Receiver Circuit Question -- What role does this antenna capacitor play?

[The Tortoise-Man]

Which role plays an additional capacity in a receiver circuit between the antenna and the matching-box part like in this example (found in https://www.frostburg.edu/personal/latta/ee/twinplex/schematic/twinplexschematic.html):

Is it necessary for this receiver circuit or just optional? What is it's proper usage?

 

[berkeman]

Is it necessary for this receiver circuit or just optional? What is it's proper usage?

That website appears to have good explanations of each part of the circuit (cool website, BTW). Is there a part of their explanations that you are having trouble with?

 

[Baluncore]

Is it necessary for this receiver circuit or just optional? What is it's proper usage?

What you call a matching box is actually a resonant tuned circuit that selects the frequency you want. If the tuned circuit is too heavily loaded, it will have a lower Q, so less sensitivity and less selectivity.

Both the antenna and the regeneration coil L2 are lightly coupled to the L1 tuned circuit. The series capacitor in the antenna circuit balances the coupling of the antenna input with feedback from the L2 winding. That circuit with the antenna coupling capacitor is suitable for a short indoor antenna.

If an external antenna is used it is necessary to provide a DC path to ground so as to discharge the static electricity that may build up. That would normally involve a tap or a third winding at the earthy end of the L1 coil.

By placing the regeneration coil L2 at the opposite end of L1 to the antenna coupling, radiation of the internal regeneration signal from the antenna is reduced.

 

[The Tortoise-Man]

That website appears to have good explanations of each part of the circuit (cool website, BTW). Is there a part of their explanations that you are having trouble with?

View attachment 290657

Unfortunately in the explanantions on this site I haven't found a satisfying explanation for the importance/ relevance of this this tagged capacity. The only part dealing with it marginaly says:

Antenna Coupling Capacitor:
The antenna coupling capacitor is a critical component in a regenerative receiver without an RF stage, like the Twinplex. In such a receiver, the antenna is an integral part of the regenerative detector, and for proper operation the coupling to the antenna must be easily adjustable. Increasing the capacitance increases the coupling and vise versa.

It is not really answered concretely there what the job of this capacitor is. Except maybe the last sentence I not fully understand: "Increasing the capacitance increases the coupling and vise versa." I guess by "Increasing the capacitance" is meant the capacitance of the antenna. As consequence this rises the coupling (= the resistence of the coupled capacitor, right?) But what is the reason to adjust there this capacitor? Does it preserves the circuit in certain situations from overloading?

 

[Baluncore]

"Increasing the capacitance increases the coupling and vise versa." I guess by "Increasing the capacitance" is meant the capacitance of the antenna.

The capacitance of the antenna is fixed by antenna geometry.
The coupling of the antenna to the tuned circuit is increased by increasing the coupling capacitance. That is why the coupling capacitor has a value adjustable from 2 pF to 18 pF.

 

[Tom.G]

A good answer to your question is on the same site at:
https://www.frostburg.edu/personal/latta/ee/twinplex/howtouse/twinplexhowtouse.html

(above found with:
https://www.google.com/search?&q=antenna+coupling+capacitor+in+regenerative+receiver)

Cheers,
Tom

 

[tech99]

The antenna has shunt resistance, and without the ant coupling cap this is connected across the resonant circuit. This resistance is in parallel with the dynamic resistance of the tuned circuit, and so it lowers the Q or resonant impedance of the resonant circuit, so reducing the gain to the extent that the circuit will not oscillate. It is essential for the circuit to be able to oscillate. The coupling cap has a transforming action, which I can describe later, which raises the antenna shunt resistance presented to the receiver. This raises the Q and allows the circuit to oscillate.
As C is reduced in value, the antenna shunt resistance is raised. The effect of this is easier oscillation but reduced signal strength, so a compromise is required. Generally the coupling cap can be very small, maybe even 1 pF, and most antennas will prevent oscillation if it is not used.

 

[alan123hk]

Is it necessary for this receiver circuit or just optional?

This so-called antenna coupling capacitor is of course necessary. This capacitor is not only used in super-regenerative receivers. Almost all types of high-frequency radio receivers, such as superheterodyne radio receivers, must add this capacitor to the actual circuit. Without this capacitor, the performance of the receiver may become very poor and unusable.

