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Z10040B Norton Noiseless Feedback Amplifier

Revision History
Created 19 October 2008
03 May 2009 Extensively revised to reflect the Z10040A kit
04 May 2009 Updated manual and added performance discussion and jump table
08 May 2009 Updated manual
10 May 2009 Revised 2nd Harmonic intercept number
11 May 2009 Added indoor enclosure information and link to IP2 measurement protocol page
14 May 2009 Added link to IP3 measurement protocol page
18 May 2009 Revised IP2, IP3 and Noise Figure specifications based on recent measurements
07 June 2009 Replaced Z10040A with Z10040B
09 June 2009 Added Noise Figure data and specification; updated Z10040B manual
14 June 2009 Updated Z10040B manual for changes for improved stability; added noise figure versus supply voltage data
26 June 2009 Added sample Z10040B bias adjustment and performance report document; added second builder comments
29 August Revision 02 printed circuit board is the current release. Instruction manual updated.
20 October 2009. Clarified pricing for enclosures.
23 November 2009. Added comments for high gain (transformer 1:29:6 turns ratio) option.
05 December 2009. Added reference to Z1203A for remote power provision
21 January 2010. Added reference to Service Bulletin No. 1.
27 January 2010. Manual updated. Current version is now 1.5. Links should return this edition.
31 January 2010. Replaced photos of Z10040 enclosure with ones reflecting current packaging.
15 March 2010. Updated manual. Current version is 1.6. Links should return this edition.
03 May 2010. Manual version 1.7 applies to Z10040B PCB revision 3. Earlier manuals are for revision 1 and 2 boards.
01 June 2010. Added reference to Z10080A bypass relay kit.
29 August 2010. Added reference to surface mount Norton amplifier kit, the Z10042A
05 September 2010. My practice has been to adjust assembled Z10040B amplifiers for optimum OIP2 performance as part of the assembly service, although no measurement data is provided to the purchaser unless the optional performance measurement package is purchased. I've now revised the price section to reflect this practice.

Table of Contents—Click  to jump on this page
Bypass_Relay_Option
Specifications_Summary
Price_and_Options
How_to_Order
Whats_all_this_IP3_stuff_anyway
Typical_Performance_Plots

 

Note: As of 07 June 2009, the Z10040A is replaced by the Z10040B. The "B" version has the same performance specifications as the "A" but has several improvements. There is no price change in the "B" version.

Note: The Z10040B will continue to be available. However, a new surface mount Norton amplifier is now available, the Z10042A. Click here for the Z10042A page.

The main changes to the "B" version are:

  • Balanced or unbalanced input based on connector pins used
  • All resistors are now 1% metal film instead of 5% carbon film
  • Two color magnet wire (red and green) are supplied for the bifilar windings of T1 and T3
  • Small changes to silk screening to improve legibility
  • Improved the pad spacing for shielded inductors L1-L4

The Z10040B is a kit (also available assembled and tested) implementing the Norton noiseless feedback amplifier, as originally developed by Dr. David Norton, and described at D. Norton and A. Podell, “Transistor Amplifier with Impedance Matching Transformer,” U.S. Patent 3,891,934, June 1975. (This patent is expired.)

In developing the Z10040B, I've been guided by Dallas Lankford's implementation of the Norton amplifier in his Internet article Common Base Transformer Feedback Norton Amplifiers.

I should mention the Norton amplifier covered in this page is not the "current difference" Norton amplifier such as in National Semiconductor's LM3900. Rather, this Norton amplifier is intended for RF amplification, and is a grounded base design with transformer feedback. The result is a very low noise, broadband amplifier

The photo below shows an assembled Z10040B Norton amplifier.
 

 
The complete Z10040B Assembly and Operating manual may be downloaded (PDF) by clicking here or from my Documents page.  [If you wish to view the Z10040A manual instead, click here or go to my Documents page. Also, the Z10040B manual for printed circuit board revisions 1 and 2 may be downloaded from the Documents page.]

The Z10040B modifies Dr. Lankford’s design in several useful respects:

  • Automatic input disconnect upon DC power removal along with over-voltage gas trap protection.

