Tonight I will be going over some questions from the General Exam Question Pool. The first set deal with S-meters so it will be a practical test of the information provided in Lee's talk of March 4, 2009.

G4D04 (C)

What does an S-meter measure?

A. Conductance

B. Impedance

C. Received signal strength

D. Transmitter power output

~~

If you have trouble remembering this just think S for strength.

G4D05 (D)

How does an S-meter reading of 20 db over S-9 compare to an S-9 signal, assuming a

properly calibrated S meter?

A. It is 10 times weaker

B. It is 20 times weaker

C. It is 20 times stronger

D. It is 100 times stronger

~~

One Bel which equals 10 Decibels is 10 times the power. So two Bels, 20 Decibels, is 10 times 10 which equals 100 times the power.

G4D06 (A)

Where is an S-meter generally found?

A. In a receiver

B. In a SWR bridge

C. In a transmitter

D. In a conductance bridge

~~

We are measuring received signal strength so the logical place to find it is in the receiver circuitry.

This next set of questions deal with connectors.

G4D07 (A)

Which of the following describes a Type-N connector?

A. A moisture resistant RF connector useful to 10 GHz

B. A small bayonet connector used for data circuits

C. A threaded connector used for hydraulic systems

D. An audio connector used in surround sound installations

~~

N connectors are screw on connectors that are not only moisture resistant but have excellent SWR properties at UHF frequencies. Ironically, the UHF connector (also known as PL-259 for the male connector and S0-239 for the female connector) is not as good at UHF as the N connector. The specifications I found for the UHF connector indicate DC - 300MHz but it is commonly used for 440MHz FM communication and works pretty well.

G4D08 (D)

Which of the following connectors would be a good choice for a serial data port?

A. PL-259

B. Type N

C. Type SMA

D. DB-9

~~

The first three connectors are all coax connectors intended for radio waves. The DB-9 is a 9 pin connector roughly in the shape of a D. On a side note, even though the computer world is leaving DB-9 connectors behind, Amateur Radio is slow to change and you will still find the DB-9 in use.

G4D09 (C)

Which of these connector types is commonly used for RF service at frequencies up to

150 MHz?

A. Octal

B. RJ-11

C. UHF

D. DB-25

~~

Based on the explanation for G4D07, you should immediately say UHF. As for the other connectors, I have no idea what an Octal connector is, an RJ-11 connector is the typical telephone connector, and a DB-25 connector is an older version of the DB-9 with 25 pins instead of 9.

G4D10 (C)

Which of these connector types is commonly used for audio signals in amateur radio

stations?

A. PL-259

B. BNC

C. RCA Phono

D. Type N

~~

As with the question above on serial data, PL-259 (UHF), BNC and Type N are all used for radio frequency transmission. The RCA Phono connector is the one commonly used for audio. This is the one where the plug has a center pin and a thin circular shield with no threads or bayonet mount. It just pushes on.

G4D11 (B)

What is the main reason to use keyed connectors over non-keyed types?

A. Prevention of use by unauthorized persons

B. Reduced chance of damage due to incorrect mating

C. Higher current carrying capacity

D. All of these choices are correct

~~

Keyed connectors ideally will only make a connection when they are correctly aligned. Therefore they reduce the chance of damage due to incorrect mating. Note it says reduce, not eliminate. Depending on how the key is implemented, it may be possible to force connectors together in a way they were not meant to go. If you ask me how I know this I will not admit to it being firsthand knowledge.

## Wednesday, March 25, 2009

## Wednesday, March 18, 2009

### Intermodulation Distortion by Lee Bond, N7KC

For the 43rd session of the Educational Radio Net, I have chosen to continue a review of basic and important concepts that cannot be avoided when dealing with radio equipment. Earlier sessions dealt with the relationship of energy, power, time, voltage, current, and resistance. The 13 parts of the Impedance series is a good starting point for individual review. Check the blog if you are interested in rehashing earlier material. This week I will delve into the subject of intermodulation distortion.