 

[DaveE]

That would normally involve a tap or a third winding at the earthy end of the L1 coil.

"the earthy end..."
Perfect, LOL. Because we all know "earth" is seldom really earth. I'd never heard that before, I hope it wasn't a typo. It's pretty much guaranteed that I'll steal this sometime.

 

[Baluncore]

It's pretty much guaranteed that I'll steal this sometime.

It is not a typo. I'll give it to you so you don't have to steal it.

I built the best ever incredible regenerative receiver, then a few years later gave it to a local ham when I left to study geology for 4 years. The earthy end... is the way I feel and think.

 

[tech99]

I have found that the antenna coupling capacitor is the best method. A coupling coil or tap has no means of easy adjustment and I have also found coil prone to unwanted resonances. The feedback coil should be at the ground end of the tuning coil to reduce capacitive coupling, but I don't think this will reduce radiation.
I have made some very good receivers of this type and I can give a lot of additional information if required. For instance, the grid capacitor may need to be much smaller - just a few pF.
By the way this circuit is for a regenerative detector and not a super regenerative detector.

 

[The Tortoise-Man]

So in summary the capacitor plays here the usual role of a capacitive coupling in the sense that it prevents the resonant circuit from possible external disturbative effects comming from antenna (like electrostatics) which could cause to stong DC's, which are bad for hypersensitive receivers. That's the point, right?

 

[alan123hk]

In my opinion, although different types of receivers may have different additional considerations and effects on this antenna coupling capacitor, its initial and most basic function is to maintain good selectivity of the receiver.

 

[Baluncore]

That's the point, right?

Not really.
The capacitor reactance is; Xc = –1 / (2·π·f·C); ohms, reactive. A coupling capacitor provides a lossless isolation between the antenna and the tuned circuit.
If the antenna, reaction coil and tuned circuit were not all isolated to some extent, then only the tuned circuit would be present, and the adjustment of the critical feedback operating point would not be possible.

DC in the antenna circuit is a quite separate issue. The antenna coupling capacitor should be made from metal with an air dielectric, on a ceramic mounting. A static buildup can then arc-over with an audible click each time, rather than destroying the insulation and shunting the capacitor with lossy combustion products that then destroy future performance.

You will appreciate an air dielectric with ceramic spacers once you have heard a crescendo rising to a scream, followed by the crack and then silence of a near lightning strike.

External antennas must have a DC path to discharge static. That is why they have an isolated antenna winding on the tuned circuit coil former, with ANT and GND terminals.

 

[The Tortoise-Man]

Not really.
The capacitor reactance is; Xc = –1 / (2·π·f·C); ohms, reactive. A coupling capacitor provides a lossless isolation between the antenna and the tuned circuit.
If the antenna, reaction coil and tuned circuit were not all isolated to some extent, then only the tuned circuit would be present, and the adjustment of the critical feedback operating point would not be possible.

DC in the antenna circuit is a quite separate issue. The antenna coupling capacitor should be made from metal with an air dielectric, on a ceramic mounting. A static buildup can then arc-over with an audible click each time, rather than destroying the insulation and shunting the capacitor with lossy combustion products that then destroy future performance.

You will appreciate an air dielectric with ceramic spacers once you have heard a crescendo rising to a scream, followed by the crack and then silence of a near lightning strike.

External antennas must have a DC path to discharge static. That is why they have an isolated antenna winding on the tuned circuit coil former, with ANT and GND terminals.

hmmm, maybe my mistake was that I wrongly assumed that the matching box only consists of the tuned circuit. Instead maybe I should think about the coupling capacitor also as part of matching box in light of the pronciple of electrical length?

Next attempt to understand it: Perhaps the main task of the coupling capacitor is to adapt the electrical length to the circuit with the antenna (which can no longer be physically changed) matching (en.wikipedia.org/wiki/Impedance_matching) in order to allow as little energy loss (= reflections) as possible?

The key to this seems to be that in order to be able to tap the maximum power by keeping the energy loss as minimal as possible (= perfect matching), the resonant waves in the tuned circuit must be related certain length ratio of the antenna length.

The physical antenna length cannot be changed, but its "electrical length" can be made longer/shorter by adding in series a coil / capacitor.

