# Impedance Graph Paper - Easy To Use

Discussion in 'Electronics Resources' started by thatoneguy, Dec 13, 2011.

1. ### thatoneguy Thread Starter AAC Fanatic!

Feb 19, 2009
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I use this sheet quite often to get a rough idea of values. I've grown to depend on it, actually!

It works for capacitor impedance, inductor impedance, or both for resonant frequencies, as well as impedance at various frequencies.

Save it and print it out. I find two thin and transparent rulers are very handy with this as well. It's sort of a 2 dimensional slide rule.

Print it out, and you can also obviously draw on it for each solution for "back of napkin" thoughts without playing with a calculator.

It is log/log/log/log, with the marked line bold, and the middle line slightly bolder. Use two diagonals and two horizontal depending on what you are trying to calculate:

Inductor reactance/impedance at frequency
Capacitor reactance/impedance at frequency
Resonant frequency of capacitor and inductor

• ###### impedance-graph-paper.pdf
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2. ### Georacer Moderator

Nov 25, 2009
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Shouldn't there be a factor for frequency in the graph? Is it the C (cycles?) bottom axis? Also, the μμF is nano or pico? It's pico, right?

So, say I want a capacitor with an impedance of 10Ω @ 100Hz. What lines do I trace?

3. ### thatoneguy Thread Starter AAC Fanatic!

Feb 19, 2009
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Go horizontal from 10Ω to 100Hz, follow the diagonal line down and right to get capacitance.

Roughly 180uF

Since 10Ω@100Hz didn't sit directly on a capacitance line, I followed the nearest one down and to the right, to get to 200uF, then I estimated that the space left between 100uF and 200uF would be about 20uF, so I subtracted that from the line I followed down.

You can extend the capacitance across the bottom, next diag left of 10uF is 100uF (by 100kHz), then 1,000uF(by 10kHz) then 10,000uF(by 100Hz). Similar as is done across the top for Henries

The uuF is pF I should edit that for clarity

For 10Ω@100Hz in an inductor, take the diagonal line up, which lands you at 18mH

--ETA: Once you print it out and work out a few like the above, it becomes extremely handy to glance at to get a rough idea for a value needed, sometimes close enough that exact doesn't matter, such as a cutoff frequency or reactance "low enough" type calculation.

Last edited: Dec 13, 2011
4. ### Georacer Moderator

Nov 25, 2009
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I got it now, thanks! Here is a .png version for ease of access.

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5. ### thatoneguy Thread Starter AAC Fanatic!

Feb 19, 2009
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I drew one up with two examples.

The first is the Fo of an 100uH inductor in parallel with a 1uF capacitor, yeilding a result of around 20kHz (Green Lines drawn for known quantity, answer line in blue, down to the frequency line) actual answer is around 15kHz

The second is the question originally asked, what capacitor has the impedance of 10Ω@100 Hz. (Orange lines for known parts of question, Blue line down to answer for capacitance)

For Capacitance, it continues by steps of 10 each log pane, so left of 10μF is 100μF, and since it is a log/log scale, each line between 10μF and 100μF is 10μF, so halfway between 10 and 100 is 50μF, which is a semi-bold line in the PDF above, after being printed out.

Let me know if you have questions. It can be expanded to the right, though not quite as easily, for higher frequencies (>10Mhz).

Yes, using the formula for exact values is best, but this will let you know if you made a typo on your calculator or computer when entering in the parameters. It's how I double check stuff if something isn't working right for a passive filter.

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Last edited: Dec 22, 2011
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6. ### thatoneguy Thread Starter AAC Fanatic!

Feb 19, 2009
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The frequency is along the bottom, with capacitance overlaid in areas, inductance is up the right side and along the top, and impedance is up the left side.

To solve for impedance or frequency, follow horizontally (impedance) or vertically (frequency) from the value (Impedance) diagonally up for the inductor, or down for the capacitor which has that impedance at that frequency.

To find the resonant frequency, pick the frequency, then desired impedance at that frequency, make a dot, then follow diagonally up for the inductor value, and diagonally down from starting dot for the capacitor value.

7. ### evilengineer New Member

Jan 3, 2013
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Can you please explain how one would be able to use this chart for calculating reactances at frequencies in the HF spectrum? A reactance/impedance notebook was purchased in hopes of being able to use it for finding values for amateur radio HF band circuits, but the graph turned out to be identical to the one you kindly shared here. I am hoping that I will still be able to use it, even if just for finding values in the 40-meter band (7.000 MHz - 7.300 MHz) but dearly dream of being able to use it up to 30MHz+.

