RF Column 18 - March 1993 Copyright (c) 1993,1995 H. Douglas Lung ALL RIGHTS RESERVED TOPICS: Measuring microwave frequencies with a transfer oscillator Setting FM deviation using Bessel functions (easy math!) -------------------------------------------------------------------- Last month we looked at methods of measuring frequency. This month, after engaging in a bit of nostalgia, I'll give you some tips on measuring FM deviation using Bessel functions. It's not as tough as it sounds. Last month I ran out of space before I had a chance to write about the best way to measure microwave frequencies. From what I've seen, many stations never bother to measure microwave frequencies, even though its fairly simple. Most of the newer microwave transmitters synthesize the frequency from a high frequency crystal oscillator. Its frequency can easily be checked with conventional counters, even inexpensive ones like I discussed last month. In most microwave transmitters, the final frequency is generated using frequency multipliers generating harmonics of a 2 GHz. oscillator. Most of today's counters will count that high. If you have a bigger budget, spectrum analyzers like the new Tektronix 2794 or the HP equivalent can display and accurately count microwave carriers up past 23 GHz. I'd have to admit these spectrum analyzers are the best way to measure microwave frequencies - you can see what you are counting! A decade or so ago, spectrum analyzers like this were not available. At $29,000 or more, they aren't cheap today. I found a suitable substitute which cost about $200 surplus. It was an old HP "Transfer Oscillator". I forget the model number. This unit had a very stable variable oscillator in the 200 MHz. range. The oscillator was connected to a circuit that generated harmonics to about 12 GHz. The harmonic generator, in turn, was connected to a 1N21 microwave mixer diode. The output of the mixer was connected to the vertical plates of a small CRT. As is usual for HP, it was built like a tank. BNC jacks on the front panel provided outputs from the mixer and from the oscillator. A frequency counter could be hooked up to the oscillator output to precisely measure the frequency. The mixer output could be connected to a low frequency spectrum analyzer for checking subcarrier amplitudes. If you never used one of these boxes, you're probably wondering it measured frequencies. Simple! Watching the oscilloscope, the transfer oscillator was tuned for zero beat and its frequency measured. The oscillator frequency was multiplied by the harmonic number to find the microwave frequency. If you knew what the frequency was supposed to be, you'd have a pretty good guess what the multiple of the oscillator frequency was. If not, it wasn't too tough to calculate. I won't derive it here, but you might want to play around with some basic algebra to figure it out. Here's a hint... Microwave Frequency = N x Oscillator Frequency at beat Microwave Frequency = (N+1) x Oscillator Freq. at next lower beat By looking at the oscilloscope you could see the beat go through sync and also through peak white, showing the video FM deviation of the transmitter. You can do the same with a spectrum analyzer by applying a white window video signal to the transmitter and measuring the difference in frequency between the white, blanking and sync tip sidebands. All things considered, I preferred seeing the waveform on the old HP transfer oscillator. Measuring FM deviation... Measuring FM deviation of video on a microwave isn't done nearly as often as checking audio deviation. Manufacturers design the transmitter for 1 volt video and in some cases don't even provide an external adjustment for video deviation. FM modulation of audio subcarriers is a different story. Input levels can vary from 0 dBmW to +10 dBmW, so manufacturers have to provide an adjustment. Worse yet, there are adjustments on both the transmit and the receive end. What do you use as a standard? A two-way radio service monitor might work, but will it cover the 6.2 MHz. frequency used for microwave subcarriers? How do you know it is accurate? Bessel functions have traditionally been used for precise FM deviation calibration. I won't describe the methods for solving Bessel functions. If you want the details, refer to Jan J. Tuma's "Engineering Mathematics Handbook" published by McGraw-Hill. The second edition I have was copyrighted in 1979. The ITT "Reference Data for Radio Engineers" also has a section on Bessel functions and a graph of the function showing amplitude versus modulation index. I used the PC program "MathCad", published by MathSoft, to generate Figure 1. I think it is easier to follow than the traditional Bessel function graphs showing the amplitude of the first dozen sidebands on a cramped scale. You'll notice there are three plots on the graph. They represent the carrier (Jn(0,x)), the first sideband (Jn(1,x)) and the second sideband (Jn(2,x)). The graph of the Bessel function shows the amplitude of these frequencies (carrier, first and second sidebands) versus modulation index. Modulation index is frequency deviation divided by the frequency of the modulating signal. One tone only, please! For example, the modulation index of a 5,000 Hz. (5 KHz.) audio tone deviating a carrier 20,000 Hz. (20 KHz.) is 4. Looking at the graph, for a modulation index of 4, the carrier will be near an out of phase peak, the first sideband will be near zero and the second sideband will be a bit less than half the amplitude of the unmodulated carrier. Still confused? Here's an experiment you can do with any FM source (microwave subcarrier, hand-held, etc.) and a spectrum analyzer. Connect the source to the spectrum analyzer, using pads as required to protect the analyzer and tune the analyzer to the carrier frequency of the source. Adjust the spread/resolution so that full deviation will occupy full width of the scope. Bandwidth should be set narrower than the modulating frequency you will be using. Three kiloHertz