of a script kiddie, and I'm not ashamed to admit it. It's a bonus if they provide matching circuits or component values for my frequency. Luckily, the Sky65047 has both. There is some weirdness, however, with the 450MHz version in the datasheet and application note. 915 MHz evaluation circuit There is a gotcha lurking in that data sheet. The specifications presented on digi-key aren't for 400 MHz. The NF at that frequency is 1.2; a bit worse than I had hoped, but the gain increases to 20 dB. Normally, the fact that this is a DFN (Dual, Flat, No-Lead) package with very fine-pitch leads would mean that I would just skip over it. Recently, however, I've developed the skills to work with these packages, and I've had good results, so it wasn't a deal breaker. A side-benefit is that it goes up to 3 GHz. I've been thinking about building an HRPT(High-resoultion picture taking, for weather satellites) receiver, which is right-around 1700MHz. There is a matching circuit for both 450MHz and 1700MHz in an app note, so I went for it. Basic general schematic The next step in the process was designing a PCB. The topology used for each of the evaluation circuits is slightly different, so I tried my best to design a board that would work with all of them. I think I mostly succeeded, at least for 400 and 1700 MHz. Breakout board design There are only a few point I'd like to make about the PCB. First, the most important thing about RF design is the minimization of parasitics; these are unintended virtual components that arise from the circuit's environment. It's not shown in the above image, but I like to keep the solder mask off of the RF portion of the board. It might be a bit ridiculous in this application, but the idea is that it would change the permitivity, and therefore, the calculations for the characteristic impedance. It's ridiculous in this case because those traces are way too short to be striplines, and with traces this short, the impedance doesn't really matter. Also, notice that I have the ground vias practically on top of the SMD pads. These are to minimize the length and inductance of current return path. There are no breaks in the ground plane under the RF section of the circuit; the only trace on the bottom layer only crosses a DC trace, and is very short. Finally: tons of vias! ## Construction and evaluation My experience with RF projects is that you get the great satisfaction of ordering a stupid number of weird-ass values of capacitors and inductors. It took quite a while to collect all the pieces that I needed, I only did so about a week ago. I was impatient and started soldering some parts onto the boards months ago, and forgot what I was doing in the mean time. This becomes obvious later. 450MHz version Something strange is happening in this example circuit. The input matching network is completely non-sensical. First of all, L1 is specified to have 4.3pF. Nope. Second, C3 is shown as an inductor and has 30nH. Hmmm, also no. I emailed Skyworks to ask for clarification, and they never got back to me. I had to just guess for what these are really supposed to be. I started by assuming that L1 is actually an inductor of 4.3nH (pH inductors can't really be bought), and that C3 is a capacitor of 30nF. Below is the same board as in the image is from the head of the post, built with the assumptions I just mentioned. Play spot the changes! 😃 First attempt ### Noise figure Now that we have a circuit, it's time to determine whether it's performing to expectation. Because the noise figure is this amplifiers reason for being, let's first discuss the concepts of measuring it. There are three primary methods used to perform this measurement, which are summarized nicely by this Maxim application note: • Noise figure analyzer such as the Agilent N8973A. The good news is that this method is the simplest and best for measuring very low noise figures; the bad news is that it's almost$40,000.
• The gain method: This method is the easiest to perform with more commonly available equipment. The downside is that it's very difficult to measure small noise figures. This will be discussed in great detail later.
• The Y-Factor method: Requires an excess noise ratio (ENR) source in conjunction with a spectrum analyzer. This is much more affordable than a noise figure analyzer, but these still go for around $1000 on ebay. There are some ~$300 ones, but they are of unknown quality.

You should know that I'm an insufferable cheapskate, so the noise figure analyzer and Y-factor method are non-starters. Therefore, we're stuck with the gain method. Given this, what kind of conclusions can we draw given the equipment on hand?

The definition of noise factor is the ratio of total output noise power divided by the output noise that would by contributed by a perfect, noise-free, amplifier. We can measure the total output noise power (within the limits of our equipment), and we can make assumptions about the input noise because we control it.

We can use a 50 Ohm terminator at room temperature for our noise source. The noise power can be derived from theory and should be equal to -174dBm. A perfect amplifier would amplify this noise without adding any of its own, and the noise power would increase linearly with gain. This means that to get noise figure ( NF ) all we have to do is a little accounting: $$NF = P + 174 - G$$, where $$P$$ is the output noise power, and $$G$$ is the gain; all of these quantities are in dBm. Measuring the noise figure