The 38th session looked at harmonic distortion in detail. I think it will be useful to review a bit of that material so that we can contrast harmonic distortion and intermodulation distortion. First, harmonic distortion is a single frequency process in contrast with IMD which is a multiple frequency process. An amplifier designed for high fidelity is expected to be completely linear in the sense that output signals are expected to be simply larger versions of the input signals. For example, an amplifier with a gain of 3 is expected to treat all input signals… regardless of frequency or phase… in the same manner. The output signal should match the shape of the input signal except for size.

There are two approaches to understanding harmonic distortion. The most elegant and more difficult is the mathematical process to analyze the effect. The second and less difficult is the empirical look at what happens when non linear amplifier processes distort the input signal. Initially lets take the empirical path and assemble on our bench an amplifier, either audio or RF… it makes no difference in what we will see... , a signal source, and a spectrum analyzer. First we look at our signal source with the analyzer and notice that it is a perfect sine wave of frequency f. The analyzer shows a single vertical line at frequency f and looking around we see no energy at multiples of frequency f over the expected range of frequencies and amplitudes that we plan to use in the demonstration.

Now connect the spectrum analyzer to the amplifier output along with a suitable load. Adjust the signal generator output level about mid range and connect it to the amplifier under test. The good news is that the spectrum analyzer shows a single vertical line in response to the input signal. Now, lets slowly increase the amplitude of the input signal within its known ‘perfect’ range while observing the analyzer. All of a sudden a second line appears to the right of the input signal… in fact at exactly twice the frequency of the input signal. This is not good news. Continuing on with increasing the input signal amplitude we notice a third signal pop up and this one is exactly three times the frequency of the input signal.

What we are observing is the practical ramifications of an amplifier being driven into some non linear region. Engineers describe the relationship between output signal and input signal as a ‘transfer function’. If the transfer function is a straight line… as in linear amplifier… then the signal, or multiple signals, will not mutually interact within the amplifier and the output will appear as distinct output signals on the analyzer. Departures from linear move toward a ‘square law’ transfer function and the amplifier output takes on the non linear character of y = x squared. If the single input signal is of the form A sin wt then a linear response would produce 3(A sin wt) if the amplifier gain were 3. When the amplifier is driven into the early square law region then the response becomes (A sin wt) squared and the mathematical result is a frequency doubling function. This is harmonic distortion… a single input signal producing output signals that are integer multiples of the input frequency.

Ok, enough of this harmonic distortion business. Lets do another demonstration with the same amplifier and input signal source but include a second signal source that is independent of the first. Lets assert that both of these ‘generators’ will produce a very clean signal on a spectrum analyzer. First we will drive the amplifier with source ‘A’ and notice that the amplifier output is well behaved and clearly in the linear region since no 2nd harmonic distortion products show up on the analyzer. Now lets add the higher frequency ‘B’ source to the amplifier input and, again, we see a very nice linear amplifier output signature on the spectrum analyzer. Outputs from A and B are clearly independent since we can vary the frequency of each signal and see the corresponding output signal change frequency in response. So far so good.

Now increase the amplitude of signal A to the point where the amplifier just starts to enter the square law region for signal A. At this point something interesting starts to happen on the analyzer attached to the amplifier output. Multiple output signals show up and they are both harmonically and non harmonically related to each other. The amplifier is now producing harmonic products plus linear combinations of the two input signals so if m and n are integers ranging from zero to two then the output signals will be generally represented by mA +/- nB where n or m can each range from 0 to higher values in integer steps. Given that we only have two signals then m or n cannot both be zero since that would mean that no input signal is present. So, assume m=1 and n=0 or m=0 and n=1 which gives us the first order products of the non linear mix and which are the fundamental input frequencies. Plugging the integer values m=1 and n=1 into the defining relationship gives B-A and B+A or the so called second order products.

Continuing in this manner let m=1 and n=2 (and vice versa) then 4 products of the form A+2B, 2A+b, 2B-A, and 2A+B are produced and which are called the 3rd order products. Notice that the order is the sum of the absolute values of the coefficients. Even order products become very large and are, generally, out of the pass band of interest but odd order products are very near to the fundamental frequencies and can wreck havoc on any desired signal. We are experiencing intermodulation distortion or IMD simply by overdriving the test amplifier with at least two signals present. If the two signals are complex such as speech then the output becomes hopelessly garbled.

