It was an extremely high temperature and infinitely small, much, much smaller than an atomic nucleus. This expanded to the universe we see today and the Cosmic Microwave Background radiation is what we see, our rather hear today that is what is left of the energy of the Big Bang. This energy having expanded and cooled has an average temperature of just under 3. Figure 4 shows the change in radiation wavelength distribution for different temperatures and figure 5 shows the noise density at lower thermal temperatures.
Figure 6 shows the spectral color change with temperature. For the 3 K CMB the spectrum will be spread to the very low microwave wavelengths and will be very flat in power vs. For 3 K this works out to 0.
See figure 7 for an example circuit. You only need to set the correct current for a certain temperature to calibrate to specific noise power outputs or ENR Excess Noise Ratio compared to cold noise power for the same impedance.
The spectrum of the output power vs. Figure 7 - Lamp Noise Source - see monode reference Plasma Noise Sources A plasma source is similar to the light bulb source, but uses the effective temperature of the plasma instead of the filament. These ENR's can be very high compared to other sources.
An amateur plasma source would be a neon light. Just capacitively RF couple the noise off the plasma bias circuit for an easy noise source.
This circuit would use a very similar circuit to figure 6, just using higher voltage to drive the plasma lamp. Electronic Noise Sources This would include Zeners, avalanche and DSP methods of generating noise output with an electrical bias input. Electronic noise sources available to amateurs include Zeners which can be used for a noise source for a antenna noise bridge, impedance bridge, noise source and more.
Numerous digital signal DAC sources can generate pseudo-white noise that can be used for test purposes. I will go more into this later. The professional test noise sources more typically use a form of avalanche diode biased at a specific current level and temperature. Again the noise power is coupled off the bias circuit with an RF Coupling capacitor or DC coupled as in this case. Noise Calculations Given that any device that carries electricity generates heat, it also creates radiated noise power.
In amplifiers we call this amplifier generated noise its noise figure. This gives us a measure of the signal to noise degradation of signals received and desired to be measured. This is the ratio to correct for the effective Resolution Bandwidth of the Spectrum Analyzer or Power Measurement device with frequency selectivity to eliminate spurious signals and give an equivalent power integration bandwidth.
Agilent typically uses 1. When the Spectrum Analyzer operator selects Noise Marker the bandwidth correction is made for you. It is the signal amplitude in watts compared to the Noise power level in watts at signal off conditions. This gives some measure of signal quality or at least signal detection capability. This measure of signal to noise degradation is called the noise factor. This is in linear numeric scale and units relate to power ratios or signal to noise.
The is the signal to noise ratio of the system calibration. The is the signal to noise ratio of the system and DUT total response. This is the minimum energy in noise for a broad white spectrum distribution in the RF and Microwave region. From this we can see that to figure to a positive F, Te must exceed To. Cold Noise To depends on the desired signal to be measured. Terrestrial thermal noise limits us to greater than approximately K or ambient temperature of the environment.
For deep space signals from gaseous clouds or other cold space targets, one would need close to 0K cooled receivers to detect the signal powers from space without being swamped by receiver noise, thus they use liquid helium coolers on these sensitive space microwave receivers.
They use a 0. This Y factor or ratio is ratio of the noise on to noise off power ratio or off with Np on must be greater than Np off to compute a noise figure. Then the Y ratio can be used to compute the Noise Figure in dB. Be sure to use sample detector mode when making these measurements. Video Averaging will reduce the specular noise by averaging across frequency to smooth to the video average.
The formula uses the 1st derivative of the from which we derive. Note that is requires 3 or 4 measurements to get the dY and dENR and each of these measurements has error, especially if not using a good spectrum analyzer with a low noise input and level of detection. Noise Measure Noise Measure is a measure of the noise quality of the part when noise factor and gain are both considered to an infinite extension of the cascade equation, e. Receiver gain includes antenna gain, preamp gain and total down-converted stage gain.