I am not very good at mathematics but am trying to teach myself how to do the calculations necessary for building HF band RF circuits. An impedance reactance chart would be a great resource to me if it was for the range of frequencies I am working with. Maybe this is a ridiculous idea, but is there a way of changing or scaling the values of the chart up? Perhaps my only option is to expand the chart further to the right.

Thank you for your time. I know this is an old post but if anyone can please advice me, I would be sincerely grateful.

8. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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Very nice. There's a similar version of this in the ARRL Handbook in the section on electrical fundamentals. I teach how to use this every semester.

9. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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This is well worth learning how to do!
Keep in mind that, by definition, resonance is where Xl and Xc are equal values. If you look at the left side vertical axis, you will find values of reactance (in ohms). Now, there are an infinite number of combinations of Xl and Xc that wil give you any resonant frequency.

So, let's pick an arbitrary point along the bottom axis....let's say 5 MHz, since it's at the extreme right end. Now remember BOTH axes are logarithmic. (The ARRL version goes up to 100 MHz) I believe. (Don't have it right handy)

Now if you scoot up along the right edge, you will see intersecting values of capacitance and inductance. Any combination of these values will give you a resonant frequency of 5 MHz. The actual reactance values at resonance will be directly horizontally to the left on the vertical axis there.

Stay tuned....more tricks to follow~ (and yes, there is a special significance to 5 MHz, in this case!

Last edited: Mar 12, 2015
10. ### studiot AAC Fanatic!

Nov 9, 2007
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Here are some reactance charts to 500Mhz, courtesy the RSGB Radio Data Book by G R Jessop, which I can heartily recommend.

The book has many more useful charts eg RF inductors, Coaxial charts, Ripple charts, SWR charts, filter charts, PCB tracks at RF and so on.

11. ### evilengineer New Member

Jan 3, 2013
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KL7AJ: Thank you for taking time to reply. I believe I am familiar with how to properly use the reactance chart at this point. For instance, to achieve an impedance of 50-Ohms at 5-MHz, One selects ~650pF and ~1.6uH. Am I correct? Thank you again for taking time to describe the use of the chart, but I am hoping that I will be able to utilize this nomograph at higher frequencies.

Studiot: Thank you for sharing this. Actually, after I received my Z/X graph paper notebooks in the mail, and discovered that they did not cover the frequency range I was interested in (HF/Lower VHF), I went to the store and made half a dozen copies of the chart in the ARRL handbook (on a personal note, I am a much bigger fan of the RSGB and their publications, despite being an ITU region 2 AR, but haven't had much luck finding their publications for cheap/free around here, like I have with ARRL publications).

Again, thank you both for your replies. I received three of these Z/X Graph paper notebooks as a gift, this notebook contains the exact same chart featured in this post. I am eager to determine if there is anyway I can adapt them for use above 5MHZ, even if I have to use whiteout & write new values in. My wish is to be able to have this on the bench for quick approximations of component values. Until I learn a way to reuse this chart, I will continue squinting to see the copies I photocopied from the arrl handbook, using the reactance calculators I downloaded and/or getting more comfortable with doing it on pen & paper. There is not a lack of resources, I simply wish to find a way to convert the values of this lower frequency chart, to higher frequencies, Is this possible?

Best wishes!

p.s. - for others that may not be aware, there are many online reactance calculators available. Here is one:

and here is a downloadable reactance nomograph for RF frequencies:
http://www.rfcafe.com/references/electrical/frequency-reactance-nomograph.htm

12. ### evilengineer New Member

Jan 3, 2013
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Okie Dokie! You've got my interest! TNX!

73

13. ### MrChips Moderator

Oct 2, 2009
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A good thing to remember is

2π = 6.3

1/2π = 0.16

100/2π = 16

So for example,

1H is 1Ω at 0.16Hz

1H is 100Ω at 16Hz

1H at 1Hz is 6.3Ω

1H at 1kHz is 6.3kΩ

160μH is 1Ω at 1kHz

Similarly

1μF is 1Ω at 160kHz

1μF at 1kHz is 160Ω

1.6μF at 1kHz is 100Ω

14. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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Closely related is the Unit Frequency. I farad and one henry gives you a frequency of .159 Hz.

15. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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I have a highly prized 1968 RSGB Hnadbook. Tis indeed a gem!

16. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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Of course radio frequency electronics is my favorite topic, so I spend a lot of time drilling this chart in to my "kiddies"' heads!