How well any particular radio receiver handles large signals in or near the passband is a measure of receiver quality. Receiver manufacturers will quote the third order intercept point to illustrate the receiver dynamic range where more db is better. Receiver dynamic range is the difference between the noise floor performance at a desired frequency and the noise floor measured by tuning to a 3rd intercept point. The bigger the difference the better the receiver can handle large in band or near band signals without overloading.

Of particular interest is the fact that any rectifying junction is, by definition, nonlinear so dissimilar metals, corroding junctions, etc. can produce IMD in the presence of at least two strong RF signals. Repeaters without circulators can be a source of IMD since many repeaters live in the vicinity of powerful commercial transmitters and RF energy near the cavity passband can enter the final amplifier and mix with the repeater frequency to produce very nasty distortion products. Modern broadband receivers are particularly prone to IMD since they freely pass energy to the input stages that would never make it through highly selective circuitry as found in narrow band equipment.

This concludes the set up discussion for intermodulation distortion. Are there any questions or comments with regard to tonight's discussion?

This is N7KC for the Wednesday night Educational Radio Net

The 38th session looked at harmonic distortion in detail. I think it will be useful to review a bit of that material so that we can contrast harmonic distortion and intermodulation distortion. First, harmonic distortion is a single frequency process in contrast with IMD which is a multiple frequency process. An amplifier designed for high fidelity is expected to be completely linear in the sense that output signals are expected to be simply larger versions of the input signals. For example, an amplifier with a gain of 3 is expected to treat all input signals… regardless of frequency or phase… in the same manner. The output signal should match the shape of the input signal except for size.

There are two approaches to understanding harmonic distortion. The most elegant and more difficult is the mathematical process to analyze the effect. The second and less difficult is the empirical look at what happens when non linear amplifier processes distort the input signal. Initially lets take the empirical path and assemble on our bench an amplifier, either audio or RF… it makes no difference in what we will see... , a signal source, and a spectrum analyzer. First we look at our signal source with the analyzer and notice that it is a perfect sine wave of frequency f. The analyzer shows a single vertical line at frequency f and looking around we see no energy at multiples of frequency f over the expected range of frequencies and amplitudes that we plan to use in the demonstration.

Now connect the spectrum analyzer to the amplifier output along with a suitable load. Adjust the signal generator output level about mid range and connect it to the amplifier under test. The good news is that the spectrum analyzer shows a single vertical line in response to the input signal. Now, lets slowly increase the amplitude of the input signal within its known ‘perfect’ range while observing the analyzer. All of a sudden a second line appears to the right of the input signal… in fact at exactly twice the frequency of the input signal. This is not good news. Continuing on with increasing the input signal amplitude we notice a third signal pop up and this one is exactly three times the frequency of the input signal.

What we are observing is the practical ramifications of an amplifier being driven into some non linear region. Engineers describe the relationship between output signal and input signal as a ‘transfer function’. If the transfer function is a straight line… as in linear amplifier… then the signal, or multiple signals, will not mutually interact within the amplifier and the output will appear as distinct output signals on the analyzer. Departures from linear move toward a ‘square law’ transfer function and the amplifier output takes on the non linear character of y = x squared. If the single input signal is of the form A sin wt then a linear response would produce 3(A sin wt) if the amplifier gain were 3. When the amplifier is driven into the early square law region then the response becomes (A sin wt) squared and the mathematical result is a frequency doubling function. This is harmonic distortion… a single input signal producing output signals that are integer multiples of the input frequency.

Ok, enough of this harmonic distortion business. Lets do another demonstration with the same amplifier and input signal source but include a second signal source that is independent of the first. Lets assert that both of these ‘generators’ will produce a very clean signal on a spectrum analyzer. First we will drive the amplifier with source ‘A’ and notice that the amplifier output is well behaved and clearly in the linear region since no 2nd harmonic distortion products show up on the analyzer. Now lets add the higher frequency ‘B’ source to the amplifier input and, again, we see a very nice linear amplifier output signature on the spectrum analyzer. Outputs from A and B are clearly independent since we can vary the frequency of each signal and see the corresponding output signal change frequency in response. So far so good.