bandwidth might work, 300 Hertz may be needed for lower frequencies. For this reason, I recommend using a fairly high audio frequency when setting deviation. With no modulation, the carrier will be a full amplitude on the analyzer. Now slowly increase the audio level to increase FM modulation and deviation. As modulation is increased, you'll see the carrier drop to zero when the modulation index hits 2.4048 then start to increase. When the modulation index hits 3.8317, the first sideband will null out. Continuing to increase the modulation level, the second sideband will null when the modulation index reaches 5.1348. Increasing the modulation just a bit more, the carrier will null again, at a modulation index of 5.5201. You should be able to match what you are seeing on the analyzer with the amplitude levels in figure 1. Note that the null is at zero on the Y-axis, not at the negative minimums on the curves. You've probably figured out by now how to set deviation using Bessel nulls. Here's a real world example. Harris-Farinon specifies the maximum deviation of the audio subcarriers on their MicroStar microwaves at 200 KHz. I like to leave 10 dB of headroom on the microwave, so at operating level (+4 dBmW in this case) the deviation will be 20 KHz. Per Orban's recommendation for use with the split chassis Optimod, no pre- emphasis is used. What frequency is needed at +4 dBmW to produce the first carrier null at 20 KHz. deviation? From the graph and more precisely, from Table 1, the first carrier null occurs at a modulation index of 2.4048. From the definition of modulation index above, we can find the frequency needed: Modulating Frequency = Deviation (20 KHz.) / 2.4048 or 8.3167 KHz. I applied a 8.3167 KHz. tone at precisely +4 dBmW to the input of the microwave subcarrier modulator. Starting the deviation control at minimum, I increased it until the carrier nulled the first time. Then I adjusted the level at the receiver on the other end of the path so it was precisely +4 dBmW. I checked the accuracy of the modulation by applying a +4 dBmW signal at the frequency needed to produce the second carrier null. From the table, the modulation index needed was 5.5201. Dividing this into 20 KHz. showed me I had to set the tone at 3.623 KHz. The spectrum analyzer showed the carrier nulled and the second sideband at low amplitude, as the graph would indicate, confirming the setting. Once we know the modulation index for a given null (carrier or sideband), it isn't necessary to actually calculate the amplitude using Bessel functions. Table 1 listed the first three nulls for the carrier and the first two sidebands. Keep a copy of this table handy and you can set deviation fairly close even with a fixed tone source (like a packet modem or test tone). Tektronix includes an accurate crystal controlled audio output at 10,395 Hz. on the 1405 Sideband Analyzer. It is the modulating frequency necessary to produce 25 KHz. deviation at the first carrier null (2.4048 modulation index). Don't forget to take the pre-emphasis curve into account when adjusting deviation. Less input will be required at higher frequencies for the same amount of deviation. The 75 microsecond pre-emphasis curve is printed in the FM section of the FCC Rules and Regulations and is also in most TV engineering handbooks. A poor man's spectrum analyzer substitute... If you've followed all this, but don't have a spectrum analyzer, don't despair. If you have a radio that tunes to the carrier frequency, you can use it to find determine when the carrier has nulled. Because there will be other sidebands, it helps if the radio has a narrow bandwidth. Turn on the radio's BFO and adjust it for a convenient tone from the unmodulated carrier. Concentrating on that tone, increase the modulation until that tone disappears. That will be the first carrier null. Using the highest possible modulating frequency is even more important here than with the spectrum analyzer. Shortwave radios will work nicely for setting microwave subcarrier deviation. For setting two-way radio or TV aural carrier modulation, a multi-mode receiver like the Yaesu FRG-9600 or Icom IC-R7000 will work. Perhaps this is the way to justify one of these radios in your engineering budget if you can't get that spectrum analyzer approved! UPS... If you use a UPS to backup your remote control or microwave, be sure to take time to check the batteries. Replacing dead batteries in equipment might solve some of those odd intermittent problems that have crept back into the system. Some transmitters have backup batteries inside. The Harris UHF transmitters have a pack in the control cabinet that allows them to come back up immediately after short power glitches. Some remote control equipment uses batteries to retain the configuration in memory. Don't forget to check them too. That's it for this month. If you are attending NAB in Las Vegas, look for me there. If you have an interesting project, tip or comments on the column, I'd like to hear them. Find me in the directory or leave a note at the message center. I've got couple projects I'm working on for future columns, including a WWV frequency standard receiver, updates for the cheap remote control and a bare-bones PC based satellite ATIS Morse code decoder. I'd like to hear your ideas too. If we don't meet at NAB, drop me a note at 2265 Westwood Blvd., Suite 553, Los Angeles, CA 90064 or leave a note on CompuServe, to my ID, 70255,460. You can also try to catch me at my office, either 305-884-9664 or 818- 502-5739. -------------------------------------------------------------- Table 1 - Modulation Index at Carrier & Sideband Nulls NULL Carrier First Sideband Second Sideband ---- -------- -------------- --------------- First 2.4048 3.8317 5.1348 Second 5.5201 7.0156 8.4172 Third 8.6537 10.1735 14.7960 -------------------------------------------------------------- ((8/95 > UPDATE! - Use dlung@gate.net for e-mail!)) Copyright (c) 1993,1995 H. Douglas Lung ALL RIGHTS RESERVED