  •  Improved performance below 500 KHz (typical -3 dB frequency is 65 KHz).

  • Over voltage and reverse voltage protection on the DC Power circuit.

  • DC power either separately or duplex power.

  • Balanced or unbalanced input via input jumper settings

Clifton Laboratories also offers the Z1202A DC power injector usable with the Z10040B to provide DC power over the coaxial cable.

These features increase the Z10040B's survivability and utility compared with an amplifier without these features. Duplex power avoids the need to run a separate DC power line to a remote amplifier.

Bypass Relay Option
The Z10040B, when power is removed, reverts to "safe" mode with the input grounded. Some purchasers have asked for a different behavior, i.e., when power is removed, the Z10040B will be bypassed, with the input connected to the output. The Z10080A bypass relay kit can be added to a Z10040B to provide bypass on power removed operation.

Specifications Summary
The following specifications are extracted from the Assembly and Operating manual. I'm still working on measuring a few of the parameters and in some cases, the Norton amplifier is so good that the normal techniques and equipment I use are not adequate to measure the performance. The performance values are for an amplifier with bias adjusted for maximum IP2 performance.

 

Parameter

Value

PCB Dimensions

3.00” x 3.50” x 0.75” vertical clearance required. (76.2mm x 88.9mm x 19mm). Four mounting holes for 4-40 screws provided, template in Appendix B.

DC Power Required

Maximum:  15V

Minimum: 13.8V

Negative to ground, typical DC current 80-100 mA depending on bias adjustment.

Maximum RF Power Input

Do not exceed 100 milliwatts (+20 dBm). IP3 performance specifications are based upon -10 dBm signal input; performance not warranted at greater input levels.

Test Conditions

Performance data is for a 1:11:4 turns ratio design, 13.8 VDC after adjusting balance trimpots for minimum 2nd harmonic distortion. Unless otherwise indicated, performance measurements are made with direct DC power, not duplexed. Figures stated as “typical” are not warranted.
 

3 dB Bandwidth

100 KHz – 30 MHz. Typical bandwidth 75 KHz - 45 MHz

3rd Order Intermodulation Intercept

+50 dBm. Measured at 12 MHz, input signal level -10 dBm. Protocol as discussed below.

2nd Harmonic intercept

+90 dBm. Measured at 5.35 MHz, input signal level -3 dBm. Protocol as discussed below.

Gain

11 dB nominal at 1 MHz.

1 dB Gain Compression

+19.5 dBm input.

Noise Figure

3.5 dB maximum 10-30 MHz. Typically less than 3 dB 10-30 MHz.

Input VSWR

When terminated with 50 ohm load, input VSWR is less than 2:1 over the range 300 KHz – 30 MHz, and is typically below 1.5:1 over this range.

Common Mode Rejection in balanced input mode Typically 50 dB at 1 MHz, decreases with increasing frequency.
 
What do all these numbers mean? Not everyone may be familiar with amplifier specifications. I've added a (I hope) simple guide to reading an amplifier specification sheet. The guide is later on this page—click here to read it.

Because the Norton amplifier's IP2 performance is of great interest, I've added a page describing how I measure IP2. I measured one Z10040A at IP2 = 98.5 dBm and a second Z10040A within a dB or two of this figure. Click Measuring IP2 for my IP2  test procedure.

I've prepared a similar page showing how I measure IP3 for the Z10040 Norton amplifier. Click Measuring IP3 for the details.

Both kits and assembled amplifiers use matched 2N5109 transistors. I measure the DC current gain of all 2N5109 transistors in my stock and match pairs within ±5%. I've added a page showing how DC matching affects the transistor's parameters as seen on a curve tracer. 2N5109 Matching I've intentionally built a prototype with large mis-matched pairs, and the effect upon the amplifier's measured performance parameters are not all that significant. Still, using matched 2N5109's provides an additional measure of assurance that the amplifier will work as expected when built.