Here's a little quiz to see how well you understand this. Since we see that there are an infinite number of pairs of L and C for any value of frequency, is there any reason for any SPECIFIC values of L/C ratio? This takes some thought.

Eric

17. ### studiot AAC Fanatic!

Nov 9, 2007
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Here is the Mullard version to 1Ghz from "Transistor Audio and Radio Circuits" .

Since the scales are all log it could be used as a pattern to rescale any log-log paper by drawing ruled lines.

18. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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Cool....well here' something to ponder on.

If we select an arbitrary resonant frequency, we notice that different combinations of L/C result in different reactance values as shown on the left vertical axis. If ALL we had in our circuit was a pure resistance and pure reactance, we could pick any L/C ratio we like, and come up with a resonant circuit at our chosen frequency of interest.

However, in the real world, we either have a resistive load, into which we're trying to do real work....or we have imperfect components. Inductors are wound with wire that has real resistance. (Capacitors tend to be closer to pure components in most cases...except for electrolytics).

For a simple LC series circuit, the value of reactance will determine the resonant circuits "Q" at resonance. Q is defined as the ratio of reactance to resistance. Therefore, we will find that a larger L/C ratio gives us a larger Q circuit. This is not strictly true for PARALLEL circuits, however.

More to follow

19. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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We now pause for reflection

20. ### evilengineer New Member

Jan 3, 2013
13
0
Wow, what an amazing group I've stumbled upon here! I was not prepared for such thoughtful and thorough responses. I can't thank you all enough for your active involvement in my pursuit of understanding. Thank you, thank you!

MrChips: I was confused at first as my browser font makes the symbol for π look like a lower case N, but quickly realized it was Pi (which is tomorrows date, 3/14/15). After writing down your examples and graphing them out on the nomogram, the pattern is starting to stand out to me more, but it will take much more repetition and practice on my end before it becomes engrained as second nature. Thank you for illustrating it as such.

KL7AJ:
Opening up my copy of J Carr's 'secrets of RF circuit design' I find the formula: F = 1/2π√LC (pardon me if my notation is incorrect, I am unfamiliar with the correct way to rewrite (type) the formula). I am taking this formula into consideration as I continue to reach for an understanding.

So, and please bear with me here, with your example of 1H and 1F at 0.16(0.159)Hz, the reactance of both L & C is 1-ohm. Is this correct?

"is there any reason for any SPECIFIC values of L/C ratio?" Hmm. Not sure if I correctly understand what your asking but the first thing that comes to mind is that one would seek specific values for the L/C ratio depending on the type of circuit stage being designed and to reach a chosen impedance for matching the stages. I think I will let you give me another clue before I get too far off track with that question.

This is fun!!

studiot: "Since the scales are all log it could be used as a pattern to rescale any log-log paper by drawing ruled lines."
Aha, I see! This was what I was wondering, and have pleasantly received a more thorough lesson along the way. I hope I can take what i learn here and apply it to rescaling these log graphs. Very cool.

KL7AJ: "If ALL we had in our circuit was a pure resistance and pure reactance, we could pick any L/C ratio we like, and come up with a resonant circuit at our chosen frequency of interest.

However, in the real world, we either have a resistive load, into which we're trying to do real work....or we have imperfect components."

So, maybe I wasn't too far off with my answer to your first question? I think I see what you are getting at.

"Capacitors tend to be closer to pure components in most cases."
Interesting and new to me.

"For a simple LC series circuit, the value of reactance will determine the resonant circuits "Q" at resonance. Q is defined as the ratio of reactance to resistance. Therefore, we will find that a larger L/C ratio gives us a larger Q circuit. This is not strictly true for PARALLEL circuits, however."

Alright, I knew that 'Q' was sneaking up on me and I'm mighty excited and eager to start taking it into consideration. I have a GDO that I hope to utilize for measuring Q but I believe there may be other ways for measuring Q. I'll keep the test gear unplugged until I start to develop a more intuitive understanding of the nature of LC resonant circuits.

Okay, so does the reactance / impedance / frequency formula & the graph apply the same to both parallel and Series LC circuits? Do I need to worry about the difference between the two yet, as I am becoming more familiar with the relation between Z,XC,XL & Frequency?

I've been studying an article from Ham Radio Magazine, Feb 1977 on Bandspread calculation techniques, that I am hoping will give me a more thorough understanding of what it is I am seeking here.

I can't thank you guys/gals enough for taking time to communicate with me about such a fascinating and fun topic. I never expected such kind, enthuesiastic and informative replies and for this I am very grateful.

Last edited: Mar 13, 2015