Network Analyzer Operation
Introduction
The first thing is Network Analyzer Operation. Network Analyzer is a piece of equipment we use in the lab. It's a very expensive piece of equipment but it's very nice.
Purpose
When I first heard about network analyzers, I didn't know what they were. They're not for analyzing networks like routers and Ethernet, and that kind of thing. The purpose of a network analyzer primarily is to measure what's called the "Sparameters" of an electronic device.
Sparameters are parameters that completely characterize a linear device. So if you have a device which is called linear, which we'll talk about in just a second, you can completely understand the operation of that device if you know what its Sparameters are. For those of you who have taken a signal analysis course, you probably talked about the transfer function, or H  it's in the frequency domain. The Sparameters are a generalization of the transfer function. They include information about the input impedance and output impedance (input resistance/output resistance) of the device. So, with a transfer function you know a little bit about how the device performs, but you don't know how it's going to interact with other devices, because you don't know what its input and output impedances are. The Sparameters give you that information.
Terminology
The device that you are testing is called the "DUT" or "Device Under Test." So if you read any kind of highspeed measurement manual, or something like that, they'll talk about the DUT, or Device Under Test.
The test fixture is just the connection between the network analyzer and your device. Usually that is just a pair of cables. So you have a cable going out of your network analyzer into the device and then, another cable, maybe, coming out of your device into the network analyzer. So the test fixture is often very simple. It's just a couple of cables.
Last thing that we will talk about is Linear TimeInvariant. This is important. The network analyzer measures linear devices. You can measure certain nonlinear characteristics, but it's really a measurement tool for measuring linear devices.
Overview of Network Operation
The first thing is that the network analyzer measures in the frequency domain. Probably some of you have used an oscilloscope. An oscilloscope measures in the time domain. It samples the input signal at fixed spaces in time and then displays the result on the screen. Whereas a network analyzer actually says, "I want to know what the response of this device is at 60 megahertz (Mhz)." And it's going to measure what the response is at 60 Mhz. And then at maybe 61 Mhz and then 62 Mhz. But it does each of those independently.
So a lot of devices, like a voltmeter or an amp meter, will measure the voltage or they'll measure the amps through a cable, but these, like most tools, are like an oscilloscope. They just measure what's happening. They don't actually provide stimulus into the network.
Now, an example of something that does provide a stimulus is, like, an ohmmeter. An ohmmeter actually puts a voltage across the resister that you're trying to measure and then measures the current. So it creates a stimulus of a DC voltage and then measures the current afterwards.
A network analyzer works in a similar way. It transmits a known sinusoid, which means you need to know the frequency, amplitude, and phase of that sinusoid. It transmits that into the device and then measures the phase and amplitude of that sinusoid. So it actually transmits the sinusoid and then receives it again. Which makes it different than most other pieces of equipment.
Typically speaking, you transmit and receive at the same frequency.You would have different frequencies only for very specialized measurements, like if you're measuring what's called a mixer or a frequency multiplier. But for 95% of the measurements that you would make with a network analyzer. the frequency that you transmit at is the same frequency that you receive at.
Linear TimeInvariant Devices
A device is called " linear time invariant" if its operation can be explained by the mathematical operation of convolution. And you might have all seen that. Convolution means if I put an input signal into a device, my output signal has to be an infinite summation of delayed and scaled versions of the input signal. OK? That's important! If you send in a certain signal, it can't send out just any signal. The signal that comes out of the device has to be something you can make by adding together delayed and scaled versions of the input. And that's what the convolution operation is. It is that mathematical operation.
Now think about what happens when you put in a sinusoid or when you add a bunch of sinusoids together that are the same frequency. What happens when you add an infinite number of these sinusoids together? Even if you scale them, and change their amplitude, and then you add a phase shift? As long as they are all the same frequency, what do you get out?
Let's say, they're all the same frequency. If you input, say, 60 Mhz sinusoid into a linear device so it can add a bunch of 60 Mhz signals together, scale them and everything. What do you get out?
You'll find if you do the mathematical operations, you will always get a sinusoid out. If you put a 60 Mhz sine wave into a linear device, you always get a 60 Mhz signal out. Which is a really nice property and that's why in signal analysis, you go into the frequency domain. Because in the frequency domain you know that if you put in a certain sinusoid, you will get a sinusoid of the same frequency out though the phase and amplitude may change.
Network Analyzer Operation
Now one of the things a network analyzer does is send an incident field, or electromagnetic field, into the device and then it measures the reflected field and the transmitted field.