The Z10040B's standard configuration is for 11 dB (nominal) gain, with a transformer winding ratio of 1:11:4. It's possible to increase the  gain to 15.6 dB (nominal, 14.6 dB typical measured) if the transformers are built with 1:29:6 ratios. I've added a new Appendix F to the Z10040B manual with  measured performance data for a 1:29:6 version. Click here to read the manual—it's a 4.5 Mb PDF file—and go to Appendix F.

As of 21 January 2010, I've added Service Bulletin No. 1 for the Z10040B covering potential instability where 2N5109s with unusually high UHF gain are used. This modification should not be necessary for any Z10040 amplifiers built or received as it is something I identified while building an amplifier with a new lot of 2N5109 transistors of exceptionally high UHF gain and all kits or assembled amplifiers using 2N5109s from this batch have the modification. However, it is possible that a Z10040 may require replacement transistors due to component failure in the future, so I have documented the fix in this service bulletin. All new kits and assembled units will include the modification as a preventative measure. Any Z10040A or B owners wish to make the modification should send an E-mail to me and I will provide the two 10pF disc ceramic capacitors. I will also update the Z10040B's Assembly Manual to reflect this change within the next few days.

 

Price and Options
 
Item Price Comment
Z10040B kit $47.50 Kit includes the printed circuit board and all parts necessary to assemble the board. Enclosure is not provided.
Z10040B assembled and tested $72.50 Bare printed circuit board, assembled and tested. Performance documentation is not included. Bias is adjusted for best OIP2, but performance documentation is not provided.  No enclosure is provided.
Bias adjustment and performance documentation

[click here to view a sample report]
$25.00 Bias adjusted for minimum IP2/IP3 (some interaction between the two is usually seen and it is not generally possible to minimize both IP2 and IP3 at the same bias setting.) IP2 and IP3 performance data and frequency  response data are provided to the purchaser. This service is available for either customer-built kits or as an option for assembled and tested units. Customer is also responsible for return shipping charges.
Indoor enclosure kit $27.50 (BNC)
$30.00 (UHF)
$35.00 (N)
Die cast enclosure with BNC, UHF or Type N connectors. Kit price includes the die cast enclosure, with all holes drilled, your choice of BNC, UHF or N connectors, power connector, Teflon coaxial cable for jumpers, four 4-40 x 0.5 inch standoffs and associated hardware and a DC power cord.
Indoor enclosure assembled $32.50 (BNC)
$35.00 (UHF)
$40.00 (N)
Assembled enclosure (connectors and stand-offs are mounted and pre-wired) with BNC, UHF or N connectors. Does not include assembly of Z10040B amplifier.
Outdoor weatherproof enclosure kit Contact Clifton Laboratories Weatherproof die cast enclosure with BNC, UHF or Type N connectors. Custom designs are also available.
Outdoor weatherproof enclosure assembled Contact Clifton Laboratories  
Z1203A DC power coupler See Z1203A page For operating the Z10040B with duplex power--DC power supplied over the coaxial cable along with the signal. If the Z1203A is ordered at the same time as a Z10040B, one shipping charge applies.
Shipping and packing $7.50 For US domestic customers. Shipping is via Priority Mail. International customers please contact Clifton Laboratories for a specific quotation.
Virginia Sales Tax 5% If the Z10040A is shipped to a location within the Commonwealth of Virginia, 5% sales  tax applies.

The photos below show Z10040B amplifiers installed in the optional indoor die-cast enclosure with BNC and UHF connectors and 5.5/2.1 mm DC power connector.
 
   
 
   
 

How to Order
 

Payment may be made with a check or money order payable to Clifton Laboratories at the address on the top of this page, or via PayPal to orders@cliftonlaboratories.com.

Please do not forget to include shipping and, for delivery within the Commonwealth of Virginia, sales tax.

Orders are normally acknowledged within 24 hours of receipt. Please contact me if you fail to receive an acknowledgement.
 

Is the Z10040B a difficult kit to assemble? I don't think so, but you should read the assembly manual and decide whether you can build it. Based on building several Z10040A boards, you should allow about 1.5 to 2 hours to assemble the kit up to the point of winding the transformers and completing the kit. Another 1.0 to 1.25 hours should be allowed  to wind the four transformers. Thus, the total time is in the range of 2.5 to 3.25 hours. The most difficult part of the build is winding the four transformers. I've done my best to explain how to wind these transformers in the assembly manual.