The gain method equation can also tell us what the minimum gain and noise figure we can measure on a spectrum analyzer when it is limited by its own noise floor. Working the problem backward, let's say that my analyzer has a displayed average noise level (DANL) of -154 dBm at 434 MHz with 10 Hz RBW and 3 Hz VBW. At that power level, the noise figure calculation would be $$NF = -154 + 174 - G = 20 - G$$. This means that a perfect amplifier ($$NF = 0$$) with 20dB of gain wouldn't change the apparent noise level of the analyzer at all. It also means that we aren't capable of measuring the noise figure of any amplifier where G + NF < 20. Unfortunately, that also means that I should only see 1.2dB of difference in noise for this amplifier. This is reasonably close to what I observed. In the above image, the pink trace is with the amplifier connected and the yellow trace is with the spectrum analyzer input terminated. There's technically a little more than the 1.2 dB of additional noise, but you can see that the variation in the noise floor is more than that, so there's basically zero confidence in the measurement. At least I know that it isn't a complete disaster, because that would show up. Note that, for now, I'm making assumptions about the gain using the datasheet values.

### Gain

Remember that the noise figure calculations depend on knowing the gain of the amplifier. I had used the datasheet values of 20dB in the above example. When it came to actually measuring the gain, things got weird. There is where my subtle lies come apart. When I recorded this video I had forgotten about the assumptions I made in the construction section. Remember that I said this project sat on the shelf for a while. While writing up this post I rediscovered those problems. Now things make are starting to make a lot more sense. My conclusions in the video aren't really accurate. I was right in that there was a matching problem in the circuit. I was able to later discover that the "ruler effect" only affected in the input section.

At least now I know that one of the assumptions I made in the construction section was demonstrably false. I started with C3, and replaced it with a 30nH inductor. This completely eliminated the ruler effect, and improved the gain from around 12 up to 17 dB. Gain after C3 fix

Not content to assume that this is the best possible performance; I also tried replacing "L1″ with a capacitor. I figured that it might be a capacitor because 4.3 pH isn't really an inductor value, you can't even buy them that small at digi-key. I had a 4.7 pF cap handy, so I tried it to see what happens. Gain improved again from around 17 to almost 20 dB, and the shape of the trace in low frequencies improved. Performance after changing L1

Unfortunately, the current draw never really changed from the ~7.5mA that I was seeing in the video. I figured that it would be prudent to re-measure the noise figure with the now higher gain. Second attempt at measuring noise figure using the gain method

Now, the results from the gain method are clearer, though still not that meaningful. At this point, it's just shy of 5dB difference. The math would indicate that the NF is around 4.59 dB, but confidence in this number is still very low. If it were true, it isn't even close to data sheet performance.

### Input return loss

The last quantity I'd like to measure is input return loss. This is, quite simply, the amount of signal applied to the input that is absorbed by the amplifier. As this number gets larger, it means that less signal is reflected back toward the source, and that's a good thing. Measuring input return loss

A common way to perform this measurement is through a directional coupler (DC). I'll discuss this more in a later post, but briefly, a DC has three or four ports. A three-port DC has an input, coupled, and output port, a four-port DC has coupled ports for forward and reverse coupled ports. A perfect DC places some of the power from the input and none of the power from the output onto the forward coupled port. If you hook it up to the spectrum analyzer "backward", you can sample the energy reflected by the device under test (DUT). Really cheesy schematic for reflection bridge

I apologize for the crudity of the above diagram, but I just wanted to show how you'd hook-up a directional coupler to measure input return loss (or reflections). I'm not so familiar with the schematic diagram for a directional coupler, but I assume that the arrows indicate the direction of coupling between the ports. This is a four-port DC, so it's a little different than what I have. In the above example the tracking generator of the spectrum analyzer is represented by the AC power source. The majority of the forward power through the coupler is passed directly through to the DUT, and a small fraction is absorbed by the 50 Ohm load. The power reflected by the DUT is mostly returned to the tracking generator, but a fraction of it is sent to the spectrum analyzer input. Ideally, none of the forward power ends up on the return coupled port. This measure is called either isolation or directivity. Input return loss

In the above plot, the magenta line is the returned power when the DUT is an open connection, and represents the maximum returned power (100 percent reflection or 0 dB input return loss). The yellow line is the return loss from a 50 ohm terminator, and shows the directivity of my DC. This is what a perfect termination would look like. The teal trace is the reflected power from the LNA. You would subtract the teal trace from the magenta to find the input return loss.

In our case, the best performance is at 382 MHz, with 16 dBm and worst (in this plot) is at 334 MHz with about 10 dB input return loss. This is near enough to the data sheet specifications (14 dB) for my needs.

## Conclusion

So, I'm really shocked that this ended up being so freaking long. I feel likeI had a lot of ground to cover, and to do it any justice I had to take my time. If you're still reading at this point, I'm humbled. I sincerely hope it was worth it. If you have any questions, please don't hesitate to comment. I try really hard to contribute meaningfully through the comments.

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2014-01-15T12:20:36