# Impedance Graph Paper - Easy To Use

#### KL7AJ

Joined Nov 4, 2008
2,229
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.
Simply put, "Q" of a resonant circuit tells you how sharply tuned the circuit is. It will also tell you the amount of voltage increase at the junction of L and C.
If you have SPICE, you can model this simply. Wire up an ac voltage source, an inductor, a capacitor, and a resistor. Next put a voltage probe at the junction of L/C, which would be node 2. Run an AC sweep test. The voltage you see at node 2 will be your supply voltage times reactance/resistance, or supply voltage times Q. This tells you how much voltage step up you can have in a resonant circuit.

But don't take SPICE's word for it! Build the circuit and see!
Eric

#### MrChips

Joined Oct 2, 2009
31,087
Lots of questions with lots of answers.

Take time-constant tau = RC as an example. For a desired value of tau you can come up with an infinite number of combinations of R and C. So how does one choose?

For one thing, there will be a restricted range of R.
If R is too low, it looks like a short circuit which results in high current.
If R is too large, it looks like an open circuit.

Hence in an RC timing circuit such as one that you will find in a 555 timer circuit, R will be limited to a range from about 1k to 20kΩ. With a CMOS 555 timer you can push the upper limit much higher.

Electrolytic capacitors are not reliable for timing or frequency dependent circuits. Hence if the calculation demands capacitances larger than 1μF you then have to reconsider the other variables in order to bring the capacitance value into a range comfortably covered by non-electrolytic capacitors.

The Q-factor of an RCL circuit is inversely proportional to R. Large R gives low Q. Small R gives high Q.
Hence if you want a narrow band pass filter or a sharp notch filter, you want high Q and hence low R.
R is not just a third component. The internal resistance of the inductor in particular has to be taken into account. A high value inductance will be accompanied with high internal resistance. Hence you want to keep the inductance low and the internal resistance low by using an inductor with heavier gauge wire.

#### MrChips

Joined Oct 2, 2009
31,087
Yes, I have never seen that impedance graph paper before though I have seen similar charts.

It was fun playing with those example numbers on the chart. Then I went and charted the L and C value from by crystal radio and sure enough the resonant frequencies were bang on or close enough.

L = 100μH
C = 200pF
f = 1100kHz

L = 100μH
C = 400pF
f = 800kHz

#### studiot

Joined Nov 9, 2007
4,998
Yes, I have never seen that impedance graph paper before though I have seen similar charts.

I know I certainly can

#### evilengineer

Joined Jan 3, 2013
13
"If you have SPICE, you can model this simply."

This has been a priority for me. I have worked with some SPICE in the past and EveryCircuit on the android, but have very restricted hard drive space at the moment (all my computers come from dumpsters) and am looking for an option for simulating RF circuits. Chris Gammel recommended LTSpice to me. I also installed QUCS on my linux box but have only scratched the surface. I am open to suggestions for a SPICE program that doesn't require too much hard drive space.

I a few hours a week with an iron & scope probe in my hand. The rest of the time is spent with a pen, paper, calculator and my collection of ebooks & zines like sprat, hotiron, qrpp, etc. I would certainly like to add time using a simulator to my regime. I understand that things can be much different in practice than they are when simulated, which is a good reason for good RF construction practices.

-
"Take time-constant tau"
I have not heard of tau before. I'm familiar with RC time constants and how 1m-ohm times 1uF = 1 second.

-

"So how does one choose?
For one thing, there will be a restricted range of R.
If R is too low, it looks like a short circuit which results in high current.
If R is too large, it looks like an open circuit."

well explained, this makes perfect sense.

-

"Electrolytic capacitors are not reliable for timing or frequency dependent circuits."
Does this come back to what Eric said earlier? "Capacitors tend to be closer to pure components in most cases...except for electrolytics"

-

"Hence if the calculation demands capacitances larger than 1μF you then have to reconsider the other variables in order to bring the capacitance value into a range comfortably covered by non-electrolytic capacitor"

Not to get too far off track, but are there any practical reasons why one couldn't just parallel non-lytics to get to the same high value?

-

"The Q-factor of an RCL circuit is inversely proportional to R. Large R gives low Q. Small R gives high Q."

Is this the same principal as when one "spoils the Q" of an inductor, perhaps acting as an RFC, with a resistor placed in series with it? I've seen this in various RF circuits. I'm very excited to learn about Q and how knowing it can help me make the decisions needed to design RF stages.

-

"R is not just a third component. The internal resistance of the inductor in particular has to be taken into account. A high value inductance will be accompanied with high internal resistance."
I have been exposed to these models of components in Wes Hayward's, W7ZOI, books and will pay particularly more attention to them now. I like how you explained that R isn't just a third component, its part of the inductors model. I wasn't aware that the higher value inductance equates to higher resistance. I was thinking more about the length of the leads, but it makes good sense that R would increase with L. Please, tell me if I am off with my reasoning here, but would it be innacurate to say that it's true because: the more windings the inductor had, the larger the inductance would be and the large the resistance would be? or is there a much more complicated reason for this?

This is SO exciting to me! Please pardon that it can take me a day to respond, I hope that doesn't "Spoil the Q" of our conversation but I have a few personal matters in life that can make it difficult to get back to this great message board as often & quickly as I would like.

-

I have a relevant situation that I hope to address with this conversation once time permits me. It has to do with the Bandspread technique article and how I am not using it correctly. I am learning how I am using it incorrectly thanks to this conversation! What came of my attempt to find the capacitance values to cover 7-7.3MHz, resulted in requiring an inductance of 0.1uH. And I need to learn how and why I need to go about this differently. I do not want to get too off topic on this great thread though, so perhaps it needs to be saved for a new post.