As an independent view of how long it takes to assemble a Z10040 and how difficult it is, a Z10040A purchaser recently noted:

It took me about 5 and half hours, but I wasn't rushing and like to measure every part before I add it to the board. It's a very nice kit and works well with my 2N5109 antenna described in the yahoo group. If someone has experience building a kit with coils, it's just beyond beginner, but certainly easier than average. I'm building a TAPR TADD-2 this weekend, so the Z10040 seems really easy by comparison!

There's no significant difference in assembly time or difficulty between the "A" and "B" versions.

Another builder reports:

I just finished the 2 preamps. I did not hurry, so it took 2 hours for the first, and 1.5 for the second. The documentation and the PCB quality are excellent! Congratulations for that, you did a superb job. I don't think you get any problems, even when you are not experienced. The transformers need a while, but it is not really difficult. Using magnetic wire that can be soldered (isolation burns off) would make things a bit easier/quicker.

After this builder's kit was shipped, I switched to a different wire source. All kits are now shipped with solderable magnet wire.

Of course, the Z10040B is also available assembled and with optional performance measurement data. (A sample performance report can be view by clicking here.)

 

What's all this IP3 stuff anyway?

With apologies to Bob Pease of National Semiconductor fame, I've borrowed his "what's this ... stuff anyway" title phrase for this section.

When considering purchasing a preamplifier, several performance parameters are useful in assessing differences amongst prospective amplifier candidates and in deciding which best meets your requirements.

I've tried to keep the discussion at a general, introductory level and I hope those readers familiar with this topic will excuse the simplified treatment. The discussion also assumes operation at 30 MHz or below, where atmospheric noise is almost always the limiting factor in usable sensitivity.

 

Gain

Gain is pretty simple, isn't it? The more gain, the better as it will boost weak signals more than a lower gain amplifier. There's some truth in this statement, but not much. In fact, too much gain can create worse problems than too little gain. And, gain can't be considered in isolation; your antenna system, receiver and "radio environment" must also be  considered.

First, all amplifiers and all receivers, are imperfect devices and hence create noise and "phantom" signals, to some degree or other. Of course, some equipment is more susceptible to these problems than others, but none are completely free from phantom signals under all conditions.

I'll use the term "phantom signal" to mean a signal that is created in the receiver or amplifier or elsewhere in your radio gear. (We'll look at these phantom signals in more detail when consider IP2 and IP3.) A phantom signal may seem real in that you can hear it, and tune through it just like a real signal, but in fact it's not really being radiated on the frequency your receiver is tuned to. (In fact phantom signals can be created in nearby objects and radiated into your receiving system, but since this discussion concerns receivers and preamplifiers, we'll leave this specialized class of "radiated phantom signals" for another time and place.)

A very important determinant of the degree to which your system produces phantom signals is the overall signal input level. All else being equal, the stronger the input signal (whether to a preamplifier such as the Z10040B) or to your receiver, the greater the number and strength of phantom signals. Your receiver may have very good frequency selective filtering to reduce phantom signals, but if the preamplifier you add itself generates the problem, all the filtering in the world between the preamplifier and your receiver won't address the problem. Or, if the preamplifier is relatively flawless, it may well be  that the increased signal level your receiver sees causes it to generate phantom signals.

All these words are a roundabout way of saying that if your receiver needs additional gain provided by a preamplifier, the added  gain should be kept to the minimum necessary level. This is absolutely a case where "more is not always better."

Unfortunately, I can't provide an easy way to determine how much gain is sufficient and how much is excessive in every particular situation. But, in general, a preamplifier is used for three reasons:

  • To overcome coaxial cable or other transmission and ancillary device (such as filter) loss. In this case, the preamplifier gain should be sufficient to cancel the loss and perhaps provide a dB or two reserve margin above the loss. Typically the total gain one needs for this purpose will be a few dB  total, perhaps 6 dB or so at the most under usual conditions.
     