Is now my approach correct?

 

[tech99]

The receiver is designed so that the gain can be increased by positive feedback. We need the receiver to be able to just commence oscillation if the positive feedback is increased using the potentiometer. If we place a resistor across the tuned circuit, its losses can be canceled out by increasing the positive feedback. If the resistor is too low in value, the receiver cannot compensate and oscillation cannot be obtained. When we connect the antenna/ground across the tuned circuit it places resistance across the tuned circuit as I have described. Therefore the antenna resistance (considered as a shunt resistor) must be high in order to allow correct operation. The antenna resistance does not have to be matched to the circuit but must have a certain value, high enough that oscillation is easily obtained but low enough so that as much energy as possible is coupled from the antenna. There is an optimum antenna resistance, which for this circuit is not a matched resistance.
The antenna coupling capacitor is a resistance transforming device whose action I will now describe. Let us suppose that the antenna/ground has a resistance of 100 Ohms, a fairly typical value for a quarter wave wave wire and an Earth rod. The tuned circuit alone has a dynamic resistance of maybe 20k. For oscillation, the shunt resistance we are adding from the antenna must be in the order of several kilohms, say 10k, in order to maintain adequate gain for oscillation. The coupling capacitor can transform the 100 Ohms of the antenna up to 10k. Let us suppose the small coupling capacitor has a reactance of 1k. It has 100 Ohms antenna resistance Rs in series so it has a Q factor of X/Rs = 1000/100 = 10. Now a capacitor having a Q of 10, if hidden on a box, might either have series or shunt resistance. If shunt resistance, the value is very high. In this case Q =Rp/X
10 = Rp / 1000
Rp = 10,000
So the capacitor gives us a shunt resistance of 10k which is suitable for the tuned circuit to still oscillate.
The transformation also introduces some reactance across the tuned circuit, but a slight tuning adjustment easily removes this.
For more detailed information look for information on series to parallel conversion.

 

[The Tortoise-Man]

A nitpick: You used several times the formulation 'connect the antenna&ground/resistance across the tuned circuit'. Do you use it synonymously to 'connect in parallel' to the tuned citcuit or do you mean something else in this formulation?

 

[Baluncore]

Is now my approach correct?

With the RF amplifier of a normal receiver, your approach is probably correct.

The key to this seems to be that in order to be able to tap the maximum power by keeping the energy loss as minimal as possible (= perfect matching), the resonant waves in the tuned circuit must be related certain length ratio of the antenna length.

You really have made it difficult for yourself and us by picking a regenerative receiver as your example, something that must be tamed and tickled before you can squeeze the best performance from it.
With a regenerative receiver, perfect coupling between the resonant circuit and the antenna is not what is required. Perfect coupling would kill the resonance in the tuned circuit and so make the receiver deaf. Instead, you must experiment to find a compromise coupling capacitance that seems to work in an acceptable way, by not damping the resonance too much, while still gathering some RF energy. You then try to recover most of the loss by tickling the reaction control.

You used several times the formulation 'connect the antenna&ground/resistance across the tuned circuit'. Do you use it synonymously to 'connect in parallel' to the tuned citcuit or do you mean something else in this formulation?

Across, in parallel and shunt, all mean the same thing.

 

[The Tortoise-Man]

You really have made it difficult for yourself and us by picking a regenerative receiver as your example, something that must be tamed and tickled before you can squeeze the best performance from it.
With a regenerative receiver, perfect coupling between the resonant circuit and the antenna is not what is required. Perfect coupling would kill the resonance in the tuned circuit and so make the receiver deaf. Instead, you must experiment to find a compromise coupling capacitance that seems to work in an acceptable way, by not damping the resonance too much, while still gathering some RF energy. You then try to recover most of the loss by tickling the reaction control.

Maybe I should simplify or say better modularize the problem. Consider following part of a receiver circuit, where the we leave a concrete realization on the right hand part literally as "black box".

Say our goal is simply to minimize the energy loss of the signal which is provided to the right for further processing. And the basic question was at the beginning which role the capacitor C_1 concretely plays in this game?