A lot of times we don't think of an electronic circuit as having waves that travel forward and backward, but that is what really happens.
And a nice example is in the optical domain. You have a light, or a wave, that's incident on a lens. The glass is a different dielectric than air, and so some of the wave will be reflected, but glass does transmit optical frequencies, so some of the wave will also be transmitted.
One of the key things about the Network Analyzer is that it is able to detect the difference between a forwardtraveling wave and a backwardtraveling wave. So it can detect what the incident wave is and it can detect what the reflected wave is, even though they're overlapped in space.
Another key point is that the incident, reflected and transmitted fields for a Network Analyzer in a linear timeinvariant device are always sine waves. Which means that we can represent them.
The incident field is going to be a sine wave which we can represent this way: Amplitude R, phase offset theta which when we write it as a complex number is Re to the j theta. We do the same thing for the reflected field. (see slide for clarification). Again we have amplitude A and the phase offset associated with that. And then, again the transmitted field has an amplitude and phase offset.
And what we're interested in usually is how much energy is reflected back. In other words,I want to know if I transmit 10 watts at 0 phase into a load, let's say, how much of that energy is going to be reflected back.
So the purpose of the network analyzer is to give you the ratio of the reflected to the incident field. That's just using those complex numbers above. What we get is A over R, and then when you divide the exponents that's the same as subtracting in the power.
And the same thing happens for transmission. You measure the incident field. You measure the transmitted field. So you know what its amplitude and phase are, and then, you just divide the two, like that.
SParameters
Think of it in terms of the Device Under Test and Sparameters, I won't go into too much of this detail, but this (points to a formula) Reflected over Incident is what we call Soneone. And the Transmitted over Incident is what we call Stwoone. Now that was if we have our incident field coming from the left.
If we have our incident field coming from the right  so this time our incident is going this way, our reflected is coming back and then our transmitted is coming out the device on the other end. And those parameters are Stwotwo and Sonetwo. That's just what we call them.
Measurement  Start/Stop Frequency
OK, so you have a device and you want to take the measurement. You want to measure a device. The first thing you have to decide is at what frequencies you want to know the properties of the device.
We'll use an example from our PRISM project. We have a SAR (synthetic aperture radar) system , and we have a lowpass filter on the output of our transmit amplifier. So this filter is right before we send it out on the antenna. And the reason for this is that we also have a differential GPS telemetry link that's operating from 450470 MHz that sends data needed by the radar and robotics groups. And the operation of our radar system is actually only at 7585 MHz.
But because of the transmit amplifier, the radar system is not a truly linear device. It actually produces what are called "harmonics" all the way up at 450470 MHz. So what we did was we bought a lowpass filter to pass the low frequencies under 90 MHz. So it's going to pass our 7585 MHz band.So, what we'd like to do is measure this device from DC up to 500 MHz, because that will tell us about the passband and stopband.
The passband is the part of the filter, or is the frequency range that you are passing. So, that would be, for a lowpass filter with a cutoff of 90 MHz, that would mean anything less than 90 MHz, you're going to pass. And so that's called your passband. And then anything above 90 MHz is called your stopband because you don't want anything to get through the filter above 90 Mhz. So usually when you define a filter you are saying, "Well, I want certain characteristics in the passband. " In other words, I want to pass all my signal power. In the stopband, I want to stop everything. So you have different parameters in that band.
Measurement  Number of Points
And the first thing you need to do is determine the number of points at which you want to measure.What I mean by number of points is, "We say we are measuring from DC to 500 MHz." Do we need to measure just at DC and then at 500 MHz or do we need to sample every 10 MHz? So 10 MHz we'll take a measurement, 20 MHz we'll take a measurement, etc. So we need to ask how often we need to sample the frequency domain. That will tell us the number of points from DC to 500 MHz that we have to measure to determine the maximum length of the impulse response.
You do this by determining the maximum length of the impulse response. In our lowpass filter (LPF) example, let's assume that we have two meters of cable with a velocity factor of 69.5%. So we have maybe a cable, going into the device,. It goes through the device and then out of the device we have another meter of cable. And if you're familiar with optical waves, in free space, optic waves travel at 3 to the 8th, or 300 million meters per second. If you're traveling through a medium, say like glass, which may have an index of refraction like 1.3 or 1.5 or 2.0 then your your wave actually travels more slowly through that or slower through that device.
In this case, we have 2 meters of cable and we're going to scale the velocity, so distance divided by rate is going to equal the time that it takes to go through the cable.If it's a 4 section filter with a cutoff of 90 MHz, this is kind of general rule of thumb.