  • To help a receiver with inadequate overall gain work with a normal antenna system. First, it's not a good idea to use a preamplifier to "fix" a defective receiver. Rather, first repair the receiver and see if a preamplifier is really necessary. If it is, then the preamplifier should provide sufficient gain so that when the antenna is connected atmospheric can be heard in the absence of a signal. A preamplifier with gain much beyond the level necessary to detect atmospheric noise is not useful.
     
  • To make a correctly functioning, sensitive, receiver work with a highly inefficient antenna. First, one should consider whether a more efficient antenna system can be constructed. Assuming  this is not the case, such as for certain specialized antenna systems, such as the Beverage, or Dr. Lankford's various anti-noise antennas, then sufficient preamplifier gain will be necessary to detect atmospheric noise. Dr. Lankford's 15 foot anti-noise antenna, for example, is commonly used with a Norton amplifier configured for 12 dB nominal gain, although other amplifiers with similar gain may be used, of course. Beverage antennas may require slightly more gain, 15 dB or so, that might be obtained from a Norton amplifier such as the Z10040B with a 1:19:5 winding ratio. (See the Z10040B manual for the relationship between gain and transformer turns.) In some extreme cases, 20 or 30 dB gain may be required, such as a very short antenna. (Short in terms of wavelength, of course.)

Before adding high gain amplifiers (or even worse, cascaded high  gain amplifiers), however, one should consider whether a more efficient approach is possible. For example, extracting a usable signal from an electrically short antenna may be better accomplished with a high impedance source follower circuit than a 30 dB  gain 50 ohm input impedance amplifier. This is, after all, how a voltage probe active antenna works. Or, a passive matching network may be in order.

Bandwidth

Practical preamplifiers have a finite bandwidth. Often greater bandwidth comes with higher prices and, frequently, lower performance characteristics. If your interest is in medium wave broadcast DX'ing, then a preamplifier with a 1 MHz lower cutoff won't meet your needs.

Amplifier gain is normally stated as the "-3 dB" point. 3 dB is half-power or 70.7% of voltage. An amplifier with 12 dB gain in mid-band, will still have 9 dB gain at the -3 db point. Depending on the amplifier design, for frequencies above and below the 3 dB points, gain may drop quickly with frequency or slowly with frequency. A good amplifier supplier will provide typical gain versus frequency data. You can then use the gain versus frequency data to judge whether the amplifier provides useful gain at the frequency of interest, with "useful" gain being based on the considerations discussed under "gain" above. If the amplifier is purchased as a kit, such as the Z10040B, it may be possible to make small component changes to shift the frequency response up or down. For special low frequency extension (below 100 KHz) of the Z10040B, please contact Clifton Laboratories.

 

1 dB Compression Point

An amplifier's gain is a function of the input signal level. At some input level, an amplifier becomes saturated and can no longer increase its output power in response to an increase in input power.

The normal parameter used to quantify this effect is the "1 dB compression point." The 1 dB compression point is determined by calculating  the amplifier's gain (output power divided by input power, or, in terms of dB, output power (dBm) minus input power (dBm)) as the amplifier's input signal level increases. At some input signal level, the amplifier can no longer perfectly increase its output power for a change in input and the amplifier gain decreases. At the 1 dB compression point, the amplifier's gain drops 1 dB below the gain when the input signal level is safely below saturation.

The figure below, taken for the first "production" Z10040A amplifier, shows the data necessary to compute the 1 dB compression point. The vertical axis is amplifier gain, with each division equal to 0.2 dB. The top of the graticule line is 11.13 dB. (I picked this odd value to make the peak gain align with the 2nd graticule line.) The "B" amplifier's performance is identical.

The horizontal scale is amplifier drive in dBm. The left edge is +15 dBm and the right edge is +20 dBm, with each horizontal division  representing 0.5 dBm.