So let's forget the complicated receiver circuit at the beginning and focus on that one:

Is then in this "toy example" the role of this capacitor exactly to change the "electrical length" of the antenna if the antenna is physically to long/short to optimally receive the waves having resonant wavelength with the LC-circuit.

Or has even in this toy example the capacitor C_1 another task?

 

[Baluncore]

Or has even in this toy example the capacitor C_1 another task?

Again, you are connecting the antenna across a resonant tuned circuit. The tuned circuit needs to have a high Q to be selective and sensitive. The coupling between the antenna and tuned circuit must therefore be light, and so cannot be optimised for maximum power transfer. That is why a small antenna coupling capacitor must be used.

 

[Vanadium 50]

Let me emphasize what @Baluncore said. You don't want efficiency. You want selectivity. You want to hear the station you want, and not everybody else. Efficiency is the last thing you want!

 

[The Tortoise-Man]

Again, you are connecting the antenna across a resonant tuned circuit. The tuned circuit needs to have a high Q to be selective and sensitive. The coupling between the antenna and tuned circuit must therefore be light, and so cannot be optimised for maximum power transfer. That is why a small antenna coupling capacitor must be used.

Ok, so our main goal is to reach high selectivity for
the tuned circuit (that's precisely the area surrounded by green
circle) and that's equivalent to requirement that it's
Q is high? (in details that's due to this relationship:
https://en.wikipedia.org/wiki/Q_factor#Relationship_between_Q_and_bandwidth)

(I haven't worked before with the concept of this factor Q and
my rudimentary understanding of it is that in a network the factor Q
can be associated to every swinging subsystem (like in our
case eg the tuned circuit) or more general to every
reactive component (https://en.wikipedia.org/wiki/Q_factor#Individual_reactive_components)
and it "measures" it's ability how underdamped it oscillates ;
is this interpretation of Q correct?)

If yes, let's continue. You wrote, that in order to keep Q of
the tuned circuit high the "coupling between the antenna and tuned
circuit must therefore be light", right?

1. What is the (formal) meaning of "light coupling"?
Can it be expressed in mathematical terms? (sorry, if the question
is too elementary, but such
expression I have never heard/read before)2. Why if we construct such "light coupling"
between the antenna and tuned circuit, the tuned circuit
consequently will have high Q? (and indeed that's what we want)

 

[Baluncore]

A1. Light coupling is when the load is more than Q times the resonant reactance.
A2. Q is higher when less energy is lost to the antenna radiation resistance.

On the back of an envelope.
An RF receiver designed for the band from 550 kHz to 1.6 MHz.
One channel, say a 20 kHz window at Fo = 1 MHz. Therefore Q = 1000 / 20 = 50.
At 1 MHz the tuning cap will have a value of about 200 pF.
Reactance Xc = -1 / ( TwoPi * Fo * C ) = -795.75 ohms reactive.
(So XL = -Xc and reactance is sum zero, the resonant inductor will have a fixed value ≈ 126 μH).
For a Q of 50, the parallel load should therefore be over 50 * 795.75 = 39.788 kohm.

A short wire antenna can be modeled as a resistance of about 377 ohms, on a good day.
That value needs to be increased by a factor of about 100 so it does not over-damp the tuned circuit, and kill the Q.
We can either wind a short antenna coupling coil (n/√100 turns) on one end of the tuning inductor;
Or we can insert a reactance of about 39.75 k in series with the antenna. That could be an antenna coupling capacitor with a value of Xc = -39.788 kohms.
C = -1 / ( TwoPi * Fo * Xc ) = 4.0 pF

 

[The Tortoise-Man]

A1. Light coupling is when the load is more than Q times the resonant reactance.
A2. Q is higher when less energy is lost to the antenna radiation resistance.

On the back of an envelope.
An RF receiver designed for the band from 550 kHz to 1.6 MHz.
One channel, say a 20 kHz window at Fo = 1 MHz. Therefore Q = 1000 / 20 = 50.
At 1 MHz the tuning cap will have a value of about 200 pF.
Reactance Xc = -1 / ( TwoPi * Fo * C ) = -795.75 ohms reactive.
(So XL = -Xc and reactance is sum zero, the resonant inductor will have a fixed value ≈ 126 μH).
For a Q of 50, the parallel load should therefore be over 50 * 795.75 = 39.788 kohm.

