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16 www.rfdesign.com January 2003

A common issue that often arises is, afterthe design and build of a receiver, it is

determined that the sensitivity is worse than ofthe calculated model. A significant amount oftime can be spent determining the exact prob-lem and why the cascaded noise figure equa-tions did not accurately represent the predictedsensitivity.

The solution usually involves issuing newcomponent requirements (lower LNA noise fig-ure or more gain) and/or changing the front-end

architecture (removing loss in the front-end).Noise figure is a critical parameter when

designing receivers. In critical situations a frac-

tion of a dB can make a huge difference in thelink budget and can play a big part in winningor losing contracts. Many times decreasing thenoise figure of a receiver may be much cheaperthan increasing the power of the transmitter.Predicting accurate noise figure then becomesof paramount importance.

Receiver Sensitivity DefinedThe sensitivity of a receiver is equivalent to

the thermal noise at the input plus the noisefigure and minimum acceptable signal-to-noiseratio (see figure 1 — the vertical axis isdBm/Hz). The receiver designer typically onlyhas control over the noise figure since thereceiver operating temperature determines thethermal noise and the type of modulation usual-ly determines the minimum acceptable signal-to-noise ratio.

The cascaded noise figure is defined by thefollowing equation:

Where the power gains and noise factors arethe linear, and not the logarithmic, quantities.

Note that the cascaded noise figure is solelybased on the individual noise figure and gain ofeach stage. The cascaded noise figure equationswork well until the mixer enters the equation.Mixers equally convert the in-channel noise aswell as the image noise into the mixer output.It is often assumed that the image noise isaccounted for in the cascaded noise figure equa-tion — it isn’t.

The cascaded noise figure equations assumethat noise contribution due to the image is zero.In many cases, in receiver design, this can be adangerous assumption that will only lead to a newdesign pass or failing sensitivity requirements.

When software design tools or spreadsheetsdo not account for image noise power across thechannel bandwidth, then simulation resultsonly show best-case noise figure instead of theworst case scenario. Worst-case noise figure ismuch more important than best-case noise fig-ure since typical receiver requirements guaran-tee sensitivity better than a specified level.Worst-case noise figure is necessary in deter-mining worst-case sensitivity. As a matter offact, if there is no image noise rejection at all,the true cascaded noise figure will be 3 dB high-er than indicated through the cascaded noisefigure equations. This would mean double thetransmitter output power to compensate forthis simple oversight.

Image and Noise Rejection IssuesImage signal rejection and image noise rejec-

tion can mean two different things. For exam-

F FF

GFG G

FG G G

cascade

n

n

= + − + − + + −−

1

2

1

3

1 2 1 2

1 1 11

......

Figure 1. Noise and receiver sensitivity

Relating CascadedNoise Figures to Real-

world PerformanceWhen the device’s performance

fails to meet specification, itisn’t always the components.

Sometimes it’s the math

By Rulon VanDyke

time & frequency

20 www.rfdesign.com January 2003

ple, a typical receiver may start outwith a front-end receiver band filterfollowed by an low-noise amplifier(LNA) and then a mixer (see figure2). The front-end filter would proba-bly be designed to adequately handle

input image signal rejection. Typical LNAs may have very high

gain to set the noise figure for the rest

of the receiver. Unfortunately, theseLNAs will also create broadband noisewhich will appear at the image fre-quency and this noise power will bedirectly converted into the IF band.This has the effect of reducing the

overall receiver sensitivity. To correctthis problem a filter must be placed atthe LNA’s output to reject the image

noise. This is ac r i t i c a l i s s u et h a t i s o f t e noverlooked andpresents signifi-cant problems ifnot addressedearly on.

A n o b v i o u ssolution to thisproblem is toaccount for theimage noise atthe beginning ofthe design cycle.This is mucheasier said thandone since thisr e q u i r e s t h edesigner to knowthe frequencycharacteristicsof al l devicespreceding the

mixer(s). Furthermore, it would berequired to integrate the image noiseacross the channel bandwidth at theimage frequency.

The time required to accuratelyaccount for these complications typi-cally prevent the designer from incor-porating them into their calculations— especially in today’s world wheredesign intervals are shrinking.Likewise, examining true noise fig-ure across receiver in-band frequen-cies is typically not incorporated intocalculations for the same reasons.This approach lends itself to the“wait-and-see” what the actual sensi-tivity is in the lab.

This “wait-and-see” approach canbe avoided by using software toolsdesigned to automatically account forthese complications. There are anumber o software tools that can beused for this. Some of these tools arespecifically designed to verify RF per-formance and optimize RF architec-tures, solving problems like imagenoise, gain line-ups affected by volt-age standing-wave ratio (VSWR),sneak paths, etc.