Now increase the amplitude of signal A to the point where the amplifier just starts to enter the square law region for signal A. At this point something interesting starts to happen on the analyzer attached to the amplifier output. Multiple output signals show up and they are both harmonically and non harmonically related to each other. The amplifier is now producing harmonic products plus linear combinations of the two input signals so if m and n are integers ranging from zero to two then the output signals will be generally represented by mA +/- nB where n or m can each range from 0 to higher values in integer steps. Given that we only have two signals then m or n cannot both be zero since that would mean that no input signal is present. So, assume m=1 and n=0 or m=0 and n=1 which gives us the first order products of the non linear mix and which are the fundamental input frequencies. Plugging the integer values m=1 and n=1 into the defining relationship gives B-A and B+A or the so called second order products.

Continuing in this manner let m=1 and n=2 (and vice versa) then 4 products of the form A+2B, 2A+b, 2B-A, and 2A+B are produced and which are called the 3rd order products. Notice that the order is the sum of the absolute values of the coefficients. Even order products become very large and are, generally, out of the pass band of interest but odd order products are very near to the fundamental frequencies and can wreck havoc on any desired signal. We are experiencing intermodulation distortion or IMD simply by overdriving the test amplifier with at least two signals present. If the two signals are complex such as speech then the output becomes hopelessly garbled.

How well any particular radio receiver handles large signals in or near the passband is a measure of receiver quality. Receiver manufacturers will quote the third order intercept point to illustrate the receiver dynamic range where more db is better. Receiver dynamic range is the difference between the noise floor performance at a desired frequency and the noise floor measured by tuning to a 3rd intercept point. The bigger the difference the better the receiver can handle large in band or near band signals without overloading.

Of particular interest is the fact that any rectifying junction is, by definition, nonlinear so dissimilar metals, corroding junctions, etc. can produce IMD in the presence of at least two strong RF signals. Repeaters without circulators can be a source of IMD since many repeaters live in the vicinity of powerful commercial transmitters and RF energy near the cavity passband can enter the final amplifier and mix with the repeater frequency to produce very nasty distortion products. Modern broadband receivers are particularly prone to IMD since they freely pass energy to the input stages that would never make it through highly selective circuitry as found in narrow band equipment.

This concludes the set up discussion for intermodulation distortion. Are there any questions or comments with regard to tonight's discussion?

This is N7KC for the Wednesday night Educational Radio Net

## Wednesday, March 11, 2009

### Extra Class Exam Grab Bag, #2, Bob, Session 42

Tonight we will take a little bit deeper look at some of the extra class exam questions. I hope that by the end of this session you will know how to answer these questions without having to memorize them and that you will have gained a little better understanding of some important concepts.

The first couple of questions will be a review of one of Lee's excellent impedance series sessions. Specifically it is Part 9 if you want to go back to review it.

E8A04 (C)

What is the equivalent to the root-mean-square value of an AC voltage?

A. The AC voltage found by taking the square of the average value of the peak AC voltage

B. The DC voltage causing the same amount of heating in a given resistor as the corresponding peak AC voltage

C. The DC voltage causing the same amount of heating in a resistor as the corresponding RMS AC voltage

D. The AC voltage found by taking the square root of the average AC value

~~

This is based on the concept that root-mean-square (RMS) of AC gives you an indication of the power provided by that AC signal. As Lee pointed out in his session. The resistor will heat up until it reaches some equilibrium point. At that point it is dissipating as much heat as it is generating. You can be assured that it is the same amount of average power generated no matter what kind of waveform you pass through it. In the two special cases of a flat DC current and an AC sine wave, you have this special relationship where the root of the mean of the square of the sine wave will yield the DC voltage that would heat the resistor to the same temperature. This means that the power provided to that resistor is the same for the RMS AC and the DC.

Related question:

E8A05 (D)

What would be the most accurate way of measuring the RMS voltage of a complex waveform?

A. By using a grid dip meter

B. By measuring the voltage with a D'Arsonval meter

C. By using an absorption wavemeter

D. By measuring the heating effect in a known resistor

~~

Here are a few related questions on digital signals:

E8A12 (D)

What type of information can be conveyed using digital waveforms?