On A1: Which parameter of the load do you mean?
To make it clearer let make an intermediate step and consider the picture for the general case:

We have a source with impedance Z_S (= X_S + i Y_S with
resistance of the source X_S and reactance Y_S) and
similary for the load with impedance Z_L= X_L + i Y_L.

You wrote on definition of 'light coupling':

A1. Light coupling is when the load is more than Q times the resonant reactance.

And as far as I understand you correctly the coupling capacitor is then considered here as part of the source:
In our example the source consists of the antenna + coupling capacitor (considered
as 'single object' with impedance Z_S) and the load is the tuned circuit, right? Then the
'resonant reactance' is Y_S, but what do you mean by 'load' as numerical value
that you are going compare with Y_S?

My guess: do you mean maybe the amount |Z_L|?And as far as I understand you correctly the coupling capacitor is
then considered here as part of the source; so retrospectively
the source is antenna + coupling capacitor, I asked about the effect of.

 

[Baluncore]

You wrote on definition of 'light coupling':
A1. Light coupling is when the load is more than Q times the resonant reactance.

You are confusing the original source of the energy, with the greater energy circulating in the high Q tuned circuit. For Q analysis, the tuned circuit is the source, the antenna is a load.

A resonant circuit rings with the energy stored in the circuit. For this analysis, where the circulating energy came from is irrelevant, (it is the long term complex sum of historical regeneration and antenna signal energy). The important thing is where the circulating energy can go, and how long it takes the resonance to decay.

At the resonant frequency the reactance is sum zero. XL = -XC.
The resonant circuit can be loaded by resistance in two ways.
1. The series resistance Rs, of the resonant circuit components, Rs < XL/Q. That series component resistance was minimised during construction of the resonant reactors, so it can be ignored here.
2. The several connected parallel resistive loads, Rp > XL * Q.

We will consider only the external connections.
There are three loads on the tuned circuit.
1. The vacuum tube grid connection, which is very high impedance so only a minor loss.
2. The regeneration winding and circuit, which is reactive, so not a resistive loss.
3. The antenna connection, is here the most important load on the tuned circuit.
The coupling capacitor is essential to operation here because there is no primary antenna coupling winding on the tuned circuit.

 

[The Tortoise-Man]

You are confusing the original source of the energy, with the greater energy circulating in the high Q tuned circuit. For Q analysis, the tuned circuit is the source, the antenna is a load.

A resonant circuit rings with the energy stored in the circuit. For this analysis, where the circulating energy came from is irrelevant, (it is the long term complex sum of historical regeneration and antenna signal energy). The important thing is where the circulating energy can go, and how long it takes the resonance to decay.

Let me try to rephrase it (at first glance that sounds like an issue needs getting used to):
So you claim that if we analyse the Q of a circuit consisting of an antenna coupled to tuned circuit modeled by circuit from post #24 then it doesn't matter if we consider it as receiver or transmitter: the tuned circuit is always the source there, the antenna is the load, right?

And the coupling capacitor belongs then also the load, that is the antenna and the coupling cap in series form the load? Or am I wrong again?

 

[Baluncore]

So you claim that if we analyse the Q of a circuit consisting of an antenna coupled to tuned circuit modeled by circuit from post #24 then it doesn't matter if we consider it as receiver or transmitter: the tuned circuit is always the source there, the antenna is the load, right?

Yes. But for analysis of Q, the diagram in post #24 is labelled backwards with source and load.

It does not matter if the circulating energy in a resonator is increasing or decaying, it will take Q cycles to increase or decrease to within 4% of the final amplitude.

Most of the time it does not matter if it is a receiver or a transmitter being analysed. If it is a high power transmitter you must impedance match better for the frequency being transmitted, or components will be destroyed.

And the coupling capacitor belongs then also the load, that is the antenna and the coupling cap in series form the load? Or am I wrong again?

Correct.

 

[alan123hk]

Below is what a one tube regenerative radio receiver looks like for reference.
To give another example, this gentleman patiently explained the circuit diagram of his valve regenerative radio receiver, but I haven't listened to what he said in detail.
How to choose the best vacuum tube to make a regenerative radio seems to be a professional knowledge, but perhaps the more important question is where can we buy the tube and tube sockets we want. I believe that radios made of tubes always sound more comfortable than radios made of semiconductor devices, and the tube radio is more nostalgic.