 

Looking at the plot, we see that for input signal levels between +15 and +17.5 dBm, the gain is essentially constant. At the 5th graticule line (corresponding to +17.5 dBm input to the Z10040A), however, we see the gain begin to drop. The blue arrow shows when the Z10040A's  gain drops 1.0 dB (5 divisions) from the peak linear value. The corresponding input signal level is +19.45 dBm. The gain at this point is 9.98 dB, so the Z10040A's output power at the 1 dB compression point is +19.45 dBm +9.98 dB = +29.43 dBm. This is not far below 1 watt output power.

Why is the 1 dB compression point of interest and what does this value mean? As an amplifier becomes non-linear, its distortion increases and thus its propensity to produce phantom signals. All else being equal, the higher the 1 dB gain reduction value, the less likely the amplifier is to produce phantom signals of significance.

The 1 dB compression point performance of a particular amplifier should not be considered in isolation. For example, if your antenna is located in an area of very strong AM broadcast signals an amplifier with a high 1 dB compression value will be of more value than if you are far from strong signal sources.

A word on dBm may also be useful. Most of us are familiar with the term decibel, or dB, as a relationship between two power levels P1 and P2: dB = 10*Log10(P1/P2). The inverse relationship, given dB with the desired result being the power ratio (PR) is PR= 10(dB/10).

The  term dBm is an absolute power level, with the reference power being 1 milliwatt, or 0.001 watts. Hence, a signal of 0 dBm has 1 milliwatt power, a signal of 29.43 dBm has 10(29.43/10)  power, or 877 milliwatts or 0.877 watts.

One more thing to watch for. Normally the 1 dB compression figure is quoted with respect to the input signal level. If quoted with respect to the output signal level, it will be inflated by the amplifier's gain.

 

Noise Figure

All amplifiers create noise, some more than others. Consider an noisy signal consisting of  -100 dBm noise and a -90 dBm signal. The input signal to noise ratio is 10 dB, i.e., the signal is 10 dB stronger than the noise.

Suppose a perfect, noiseless amplifier has 20 dB gain. It will increase the signal by 20 dB to -70 dBm and also amplify  the input noise by 20 dB to -80 dBm. At the amplifier output, therefore, the S/N ratio remains 10 dB as the signal and the noise are identically increased.

A practical amplifier, however, generates internal noise. This internally generated noise adds to the amplified input noise and degrades the output S/N ratio. Noise figure is a method of quantifying the amount of output S/N degradation caused by the amplifier. (Noise figure applies to things like attenuators and mixers as well as amplifiers, of course.)

The following discussion is abridged from Hayward, et al., Experimental Methods in RF Design. If not on your library shelf, this book should be.

The noise factor is defined as:

where

F is the noise factor
Nout is the output noise power delivered to the load
Nin is the noise power available from the input resistance
G in the power gain

This definition is in algebraic, not decibel form. For example, G=100 for an amplifier with 20 dB gain, and the noise power values are in watts (or microwatts or nanowatts, as you might prefer.)

Nin is the noise power available from the source resistance at room temperature, considered to be 290 K (or 17 °C or 62.3 °F). If the amplifier is perfect and contributes no noise of its own, then Nout = G*Nin and F=1 or 0 dB.

The noise factor equation can be recast in terms of the input and output signal to noise ratios:

where
Sin/Nin is the signal-to-noise ratio at the amplifier input
Sout/Nout is the signal-to-noise ratio at the amplifier output

As with the earlier equation, signal and noise values are algebraic, not decibel.

The noise figure is 10log(noise factor) and is in dB.

What noise figure is needed? A simplistic answer is as low as possible, but in fact the lowest noise figure amplifier may not be the best in terms of intermodulation performance or other key factors that are more important for low, medium and high frequency reception. The Radio Society of Great Britain's Radio Communications Handbook (8th ed.) notes the following:

Because of galactic, atmospheric and man-made noise always present on HF, there is little need for a receiver noise figure of less than 15-17 dB on bands up to about 18-20 MHz, or less than about 10 dB on 30 MHz, even in quiet sites. It may, however, be an advantage if  the first stages (preamplifier or mixer or post-mixer) have a lower noise figure since this will permit good reception with an electrically short antenna or allow the use of a narrow-band filter, which attenuates the signal power...