Small signal level of broadband modulated signals can easily swamp receiver front ends. The added G factor for gain is to account for the total system noise power after receiver system gain.
The 1. Signal to Noise Level Power Average Error When measuring CW signals close to the noise floor, as Power mW or W and you measure the signal and noise power and remove the signal and measure just the noise, you can figure what the actual signal power is without the added noise power.
This is true even if the power is displayed as dBm. Agilent is using this formula and the individual noise characterization of each PSA and PXA to compute actual signal power down into the noise floor. This technique requires a full spectral noise density characterization of the instrument.
Agilent uses the Power Average or Log Average Noise Correction techniques previous to pull the noise floor down and the signal out of the noise. In noise factor and linear gain units the formula is: For the 2 stages case: or or Use to convert to dBF. This can be used to compute the noise figure of a DUT embedded inside a test fixture. We will see these formulas again with input and output loss correction of DUT measurements.
We will also see this in the cold power noise measurement technique. In addition the equivalent Temperature cascade formulas are Figure 15 - Cascade Noise Figure - courtesy Agilent Temp Corrected Noise Figure of Passive Loss With a Loss in linear units and a Ta ambient temperature the Te effective temperature of the loss is from which we compute the noise factor.
Temp Corrected ENR The temperature corrected ENR of a calibrated Noise source at a temperature other than K can be computed to correct for the actual temperature offset error factor. This would be an input loss direct error factor on the measurement that is F1 in the cascade noise equation along with the input network loss added for the total loss.
The operator must also remember to add system gain in the measurement output path into the NFM to overcome any input loss. If this is not accounted for, the noise figure meter may fail to calibrate. This does not account for match or other corrections. This changes if the device under test has low gain or is lossy. Figure 18 - Noise Measurement with Output Loss To correct the DUT temperature for the output loss of the DUT fixture system use the formulas: Combined Input and Output Loss Correction Combining the previous equations for input and output loss to be applied to noise figure measurements on a Noise Figure Meter when applying the input and output losses or matching losses to the corrected noise path measurement.
The NFM would be calibrated without these losses and these input and output losses added to the DUT would be applied to the measured results to correct for the losses. This gain is useful to calculate the network gain or loss of an input network to a device being tested for noise figure. A mixer may be necessary if you want to convert the RF frequencies to desired IF frequencies. Calibration procedure: First the equipment needs to be calibrated.
This will establish the base level against which the DUT noise figure will be measured. The following figure shows the diagram with required connections with DUT.
It is possible that you use any connector adapters or attenuators during the measurement process to ensure that the measured values are within the range of the Noise Figure Analyzer. In such case, you may to include the adapters or attenuators during the calibration process itself not shown in the figure. Therefore, we can compute the NF in dB by measuring Ndut.
Note that the Y factor method is a relative method and does not depend on the rest of the equipment. Note that the above parameters are in linear units. Normally, the ENR provided on the noise source is in decibels. This needs to be converted to linear units for computing the noise figure. Toggle navigation. Noise Figure And Measurement Techniques 6. Yes, this is a good approach, if the attenuator is not too large. A good choice is 3 to 6 dB.
Anything more than this causes the raw directivity of the system to degrade such that calibrations can become noisy and drifty. Scalar-noise-calibrated measurements are faster than vector-noise measurements less noise-power measurements are performed and the attenuator can make the accuracy almost as good or in some cases, equal to that obtained using vector-noise calibration.
In cases where there is a lot of cable loss at port one perhaps in an on-wafer setup at high frequencies for example , scalar noise calibration is often the best choice, since the vector-noise algorithm can produce measurement spikes when the tuner impedance states do not have enough gamma spread see next question.
Why does vector-noise calibration produce spikes or ripple in my measurements that are not related to interference, especially between 45 and 50 GHz? This typically occurs in an on-wafer test setup when excessive cable loss at port one causes the cluster of impedances presented to the DUT to get too close to one another for the vector-noise algorithm to properly solve for the noise parameters of the DUT.