 

[The Tortoise-Man]

Yes. But for analysis of Q, the diagram in post #24 is labelled backwards with source and load.

It does not matter if the circulating energy in a resonator is increasing or decaying, it will take Q cycles to increase or decrease to within 4% of the final amplitude.

Most of the time it does not matter if it is a receiver or a transmitter being analysed. If it is a high power transmitter you must impedance match better for the frequency being transmitted, or components will be destroyed.Correct.

It's getting clearer now. So in summary, if consider
our circuit modeled by picture in #24 after swapping
right with left side, so consisting of tuned circuit
as "source" with impedadance Z_S= X_S + i Y_S and
the antenna as "load" with impedance Z_L= X_L+i Y_L .

Finally, what is the essential role of the coupling capacitor?

How I understand it so far:
As you explained in #20 we want our circuit to be selective, so
formally can we archieve it if we make Q of the source
high, right? So we have to do something with our load.

Ok, then as far as I understand it correctly, we do it by adding a capacitor in series to the antenna aka load.
We obtain now a new "load" consisting of antenna + this capacitor, and therefore we obtain new load impedance Z_L= X_L+i Y_L simply as sum of the impedance of old load (=the antenna alone) +
the impedance of this coupling capacitor as "new modification".

Are my reasonings correct up to now?

Next, in A1 you wrote the mathematical conditions which we want to archieve by adding this capacitor. We want that the load is more than Q times the resonant reactance;

As far as I interstand it correctly, the "reconant reactance" is Y_S, ie the reactance of the source
(=tuned circuit), right?

The "load", what is it in terms of
Z_L, X_L, Y_L?

 

[Baluncore]

We have a source with impedance Z_S (= X_S + i Y_S with
resistance of the source X_S and reactance Y_S) and
similary for the load with impedance Z_L= X_L + i Y_L.

You really are confusing things by making notation soup.
Your post #24 is a foundation of sand.
Please stick to the standard electrical complex number notation. Z, R, X, Y, G, B, j.

An impedance is a complex resistance, Z = R + X j;
Where R is real resistance, and the imaginary X is reactance.
To identify the imaginary part we use a late j, not an early i.
That is because i tends to get confused with current; i1 = i 2 + i3 j.

The reciprocal of impedance is admittance, Y = 1 / Z.
Y = G + B j; where real G is the conductance, and the imaginary B is the susceptance.

Converting either way between the two involves the complex reciprocal of z = a + b j;
First compute the sum of squares, s = a² + b²; The reciprocal of z is then; y = (a/s) + (-b/s) j.

For a series circuit, convert all to impedances, then add.
For a parallel circuit, convert all to admittances, then add.

The general term for complex impedance or admittance is a hybrid term, immittance.

 

[DaveE]

The general term for complex impedance or admittance is a hybrid term, immitance.

OK, that is something you may read in books. However, no practicing EEs use it to my knowledge. Normally, it is just assumed that impedance and admittance are complex numbers. If the imaginary part is zero, impedance is called resistance (or impedance). If the real part is zero it is generally called capacitance or inductance, depending on the sign. Same for admittance and conductance. But honestly, it's all just called impedance, really.

immittance isn't wrong, it's just not really used.

 

[Baluncore]

immittance isn't wrong, it's just not really used.

I gave a succinct summary of the terms found in the field, along with the symbols used to identify them. The term immittance needed to be mentioned once, even if only for the sake of completeness.

I wonder then why you set out to confuse the issue with the argument that the term immittance should not be used nor mentioned, and that all admittances are really impedances. There is as much admittance in any ladder network as there is impedance. A ladder is fundamentally an immittance network. You can safely ignore admittance and immittance if you have no use for concepts that don't fit your way of thinking, but then you will not survive in circuit analysis.

I agree that most people don't need to know the term immittance. But anyone who knows how to use an Immittance Smith Chart, knows that immittance is NOT wrong. It has it's place.
https://www.antenna-theory.com/tutorial/smith/smithchartA.php

If the real part is zero it is generally called capacitance or inductance, depending on the sign.