A. Human speech

B. Video signals

C. Data

D. All of these answers are correct

~~

This should be obvious to all considering that we have phased out analog cell phones so that all human speech is using digital waveforms there and with all the recent news about digital TV there should be no question that video signals can be carried by digital waveforms. Data is what digital waveforms are primarily for.

E8A13 (C)

What is an advantage of using digital signals instead of analog signals to convey the same information?

A. Less complex circuitry is required for digital signal generation and detection

B. Digital signals always occupy a narrower bandwidth

C. Digital signals can be regenerated multiple times without error

D. All of these answers are correct

~~

This one could be a little tricky considering it could appear to be D, all of the above. But A is definitely not always true and in fact is usually not true in my opinion. B is often true but not always and this answer specifically says always. But C, signals can be regenerated multiple times without error is true and is one of the defining differences between digital and analog signals.

E8A14 (A)

Which of these methods is commonly used to convert analog signals to digital signals?

A. Sequential sampling

B. Harmonic regeneration

C. Level shifting

D. Phase reversal

~~

I have to admit that I have only half educated guesses of what harmonic regeneration, level shifting and phase reversal are or how they would be used. What I do know is that they would not be used to convert analog signals to digital. The common way (note the question said common) to convert analog to digital is to measure the amplitude at specific times and transmit that amplitude information. You are taking a sample of the waveform sequentially that is to say in regular steps of time, one after another.

E8A15 (B)

What would the waveform of a digital data stream signal look like on a conventional oscilloscope?

A. A series of sine waves with evenly spaced gaps

B. A series of pulses with varying patterns

C. A running display of alpha-numeric characters

D. None of the above; this type of signal cannot be seen on a conventional oscilloscope

~~

This one also is a bit tricky as you might think that A should be a possible answer. It's possible that a modulated digital signal could look like this but the straight digital signal will look like B, a series of pulses with varying patterns.

The first couple of questions will be a review of one of Lee's excellent impedance series sessions. Specifically it is Part 9 if you want to go back to review it.

E8A04 (C)

What is the equivalent to the root-mean-square value of an AC voltage?

A. The AC voltage found by taking the square of the average value of the peak AC voltage

B. The DC voltage causing the same amount of heating in a given resistor as the corresponding peak AC voltage

C. The DC voltage causing the same amount of heating in a resistor as the corresponding RMS AC voltage

D. The AC voltage found by taking the square root of the average AC value

~~

This is based on the concept that root-mean-square (RMS) of AC gives you an indication of the power provided by that AC signal. As Lee pointed out in his session. The resistor will heat up until it reaches some equilibrium point. At that point it is dissipating as much heat as it is generating. You can be assured that it is the same amount of average power generated no matter what kind of waveform you pass through it. In the two special cases of a flat DC current and an AC sine wave, you have this special relationship where the root of the mean of the square of the sine wave will yield the DC voltage that would heat the resistor to the same temperature. This means that the power provided to that resistor is the same for the RMS AC and the DC.

Related question:

E8A05 (D)

What would be the most accurate way of measuring the RMS voltage of a complex waveform?

A. By using a grid dip meter

B. By measuring the voltage with a D'Arsonval meter

C. By using an absorption wavemeter

D. By measuring the heating effect in a known resistor

~~

Here are a few related questions on digital signals:

E8A12 (D)

What type of information can be conveyed using digital waveforms?

A. Human speech

B. Video signals

C. Data

D. All of these answers are correct

~~

This should be obvious to all considering that we have phased out analog cell phones so that all human speech is using digital waveforms there and with all the recent news about digital TV there should be no question that video signals can be carried by digital waveforms. Data is what digital waveforms are primarily for.

E8A13 (C)

What is an advantage of using digital signals instead of analog signals to convey the same information?

A. Less complex circuitry is required for digital signal generation and detection

B. Digital signals always occupy a narrower bandwidth

C. Digital signals can be regenerated multiple times without error

D. All of these answers are correct

~~

This one could be a little tricky considering it could appear to be D, all of the above. But A is definitely not always true and in fact is usually not true in my opinion. B is often true but not always and this answer specifically says always. But C, signals can be regenerated multiple times without error is true and is one of the defining differences between digital and analog signals.

E8A14 (A)

Which of these methods is commonly used to convert analog signals to digital signals?