The algorithm needs enough spread in the impedances to give a good estimate of ohm noise power. There are a few things that can help prevent this. One is to use as short and as low-loss cable at port one as possible. Increasing the amount of noise averaging also helps. Since cable loss is frequency dependent, broadband noise figure measurements can be split into two bands, where the lower band uses vector noise calibration, and the higher band uses scalar noise calibration.
The best way to avoid this problem is to use an external ECal as a tuner, along with an external bias tee if needed and test-port coupler, placed as close to the wafer probe as possible.
These components are connected to the PNA-X via its front-panel jumpers. This configuration puts the impedance tuner closer to the DUT, eliminating the effect of cable and test set loss. Measured noise power is affected by the gain, bandwidth, and noise figure of the receiver. Gain and bandwidth can be measured separately or together as a single product. The most common way to characterize the noise receiver is to use a noise source and the Y-factor method.
The gain-bandwidth product and noise figure are directly measured by applying a known amount of excess noise to the receiver. The PNA-X offers an alternative approach that uses a power meter and power sensor as a calibration standard in place of a noise source. This method relies on separate measurements of receiver gain and bandwidth.
There are three steps to the process. The calibrated source is then used to calibrate the gain of the noise receiver. Once this is known, a cold-source noise figure measurement can be done. What are the differences between using a noise source or power sensor during the noise calibration? From an accuracy standpoint, power-meter-based measurement uncertainty is likely to be a bit better compared to using an off-the-shelf noise source, or comparable to using an NPL-calibrated noise source.
Also, power sensors are more commonly available than noise sources, especially at 50 or 67 GHz. They also work better in cases where excessive loss at port two due to a long cable for example attenuates the excess noise coming from a noise source. The tradeoff to using a power meter is that calibrations and sometimes measurements are slower.
The power-meter method only works with noise bandwidths up to 4 MHz, whereas the noise-source method works with noise bandwidths up to 24 MHz, which usually results in faster sweeps. During calibration, the power-meter method sweeps out the IF response for each data point, which adds time to the calibration process.
Depending on the number of data points, this additional time can be several seconds to several minutes. Q: Why is the noise source left on when not used during calibration? A: It was determined during development of the noise figure application that noise figure measurement results were more repeatable if the noise source was left on when not in use, to stabilize its temperature.
Its temperature can also be determined using some type of external thermometer. What power level should I use during the power-sensor portion of the calibration? It is best to use as close to 0 dBm as possible, as this is the level used to calibrate most power sensors.
The power used during this step is independent from the power used for the S-parameter portion of the calibration, which is determined from the channel-power value entered prior to starting the calibration. When the noise receiver is calibrated with a power sensor, the source attenuator is automatically set to whatever value is needed to provide the specified power during the power-sensor step.
In most cases, this will be 0 dB of source attenuation. In this case, set the power as high as possible without causing the source to unlevel, and make sure the power setting is at least 6 dB above the noise floor of the power sensor a wide-dynamic-range, diode-based power sensor is helpful in this situation. Is it necessary to use noise averaging during calibration? It is not required, but it is a good idea to use noise averaging during the calibration to produce a clean calibration.
Noise that is present in the calibration cannot be removed in subsequent measurements. When using the low-noise receiver, a noise-average value of 10 or more is recommended during calibration. For the measurement, this value can be lowered if faster measurements are desired, at the expense of more trace noise and less accuracy. When using a standard receiver, or more noise averages are needed. Note that noise averaging only affects the noise power measurements.
During calibration, channel averaging affects S-parameter measurements only. In this way, the amount of averaging used for noise-power measurements and S-parameter measurements can be individually optimized. To avoid compressing my high-gain amplifier, I set the input power very low, but this makes for noisy calibration and measurements.