But the imaginary ±Xj is not the capacitance nor the inductance, it is the frequency dependent reactance of the physical components. When you make an LC tuned circuit, the sum of the reactances or susceptances is zero at the resonant frequency, but both L and C are still there, often in parallel admittance.

 

[The Tortoise-Man]

You really are confusing things by making notation soup.
Your post #24 is a foundation of sand.
Please stick to the standard electrical complex number notation. Z, R, X, Y, G, B, j.

An impedance is a complex resistance, Z = R + X j;
Where R is real resistance, and the imaginary X is reactance.
To identify the imaginary part we use a late j, not an early i.
That is because i tends to get confused with current; i1 = i 2 + i3 j.

The reciprocal of impedance is admittance, Y = 1 / Z.
Y = G + B j; where real G is the conductance, and the imaginary B is the susceptance.

Converting either way between the two involves the complex reciprocal of z = a + b j;
First compute the sum of squares, s = a² + b²; The reciprocal of z is then; y = (a/s) + (-b/s) j.

For a series circuit, convert all to impedances, then add.
For a parallel circuit, convert all to admittances, then add.

The general term for complex impedance or admittance is a hybrid term, immittance.

The question is if what I wrote in #29 is
wrong in content or just causes confusion
due to usage of non standard notations?

If it makes it easier to read it with notations
you are suggesting, I can try to rewrite it.

If there are other fundamental errors except
this notation issue in #24 and the following
post, please call them by name.

If it's only due to bad notation, let go back to my concern in #29:
Our starting position was that we are going
to model our circuit consisting of a tuned circuit
and an antenna by image in #24.

As you said it's standard to to consider
tuned circuit as "source" and the antenna as "load".
The impedance of the source we call
Z_S= R_S +X_S j and the impedance of the load we call
Z_L= R_L +X_L j.
And what we want is to study what advantage does it bring by adding
a coupling capacitor between the antenna and the tunned
circuit.

As you said the main effect we want to archieve is
to make Q of the source high, right?

Therefore we want to
look how the Q of the source changes if we add a
capacitor ("the "coupling capacitor") in series to the antenna
(= load).

As far as understand it correctly when we add this capacitor
we have to treat it as a part of the new "load"
consisting of antenna + this capacitor, and therefore we
obtain new load impedance beeing the sum of the "old load" -
the antenna impedance Z_L= R_L +X_L j - and the
impedance of the added capacitor.

Next, as you already said we recall that making Q high means
that We want that the load is more than Q times the resonant
reactance X_S?

Now my questions are: Firstly, is what I have written up to now
correct?

And secoundly, as I already asked in #29, The "load",
what is the "load" here it in terms of Z_L, R_L, X_L?

Is my concern a bit clearer now?

 

[DaveE]

I wonder then why you set out to confuse the issue with the argument that the term immittance should not be used nor mentioned, and that all admittances are really impedances.

I didn't say immittance shouldn't be used. I said it seldom actually is used. So go for it, use it all you want. What some think is precision others may view as pedantry. I also find most EEs switch between impedance and admittance at a whim and choose the most convenient form at the moment. The need to refer to a function generalized as 'either impedance or admittance', without just choosing one, is very rare in my experience.

Also, yes, I agree, networks are usually a bit too complicated to summarize simply except as an impedance function (or equivalent).

In any case your reply was good, and my post was off target, confusing. Notation soup isn't helpful, but immittance can be left out of that recipe too.

 

[Baluncore]

Now my questions are: Firstly, is what I have written up to now
correct?

Yes.

As you said it's standard to to consider
tuned circuit as "source" and the antenna as "load".
The impedance of the source we call
Z_S= R_S +X_S j and the impedance of the load we call
Z_L= R_L +X_L j.

It is easier to read computer code or text like subscripts, without underline.
Zs = Rs + Xs j ; the source resonator.
Za = Ra + Xa j ; the antenna.

And secoundly, as I already asked in #29, The "load",
what is the "load" here it in terms of Z_L, R_L, X_L?

Xc, is the coupling capacitor reactance, which is in series with the antenna.
ZL = Ra + ( Xa + Xc ) j; the effective load impedance.
The magnitude of the load vector is then compared to the reactance of one component in the tuned circuit.