As a practical matter, therefore, in most circumstances, it will be difficult to distinguish between a preamplifier with a noise figure of 2 dB versus one with a noise figure of 3 or 4 dB when used below 30 MHz.

 

IP3 and IP2

The major source of phantom signals created in the amplifier are from "intermodulation distortion." Intermodulation distortion creates new, unwanted, phantom signals from combinations of input signals.

If amplifiers only had to handle one simple signal, life would be easy. Our concerns would be limited to harmonics. However, a typical preamplifier is faced with an input of hundreds or thousands of individual signals, some of which may be very strong and others just above the noise level.

The two simplest, yet useful, test protocols quantifying how an amplifier deals with multiple signals are the 2nd and 3rd order intermodulation tests. The output of these tests is reduced to two single numbers, the "second order intercept" or IP2 and the "third order intercept" or IP3.

The mathematical relationship between the two input signals on frequencies f1 and f2 and the frequencies of the resultant intermodulation products is:

where n+m equals the "intermodulation order."

Thus, for second order intermodulation products, possible values of n and m are:

n=0, m=2
n=1,m=1
n=2,m=0

The corresponding intermodulation product frequencies are:

2f1
f1+f2
f1-f2
2f2

This relationship is shown below, in the illustration from Anritsu's Application Note Intermodulation Distortion (IMD) Measurements Using the 37300 Series Vector Network Analyzer.

With third order intermodulation, n+m=3, so we have the following possible frequency combinations (valid n and m values are 1,2 and 2,1):

2f1+f2
2f1-f2
f1+2f2
f1-2f2

Some of these combinations may yield "negative" frequencies. It's the absolute value of the frequency difference that counts.

The figure below, also from Anritsu's Application Note shows the second and third order intermodulation products from a pair of signals.

To put this mathematical argument in prospective, consider what happens if f1 and f2 are  980 KHz (f1) and 1400 KHz (f2), typical AM broadcast band channels.

These two signals, when passed  through any practical amplifier, will combine and create new phantom signals. Specifically:

Second order intermodulation products will be found at:

2800 KHz (2f1)
2380 KHz (f1+f2)
420 KHz (f1-f2)
1960 KHz (2f2)

Third order products will be found at:

3360 KHz (2f1+f2)
560 KHz (2f1-f2)
3780 KHz (f1+2f2)
1820 KHz (f1-2f2)

If you are an amateur radio operator, the phantom signals at 1960 KHz and 3780 KHz will be objectionable. Or if you are a medium wave DX'er, you won't care for the 560 KHz IMD signal either. Worse yet, additional, higher order, IMD products are also created although their amplitude diminishes with increasing IMD order.

The relationship the input and IMD signals is that for a 1 dB change in the f1 and f2 amplitude levels, the nth order intermodulation product changes by n dB. Thus, if the two input signals increase by 10 dB, the 2nd order intermodulation signals increase by 20 dB. Likewise, the 3rd order intermodulation product signals increase by 30 dB. (The same rule applies to decreases, of course.)

If we test an amplifier by inputting two equal level signals and vary their levels while measuring the second and third order IMD products, and then graph the  results, the plot will resemble the one below, extracted from the ARRL's 2006 Radio Amateur's Handbook.

The plot show the effects of gain compression, previously discussed. It also shows the second and third order IMD levels and how the increase at different levels. (When speaking of the IMD level, we mean  the level of any one of the products, as in theory all nth order products are of equal level. In practice, there can be differences in level among the various individual IMD products comprising the set of nth order products. In this case one normally takes the strongest IMD product as the measured value.)

If we project the desired output, and the 2nd and 3rd order IMD product levels, we see that the projected lines intersect. The intersection of the desired output and the 3rd order IMD product is the "third order IMD intercept point" or IP3, and the corresponding 2nd order intercept point is IP2.