Are there ways to overcome this? Yes, there are several things you can do. Cal All is a good calibration choice as the setup used during the calibration can be optimized independently from the measurement setup, so higher powers can be used. Channel averaging can also be used to lower S-parameter trace noise which in turns lowers the jitter on the noise figure trace. When doing an on-wafer TRL cal, why do I get an error that states that there are not enough standards for the cal?
This appears because at least five impedance states must be presented to the noise receiver to determine its noise parameters, requiring more standards to be defined than normal for a typical TRL impedance-standard-substrate ISS cal kit this problem also occurs with coaxial TRL cal kits.
To correct this situation, you must define additional standards using the Modify Cal Kit feature see the Help file for more detail on how to do this. The extra impedance standards can be created by reusing the through and line standards or multiple line standards as reflection standards. This is done by probing one end of the transmission line and leaving the other end open, thereby creating a pair of offset opens.
However, extra on-wafer impedance standards are not required when you use an ECal module to perform de-embedding of a noise-source adapter on port two. In this case, the ECal module is used to present five different impedance states to the noise receiver. Can the ECal module that is used as an impedance tuner also be used to perform the 2-port calibration?
A separate ECal module or mechanical cal kit must be used for the S-parameter portion of the calibration process. Which ECal modules are supported with the noise figure option?
Any ECal can be used for the S-parameter portion of the calibration. For use as an impedance tuner, only the N Series of two-port ECal modules are supported.
Which noise source do you recommend? The B is also a good choice for coverage up to 18 GHz. For measurements in the 1 to 50 GHz range, we recommend the C-K As an alternative to a noise source, a power sensor can be used for the noise-receiver calibration. Can the A noise source be used? When using a A, a lot more noise averaging should be used during calibration to help overcome the lower ENR. During calibration, is the match of the noise source measured in its hot and cold state?
This value helps get a more accurate measurement of noise power. During calibration, all three gain stages 0, 15, 30 dB are measured, so they can be changed after the calibration according to the gain and noise figure of the DUT. After calibration, can I change the noise bandwidth setting without having to re-calibrate? The user interface allows you to do this, but it is not recommended. Changing the noise bandwidth changes the gain-bandwidth product of the noise receiver slightly, causing measurement error.
It is recommended to use the same noise bandwidth for calibration and measurements. Can I view the error terms from a noise figure calibration in the Cal Set Viewer, including the gamma values of the impedance tuner?
Can I calibrate my system if the noise source or power sensor does not mate directly to the test port cable? The calibration can remove the effect of an adapter used to connect a noise source or power meter during calibration.
An extra 1-port calibration is required at the point where the noise source or power sensor is connected in order to align the noise cal plane with the 2-port cal plane. This feature is also very useful when using a noise source in 50 GHz on-wafer test systems, as the noise source can be connected directly to test port two with a short adapter, eliminating the adverse effect that cable loss would have on the receiver characterization.
There are two approaches. One approach is to perform the noise calibration entirely with coaxial calibration standards and deembed the wafer probes.
The calibration routine adds an extra 1-port calibration so that the noise-calibration plane can be extended to the on-wafer calibration plane. The calibration routine handles the cases when an adapter is needed to connect the noise source or power sensor and it is left in place for the on-wafer cal, or the adapter is removed after the 1-port cal, in order to connect the wafer probes to the test system.
When measuring devices with two female connectors, I use an ECal module for the 2-port cal. However, when I try to do the 1-port cal on the adapter used to connect the noise source or power sensor to the test system, my ECal does not show up as a cal kit choice.
Why not? Only ECals with at least one connector that will mate to the adapter will show up. If you are using a female-female ECal module, you cannot use it to perform a 1-port cal on an adapter with a female connector.
Instead, you need an ECal with at least one male connector. The most flexible ECal module is one with both male and female connectors, which will handle all different combinations of DUT-connector gender. When using a male-female ECal for female-female devices, the calibration routine is broken into three steps instead of one. Step one uses the female connector of the ECal for port one, step two uses the female connector for port two, and step three requires an external through adapter.