A Simple ModelReference the example of a basic

receiver front end consisting of areceive filter, LNA, and mixer andan IF chain consisting of a IF filterand amplifier (see figure 2). Thereceiver filter has a nominal inser-tion loss of 1 dB; the LNA has a noisefigure of 2.5 dB with a gain of 30 dB.We will place a disabled image noiserejection filter (to be used later)between the LNA and mixer that hasan ideal insertion loss of 0 dB.

The mixer is a passive mixer witha conversion loss of 8.0 dB. The IFfilter is centered at 140 MHz and hasan insertion loss of 5 dB. The IFamplifier has a gain of 20 dB and a 4dB noise figure.

Cascaded noise figure calculationsshow that the noise figure for thisreceive system is 3.62 dB. However,after examining this lineup andaccounting for image noise in usingthe software, it is see that the actualnoise figure is 5.18 dB. This is over1.5 dB above the predicted value. Thetable in figure 3 shows the Nodesequence along with measurements ofchannel frequency (CF), channelpower (CP), channel noise power(CNP), cascaded noise figure (CNF),

Figure 2. A typical receiver front-end with no image noise rejection after the LNA

Figure 3 - Channel noise and image channel power without an image noise filter

Figure 4. The cascaded noise figure of the image noise versus the cascadednoise figure equations

22 www.rfdesign.com January 2003

image frequency (IMGF), and imagechannel power (IMGP) along theinput to output path. The channelbandwidth used for these measure-ments is 1 Hz, since continuous wave(CW) signals are used in this example.

The true cascaded noise figure andthe predicted noise figure is also

shown on the level diagram in figure4. Image noise can easily be detectedon a level diagram since the noise fig-ure will jump up at the mixer output.

Next, integrating the simple 1st

order bandpass filter (image noiserejection filter) after the LNA willprovide about 20 dB of rejection at

the image frequency of 1860 MHz(see figure 5). After re-running thesimulation a noise figure of 3.66 dB,which is 0.04 dB higher than thecascaded noise figure equations pre-dict, is achieved. This is becausethere is sti l l a small amount ofimage noise contribution and theVSWR effects of the filters have alsobeen accounted for.

Figure 6 shows a table of theresults of the lineup with imagenoise rejection fi lter enabled.Comparing CNP and IMGP measure-ments, the designer can quickly seethe amount of image noise rejectionneeded to minimize the impact ofimage noise. This can be seen bycomparing the results shown in fig-ure 3 with those of figure 6.

Since the software used for thisparticular scenario is a channel-based tool that integrates powerspectral density over a channel band-width, measurements show powerwithin a channel along a user-defined path. The CNP measurementintegrates the absolute power of allof the noise within the channel band-width at the channel frequency. TheIMGP measurement integrates theabsolute power of all of the energywithin the channel bandwidth at theimage frequency.

Obviously, the IMGF will becomethe CF at the output of the mixer.Such image measurements help theRF designer determine the amount ofimage rejection needed in the designeliminating the guesswork and “wait-and-see” sensitivity approach.

ConclusionThe spectral domain engine used

in this scenario in gives RF designersthe ability to view, analyze, and opti-mize designs in a manner to optimizetime and resources. Modern softwarenow includes compensation for tradi-tionally troublesome anomalies thatoften don’t show up until the receivehad been built and tested.

With such tools, broadband noise,for example, can automatically befolded into the output of the mixer.Such cascaded NF measurementswill automatically take into consider-ation this folded noise (such as imagenoise). Furthermore, the cascadednoise figure measurement can easilybe swept over frequency and theresults displayed on a level diagram

Figure 6. Channel noise and image channel power with an image noise filter

Figure 7. The cascaded noise figure versus frequency

Figure 5. A typical receiver front-end with image noise rejection after the LNA

24 www.rfdesign.com January 2003

or in a table (see figure 7) for a fre-quency channel sweep on a level dia-gram and figure 8 for a receiverfront-end Monte Carlo analysis.

Furthermore, impedance mis-matches are automatically accountedgiving the RF designer a completepicture of the design before commit-ting to layout. Design trade-offs andexact performance requirements canbe determined and optimized for eachstage and different RF architecturescan be compared. This eliminates theover simplification typically createdin other RF design tools, spread-sheets, and math packages. The“wait-and-see” approach to receiversensitivity can be eliminated.

Figure 8. A Monte Carlo analysis of the receiver

RF Design www.rfdesign.com 25

About the authorRulon VanDyke is the lead engineer in systems simulation at Eagleware Corp.

(www.eagleware.com). He received both a BS degree and MS degree in electricalengineering from Brigham Young University in 1990. For 10 years, he designedfirst-, second-, and third-generation digital cellular transceivers and base stationsfor AT&T Bell Labs and Lucent Technologies. In 2001, he joined Eagleware todevelop Spectrasys, which is the software used in this article. He may be reachedat rulon@eagleware.com, or at (678) 291-0995 — voice or (678) 291-0971 — fax.

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