So this is the time it takes to get through the cable, through the device, through the other cable one time. And we want to allow it to reflect back and forth 10 times. So we do 10 times that. And we get 511 nanoseconds. So, if we send an impulse into the system, or a sine wave into the system, we'd have to wait approximately 511 nanoseconds to get the response out.
The other thing is we know the bandwidth of our measurements. It's DC to 500 MHz, so that's 500 MHz of bandwidth. And we e just calculated the maximum length of the impulse response that we're interested in. And the way that you calculate the number of points is, you look at the time bandwidth product  the bandwidth, 500 MHz, the time of the device (the measurement) is 511 nanoseconds. Then multiplying these together we got 256 points and our network analyzer doesn't allow us to set arbitrary numbers of points, so, we'll say 401 points. So that means that between DC and 500 MHz, we're going to have about 1.25 MHz as our step size. So, we're going to take measurements at 1.25, 2.5, 3.75 etc.
Measurement  Transmit Power
The next thing we need to think about is, "What is our transmit power?" It's a lowpass filter and happens to be a highpower, lowpass filter. So we're going to transmit at the maximum power that the network analyzer can handle.
You always want to put as much power into the device as possible because you want to maximize the ratio of your signal power to your noise power. If you don't have a strong enough signal you won't be able to see the signal after you do the measurement.
As the next thing, we set our transmit power to 10 dBm, which happens to be the max power of the network analyzer we're using. And then, what we'd like to do is measure the stopband attenuation down to 90 dB. In other words, if I send a 1 watt, 450 MHz, signal into this lowpass filter, I want to see if it's 90 dB down. In other words, that's one billionth the power coming out. So I really want to suppress energy at 450 MHz.
Using a noise figure of 53 dB for the network analyzer, which is, what it is. The noise power is measured 10 log 10(KTBF) and that's a standard equation if you remember this.
This is in watts here. Then we convert it to dBw which is just the intensity version. I mean, just like in physics, you're taking intensities. 10 log 10 and then we add 30 because that converts from dBw (that's dB with respect to watts) to dB with respect to milliwatts, which is dBm, since that fits the units we happen to be using.
Measurement  IF BandwidthSo, to achieve an SNR of 16 dB, we need to set our receiver bandwidth. So that term (points to it in equation) is 25 dB. Therefore B needs to be 300 Hz or less. So if we plug 300 here and you take 10 log 10 of 300, you'll get approximately 25. That's what we want. So that's our next parameter. That's where we're going to set our receiver bandwidth. On the network analyzer, this receiver bandwidth is referred to as the IF bandwidth. So that's another parameter you need to set when you're taking measurements.
Measurement  Averages
There's another possibility. One way to increase the signal to noise ratio was to lower our receiver bandwidth. OK?
Another way to increase your signal to noise ratio is to average. And that should make some general sense. It's like if you average your measurement when measuring the length of a table or something. If you take multiple measurements and average them, hopefully you can reduce your random error. Right?
Let's say we want our IF bandwidth to be 10,000 Hz. There might be some cases where that's a constraint. And, now 10 log 10 of B is 40 dB, but that's 15 dB bigger than we want it to be. So what we do is we average 40 times. And what this does is effectively put 40 times the amount of energy through the device. And so our signal power increases by 40 times. So the idea is, if we pulse, and then we send another pulse, we've doubled our energy. We send another pulse, we've tripled the energy. And the signal that we're getting back stays coherent.
So the whole equation:
Signal to noise ratio (SNR) starts out 10 log 10, your input power (transmit power) and then you get higher signal/noise ratio if you increase your transmit power.
You get a higher signal/noise ratio if you increase the number of averages which I've called "N" here. The attenuation that you want to measure, 90 dB in this case, subtracts, or hurts, your signal to noise ratio. So, the more you attenuate a signal, the harder it is to measure it, because it's starting to look a lot like noise.
And then the other thing that hurts you is what's called "thermal noise," which is what that KTBF is. In other words, just standing here with an antenna, there's a certain amount of electromagnetic noise in the background. If you have an object that's 290 Kelvin or 6000 Kelvin, it emits all frequencies across the whole spectrum, just like say, a light bulb that glows. You know, it gets hot and then starts emitting light. At 290 Kelvin this table only emits in the infrared region  we can't see it. The optical region is the higher frequency, but if we heated the table up, it would begin to glow. So you have this sort of thermal background noise that's approximated by KTBF.