When two ECal modules are present during calibration one as the tuner, one for calibration , the one that is used for the 2-port calibration portion is also used to present a set of variable source impedances to the noise receivers to characterize their noise parameters. This is done because this ECal is closest to the noise receivers, and therefore provides a wider range of impedance values due to lower loss.
This means that the ECal that will be used as an impedance tuner during measurements is not used as an impedance tuner during calibration if a second ECal module is available. When only the tuner ECal module is present during calibration, then it will be used in combination with the mechanical standards used during the 2-port calibration to provide the variable source impedances needed for a noise-parameter characterization.
Is there a way to verify the absolute accuracy of a noise-figure measurement, using some type of verification kit? At this time, there are not any commercial, off-the-shelf noise-verification kits. However, Keysight and NIST have published a paper showing how a mismatch transmission line Beatty standard and an amplifier can be used as a verification standard. Walker, and Roger D. A more practical alternative to verify a noise figure calibration is to verify the two parts of the calibration independently.
The S-parameter portion can be verified with a normal Keysight VNA verification kit or more simply, by measuring a through and a high-reflect standard like a short or open. The noise receiver calibration can be verified by measuring the ENR of a trusted noise source that was not used for the noise-receiver characterization. Keysight also has a PNA-X noise figure uncertainty calculator, which can be used to calculate the accuracy of noise figure measurements.
Is measuring a through connection or an attenuator a good way to verify noise figure accuracy? No, these are poor verification devices for two reasons. Firstly, neither a through nor an attenuator produce excess noise, as would a device with gain. This means that the noise power measured with the through or attenuator is the same amount of noise power measured during the calibration process.
When two sets of small and noisy data are subtracted, the result shows high levels of noise variation. This can be observed when measuring a through connection — while the trace is centered around 0 dB as expected, the trace shows large peak-to-peak variation of more than a couple of dB.
See the previous question for better ways to verify noise figure accuracy. It is available at www. It is limited to amplifier measurements using the low-noise receiver provided with Option Both vector and scalar noise calibrations are supported, as well as characterization of the noise receiver using a noise source or power meter.
Do all PNA-X models offer a low-noise-receiver option? Option adds an internal low-noise receiver at port two.
For B-models, the application must be purchased separately as SB. SB can be used without Option , but then only the standard S-parameter receivers are available for noise figure measurements. How do I measure noise figure above 67 GHz? For measuring down converters where the output is below 50 GHz, no external hardware is needed.
For this case, the system can be configured with one millimeter-wave extender connected to the input of the DUT, while the output of the DUT can be connected directly to port 2 of the PNA-X if using the low-noise receiver , or another port if there is enough excess noise to use a standard S-parameter receiver. The downconverter is bypassed for the gain or conversion-gain measurement, and then switched in to measure the down-converted noise on one of the native PNA-X test ports.
The block downconverter must be provided by the user, or from a third-party supplier such as Challenge RF. While the internal noise figure is quite good, the loss of the internal test-set components cables, switches, couplers, etc.
Guaranteed specifications for the noise figure of the noise receiver can be found in the instrument data sheets. Which ports are available for noise figure measurements? When using the low-noise receiver of Option on an A-model PNA-X, measurements must be made between ports one and two. This was done originally because the tuner or tuner switch is only at port one, and the low-noise receiver is only at port two.
When using vector noise calibration with source port three or four, the user must make sure the ECAl impedance tuner is configured correctly. When making noise figure measurements using a standard S-parameter receiver as the noise receiver, then any combination of available test ports can be used as the source and receiver see section Using S-parameter receivers.
Yes, with some caveats. For applications like noise figure, the port selection is referenced to the PNA-X itself, so the user may not specify a noise figure measurement directly between ports of the test set. The different path settings of the multiport test set must be set with SCPI commands unique to the test set. This can be accomplished with an external program, or by including the path commands in the Interface Control dialog.
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