A. Sequential sampling

B. Harmonic regeneration

C. Level shifting

D. Phase reversal

~~

I have to admit that I have only half educated guesses of what harmonic regeneration, level shifting and phase reversal are or how they would be used. What I do know is that they would not be used to convert analog signals to digital. The common way (note the question said common) to convert analog to digital is to measure the amplitude at specific times and transmit that amplitude information. You are taking a sample of the waveform sequentially that is to say in regular steps of time, one after another.

E8A15 (B)

What would the waveform of a digital data stream signal look like on a conventional oscilloscope?

A. A series of sine waves with evenly spaced gaps

B. A series of pulses with varying patterns

C. A running display of alpha-numeric characters

D. None of the above; this type of signal cannot be seen on a conventional oscilloscope

~~

This one also is a bit tricky as you might think that A should be a possible answer. It's possible that a modulated digital signal could look like this but the straight digital signal will look like B, a series of pulses with varying patterns.

## Wednesday, March 4, 2009

### The Decibel verses the S meter

**The Decibel and its relationship to S meter displays by Lee Bond, N7KC**

March 4, 2009 Educational Radio Net, PSRG

For the 41st session of the Educational Radio Net, I have chosen to continue a review of basic and important concepts that cannot be avoided when dealing with radio equipment. Earlier sessions dealt with the relationship of energy, power, time, voltage, current, and resistance. The 13 parts of the Impedance series is a good starting point for individual review. This week I will delve into the decibel and its relationship to S meter displays.

Before I start let me say that I was poking around Wikipedia looking for information on ‘bels’ when I ran across the decibel offerings. Turns out that TU or transmission unit was a popular telephone unit of transmission gain or loss in the early days of miles of wire associated with the telephone industry. Eventually the attenuation resulting from about 10 miles of wire loop become known as a ‘Bel’. Since the Bel is a large unit, the decibel, or 1/10 of a bel became a more useful unit of measure. Wide usage of the decibel followed.

We humans like to compare things. For example, how much is a gallon of gasoline in Washington compared to a gallon in Oregon or what is the price of a certain apple at QFC compared to the same apple at Safeway? One might say that Washington gasoline costs 1.5 times as much as Oregon gasoline which is the same as saying that the cost ratio of Washington gas to Oregon gas is 1.5. Notice that there are no units associated with this ratio. Dollars per gallon in the numerator cancels with dollars per gallon in the denominator yielding a sterile number of simply 1.5… that is, a number with no units.

So it is with the decibel. The decibel is a comparison of two like objects in the sense that these objects must have the same units. For example, by using decibel notation you can compare two voltages or two powers. In both cases the units of voltage or power will cancel yielding a sterile ratio. The sterile ratio is processed by the decibel conversion mathematics to produce a number associated with base 10 logarithms. Decibel notation for power comparisons is always 10 log (ratio). Decibel notation for voltage ratios is always 20 log (ratio) since power goes as the square of the voltage.

Uh oh… did I mention logarithms? Well, lets try to make some sense of this mysterious thing called a logarithm or log for short. To be complete I must say that there are two systems of logarithms. One system is based on the number e and is called the Naperian or natural log system and is very important in a certain branch of mathematics. The other is based on 10 and is called the common log system. Our interest is with the common log system so lets get a feel for just what is going on with the use of these logarithms.