Thanks again, to each of you, for taking time to teach me! This is so thrilling to me. I don't often reach out with questions, but I am finding that it is essential if I am going to continue on this path of learning.

#### studiot

Joined Nov 9, 2007
4,998
In electrics we add the further dimension electric current, A, to the familiar mass (M), length (L) and time (T) from mechanics.

In this scheme the dimensions of

Resistance are $$M{L^2}{T^{ - 3}}{A^{ - 2}}$$

and Capacitance $${M^{ - 1}}{L^{ - 2}}{T^4}{A^2}$$

Multiplying these together we are left with a single T (time).

So the product of resistance and capacitance has the dimension of time, which we measure in seconds.

This product has been granted the symbol tau, which is a Greek Letter. We employ the lower case, $$\tau$$

Tau is connected to frequency by the equation

frequency in hertz, $$f = 2\pi \tau$$

In each period, tau, the voltage in an RC network will reach a point approximately 2/3 of the way between the value at the beginning of the period and the eventual endpoint of the rise or decay.

#### KL7AJ

Joined Nov 4, 2008
2,229
"If you have SPICE, you can model this simply."

This has been a priority for me. I have worked with some SPICE in the past and EveryCircuit on the android, but have very restricted hard drive space at the moment (all my computers come from dumpsters) and am looking for an option for simulating RF circuits. Chris Gammel recommended LTSpice to me. I also installed QUCS on my linux box but have only scratched the surface. I am open to suggestions for a SPICE program that doesn't require too much hard drive space.

I a few hours a week with an iron & scope probe in my hand. The rest of the time is spent with a pen, paper, calculator and my collection of ebooks & zines like sprat, hotiron, qrpp, etc. I would certainly like to add time using a simulator to my regime. I understand that things can be much different in practice than they are when simulated, which is a good reason for good RF construction practices.

-
"Take time-constant tau"
I have not heard of tau before. I'm familiar with RC time constants and how 1m-ohm times 1uF = 1 second.

-

"So how does one choose?
For one thing, there will be a restricted range of R.
If R is too low, it looks like a short circuit which results in high current.
If R is too large, it looks like an open circuit."

well explained, this makes perfect sense.

-

"Electrolytic capacitors are not reliable for timing or frequency dependent circuits."
Does this come back to what Eric said earlier? "Capacitors tend to be closer to pure components in most cases...except for electrolytics"

-

"Hence if the calculation demands capacitances larger than 1μF you then have to reconsider the other variables in order to bring the capacitance value into a range comfortably covered by non-electrolytic capacitor"

Not to get too far off track, but are there any practical reasons why one couldn't just parallel non-lytics to get to the same high value?

-

"The Q-factor of an RCL circuit is inversely proportional to R. Large R gives low Q. Small R gives high Q."

Is this the same principal as when one "spoils the Q" of an inductor, perhaps acting as an RFC, with a resistor placed in series with it? I've seen this in various RF circuits. I'm very excited to learn about Q and how knowing it can help me make the decisions needed to design RF stages.

-

"R is not just a third component. The internal resistance of the inductor in particular has to be taken into account. A high value inductance will be accompanied with high internal resistance."
I have been exposed to these models of components in Wes Hayward's, W7ZOI, books and will pay particularly more attention to them now. I like how you explained that R isn't just a third component, its part of the inductors model. I wasn't aware that the higher value inductance equates to higher resistance. I was thinking more about the length of the leads, but it makes good sense that R would increase with L. Please, tell me if I am off with my reasoning here, but would it be innacurate to say that it's true because: the more windings the inductor had, the larger the inductance would be and the large the resistance would be? or is there a much more complicated reason for this?

This is SO exciting to me! Please pardon that it can take me a day to respond, I hope that doesn't "Spoil the Q" of our conversation but I have a few personal matters in life that can make it difficult to get back to this great message board as often & quickly as I would like.

-

I have a relevant situation that I hope to address with this conversation once time permits me. It has to do with the Bandspread technique article and how I am not using it correctly. I am learning how I am using it incorrectly thanks to this conversation! What came of my attempt to find the capacitance values to cover 7-7.3MHz, resulted in requiring an inductance of 0.1uH. And I need to learn how and why I need to go about this differently. I do not want to get too off topic on this great thread though, so perhaps it needs to be saved for a new post.

Thanks again, to each of you, for taking time to teach me! This is so thrilling to me. I don't often reach out with questions, but I am finding that it is essential if I am going to continue on this path of learning.
D0wload AIMSpice...it's lean and mean....It's just missing the graphical interface...but you know how to write Net files don't you?

#### atferrari

Joined Jan 6, 2004
4,798

#### KL7AJ

Joined Nov 4, 2008
2,229
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.
Here's a family of curves of different Qs for the same resonant frequency.

#### Attachments

• 326.8 KB Views: 42

#### KL7AJ

Joined Nov 4, 2008
2,229
Hmmm...I hope this thread hasn't entered a dead end because I was just getting started.

#### t_n_k

Joined Mar 6, 2009
5,455
Hmmm...I hope this thread hasn't entered a dead end because I was just getting started.
Unfortunately, that is occasionally the case on AAC. There's a thread actually worth following to a useful conclusion and inexplicably interest wanes.

#### evilengineer

Joined Jan 3, 2013
13
I got distracted by spice, its a lot to take in.

Still trying to find the easiest way to rewrite the nomographs in my book for higher frequencies. It was explained to me very well, I am just not that confident in my math skills.

Sorry for the long delays. Life can be a very demanding hobby.

#### evan_wang

Joined Apr 27, 2015
7
this software is very easy to calculate the impedance control .

#### Attachments

• 448.3 KB Views: 18