As should be apparent from the plot, it is normally physically impossible to operate a practical amplifier such that the desired output has the same level as the third order intermodulation product or the second order intermodulation product. Practical amplifiers will saturate long before this occurs. Hence, it is necessary to develop IP2 and IP3 specifications by projecting or extrapolating measurements  taken at lower signal levels. To this degree, therefore, IP2 and IP3 are fictitious values, although they are firmly grounded in real data.

I should also mention that not all amplifiers are well behaved and follow the nice 1:n amplitude relationship. This can cause some difficulty in deciding how to extrapolate the lower level data. If, for example, the third order IMD product increases at 2.5 dB for every 1 dB increase in input level over some range of input levels and at 3.5 dB for other input levels, how then should the third order intercept be determined?
 
All this theoretical discussion is well and good, but what does it mean when it comes time to evaluate a preamplifier? As with the other specifications, all else being equal, it's better to have an amplifier with higher IP2 and IP3 performance than lower. Of course, seldom are all things equal.

We can, from IP2 and IP3 intercept data, estimate the level of interference expected from a pair of input signals. (And, of course, all this discussion is  greatly simplified because seldom is it  the case that only  two signals are the cause of IMD and that even rarer will it be the case that the two signals are of equal amplitude. It is possible to extend these prediction techniques to multiple signals of arbitrary levels, but that's way beyond the purpose of this discussion.)

Suppose we are considering  two amplifiers, A1 and A2, both with 10 dB gain. A1 has an IP3 of +15 dBm and A2 has an IP3 of +25 dBm. The two interfering signals are local AM broadcast stations at 980 KHz and 1400 KHz and the measured signal at the amplifier input of both of these stations is -20 dBm, very strong signals, 53 dB over S9 assuming S9 is 50 microvolts an a 50 ohm system. After passing through either A1 or A2, the signal level is -10 dbm.

Consider amplifier A1, with an IP3 of +15 dBm. At the IP3 point, both 980 and 1400 KHz fundamental signals and the 3rd order IMD product would be at +15 dBm. However, in fact the f1 and f2 output signals are at -10 dBm, or 25 dB below A1's IP3 point. Since 3rd order intermodulation interference products drop 3 db for every 1 db reduction in input level, the 3rd order products will be at 15 dBm - 3 * 25 dB = -60 dBm.

Performing the same calculation for A2, we note the f1 and f2 signals are 35 dB below A2's IP3 point and hence the resulting 3rd order IMD products will be 3 * 35, or -105 dB from the IP3 point, corresponding to a 3rd order interference level of -80 dBm.

A shortcut to this comparison is to simply note that the nth order IMD product level difference between two amplifiers with identical gains is (n-1) times the difference in IP3 levels in dB. In this example, n=3 and the difference in IP3 levels is 10 dB. Hence the amplifier with +25 dBm IP3 will have 20 dB lower 3rd order IMD products than one with an IP3 of +15 dBm.

To help put this in prospective, the strongest medium wave AM broadcast signal I see using an 80 meter inverted vee antenna in my suburban Washington DC location is -18 dBm, not far from our sample calculation.

The spectrum analyzer plot below shows the medium wave band in mid-morning on January 2009.

The spectrum analyzer image below, in contrast is from Ron, K8AQC, who lives in suburban Detroit, a couple miles north of a 50 KW AM directional station at 1500 KHz. That signal is -0.4 dBm into a short whip receiving antenna. In addition there are two stations at -10 dbm and a total of 7 stations at -20 dBm or stronger. That's a much denser RF environment than I experience.

 

 
 
 

Typical Performance Plots

The data below is from the production Z10040A printed circuit board and should be fully representative of assembled kits or wired and tested amplifiers. These are not warranted performance values, however. The Z10040B has identical performance.
 

Gain versus Frequency, direct DC power feed.

Gain versus Frequency, duplex DC power feed with Z1202A Power Coupler


Input VSWR versus frequency, 50 ohm system

1 dB Compression Point


IP3 Typical

IP3 intercept computed from this measurement is +46 dBm. This number is subject to revision when I complete a better test setup.

Noise Figure

Measured with an HP8970A noise figure meter and AIL 7615 noise source. Noise figure performance varies significantly between units and with supply voltage and the figure below is representative of only a limited sample set.