The common log is a combination of two things… something called the characteristic in conjunction with something called the mantissa. Once you know the underlying idea behind each of these two parts you can use them very effectively in your radio work. Lets start with the number 100 as an example. We all know that 10x10 equals 100. Another way to say 10x10 is 10 squared so 10 with the little ‘exponent’ 2 equals 100. Guess what… the little exponent number 2 is the log of 100. Now, lets look at the number 1000. We also know that 1000 can be written as 10x10x10 or 10 cubed or 10 with a little exponent 3. Easy enough. The log of 1000 is the exponent 3. We have just determined the characteristic by inspection. Providing the number is positive, the characteristic is one less than the number of digits left of the decimal point. Wait you say… what if I have a number between 100 and 1000… perhaps 300. Clearly the log of 300 must be greater than the log of 100 and less than the log of 1000. Enter the mantissa. The log of 300 is 2.4771 which is simply one way to say 10 to the 2.4771 equals 300. The 4 decimal places to the right of the decimal point is the mantissa so the complete log is the sum of the characteristic and the mantissa. Old timers from the slide rule era will know that numbers on their rules were located according to the logarithm of the number so the log of 3 is located about mid point on the rule. Logs are a good way to represent very large numbers in a compact form. When multiplying scientific notation numbers one just adds the exponents which is consistent with adding lengths on the slide rule. Finally, I am going to divulge the big secret… if the base 10 log of the number N equals Y then this is exactly the same thing as writing 10 raised to the Y power equals N. Exponential and logarithmic notation are completely consistent. Simply different ways of saying the same thing. Before the hand held electronic calculator reigned supreme one would determine the characteristic by inspection and then look in a table of common logs for the mantissa then add the two or use the slide rule to find the log. Today you just punch in a number and the log magically appears on the display.

Back to the decibel. If your transmitter develops 150 watts output power with two watts input power then, clearly, there is some power gain. The ratio is 150/2 or 75. The log of 75 is 1.8751 and 10 times that is 18.751 db. Thus you have two ways of expressing the same phenomenon… one as a ratio of 75:1 or another as +18.751 decibels. Why would you choose one over the other? Probably the best answer is that decibels are additive so, for example, if you have one amplifier following another then the overall power gain is simply the sum of the individual gains expressed as decibels. Decibel notation without any reference power is simply a ratio expressed in logarithmic form.

So much for db’s. What about dbm? Enter the reference power. In the previous example where the transmitter output power was 150 watts, the question becomes what is the ratio relative to 1 milli-watt. Given that 1 milli-watt is defined as 0 dbm we need to find out how 150 watts compares to 1 milli-watt. The answer is found by comparing 150 to 0.001, taking the common log and then multiplying by 10. So, key into your calculator 150 divided by .001, find the common log to be 5.1761, multiply by 10 to end up with 51.761 dbm. We can also convert the 2 watt input power to dbm and we find the answer to be 33.01 dbm. What is the difference between 51.761 dbm and 33.01 dbm? 18.751 db. Notice that we say that the gain of the amplifier is 18.751 db… not 18.751 dbm. Dbm is a measure of absolute power whereas db is a measure of relative power.

Now that we have some feel for decibel notation we can move on to signal strength meter displays and make some sense from what we see. As you know, these meters start with S1 through S9 then progress to S9+10 followed by S9+20 and so on. S8 is defined to be 6 db less than S9, S7 is 6 db less than S8, and so on down to S1. S9+10 is defined as 10 db greater than S9 and so on. The generally unknown fact is that S9 is equivalent to 50 microvolts rms at the receiver input terminals when measuring high frequency signals and 5 microvolts rms when measuring VHF/UHF signals. Both definitions require the receiver input impedance to be 50 ohms. Given that power goes as the square of the voltage… remember Joule’s Law… voltage decibels are defined as 20 log (ratio) and, therefore, voltage amplitude either doubles or halves for every 6 db change. Now we have enough ammunition to compute some numbers. If S9 corresponds to 50 microvolts and S8 is ½ or 6 db lower, then S8 corresponds to 25 microvolts. Going down by 2’s reveals that S7 corresponds to ½ of 25 or 12.5 microvolts and so on. Going the other way above S9 we need to compute what 10 db above 50 microvolts represents. I will not bore you with the computational details so the answer is 158 microvolts. S9+20 db pencils out to be 500 microvolts which is no surprise given that 20 db in voltage terms is a factor of 10 so 50 microvolts becomes 500 microvolts.

Unfortunately early S meter circuitry did not follow these rules perfectly and most meters were notorious for their errors. Many operators would report their S meter readings to be ‘Scotch’ if they were lower than the recipient would like to hear. Modern meters are much better performers when reading input signal strength. Measuring S meter accuracy requires some careful work with fancy test equipment so generally out of the realm of the average amateur operator.

This concludes the set up discussion of the decibel as it relates to S meter readings. Are there any questions or comments with regard to tonight's discussion?

This is N7KC for the Wednesday night Educational Radio Net

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