Author: Radoje Jankovic

Introduction

When solving, calculating and analyzing electrical circuits of alternating current of all voltage levels, industrial and radio frequencies, we almost often encounter the concept of impedance and admittance. In this article I will cover in detail almost everything about electrical impedances of all types in such a way that anyone can understand and easily solve any AC electrical circuit of any voltage level and frequency.

A. What is impedance?

In the simplest terms and understandable to everyone, imedance is a type of more or less complex electrical resistance in alternating current. A general graphical symbol for impedance is shown in Figure 1.

In Figure 2.a. a graphic symbol with letter symbols for complex electrical impedance, in Figure 2.b. is shown the graphic symbol for the same with markings in the polar form.

In alternating current electric circuits, the impedance can only be the ohmic resistance R, only the inductive resistance (XL) of an ideal coil of inductance L whose ohmic resistance can be neglected, or only the capacitive resistance (XC) or an ideal capacitor (C) with a capacity C also of negligible ohmic resistance which we will see in the next presentation.

B. Three Basic Types of Electrical Impedances-Ideal

If impedance Z consists of ohmic resistance R in ohms, its symbol and label look like in Figure 3.a. According to IEC standards, the graphic symbol from figure 3.a. is also a graphic symbol for ohmic (active) resistance, while symbol 3.b. also another form of graphic symbol for ohmic resistance R. Impedance, as well as all electrical quantities in a complex calculation, are marked with a bold letter Z, or the letter Z with a dash above the letter or below the letter.

When impedance Z consists of pure inductive resistance XL in ohms, its symbol and label look like in figure 4.a., while the symbol in figure 4.b. symbol for inductance coil L.

When impedance Z consists of pure capacitive resistance XC in ohms, its symbol and label look like in figure 5.a. while the symbol in Figure 5.b. designation for capacitor capacity C.

C) Four real impedances

In practice there are four real impedances, of which three are incomplete and one is complete impedance. These are:

– Inductive impedance graphically shown in Figure 6. It consists of an active ohmic resistor R and inductance coils L, ZL, respectively ZRL

– Capacitive impedance ZC graphically shown in Figure 7. It consists of an active ohmic resistor R and a capacitor of capacity C, i.e. ZRC

– The inductive-capacitive impedance ZX is shown graphically in Figure 8. It consists of a coil of inductance L and a capacitor of capacity C, i.e. ZLC. In practice, it is also called capacitive-inductive reactance.

– Finally, the third , the complete impedance consisting of an ohmic resistor R, an inductance coil L and a capacitor of capacity C, Figure 9., Z or ZRLC

The previous four real impedances have been discussed in the sense that they consist of only one electrical component each, the ohmic resistor R, the inductive coil L and the capacitor C. When in electrical circuit analyzes and practical calculations, each of these three main electrical components depending on its structures can consist of two or all three components in the appropriate configuration, and they must be taken into account during the appropriate calculations.

On the other hand, each electrical component can be connected to each other in series or in parallel.

In Figure 10.a1. and 10.a2. is shown the impedance consisting of one ohmic resistor R and one winding L which are connected in series and form one total impedance Z or ZRL.

In Figure 10.b1. and 10.b2. the same impedance is shown where ohmic resistance R and inductive resistance XL are ie. windings connected in parallel and which form one total impedance Z, i.e. ZRL.

In Figure 11.a1. and 11.a2. shown is the impedance consisting of one ohmic resistor R and one capacitor C, i.e. capacitive reactance XC which are connected in series forming one total impedance Z or ZRC.

In Figure 11.b1. and 11.b2. the same impedance is shown where the ohmic resistance R and the capacitive resistance XC are i.e. of capacitors C connected in parallel and forming one total impedance Z or ZRC.

In Figure 12.a1. and 12.a2. shown is the impedance consisting of one coil L of inductive resistance XL and one capacitor of capacity C, i.e. capacitive reactance XC which are connected in series making one total impedance Z or ZLC. This is actually the pure reactance X or the total reactance XT of the series connection of the coil and the capacitor.

In Figure 12.b1. and 12.b2. is shown the impedance where the coil L of inductive reactance XL and the condenser of capacity C of capacitive reactance XC are connected in parallel and which form one total impedance Z or ZLC or total reactance XT.

It should be emphasized here that with these coil and capacitor connections, the total impedance or reactance can be positive or negative depending on which component prevails in the total reactance value.

And so we arrived at the fourth and complete electrical impedance consisting of one ohmic resistor R, one coil L and one capacitor C which can be connected to each other in series or in parallel which can be clearly seen in Figure 13. and Figure 14.

D. Series impedances

In Figure 15.a. series connections  are shown;

– ideal ohmic resistors of different resistance values ​​RT – ZT (a1),

– ideal inductive resistances of different values ​​ZLT – XLT (a2) and

– ideal capacitive resistances – capacitive reactances ZCT – XCT (a3).

It should be emphasized that an unlimited number of the same electrical components can be connected in series.

In Figure 15.b. ordinal links are shown;

– ohmic resistors and inductive resistances (windings) that make up one total incomplete impedance ZRLT, resistive-inductive type (b1),

– ohmic resistors and capacitive resistances of capacitors that make up one total incomplete impedance ZRCT, capacitive-resistive type (b2),

– inductive and capacitive resistances – reactances (coils and capacitors) which also form one incomplete impedance ZLCT, but therefore form one complete – pure reactance XT, inductive – capacitive type (b3) and

– ohmic, inductive and capacitive resistances (ohmic resistors, windings and capacitors) that make up one complete electrical impedance ZT or ZRLCT.

E. Parallel impedances

Figure 16 shows parallel connections;

– ideal ohmic resistors of different resistance values ​​RT – ZT (a1),

– ideal inductive resistances of different values ​​ZLT – XLT (a2) and

– ideal capacitive resistances – capacitive reactances ZCT – XCT (a3).

It should be emphasized that an unlimited number of the same electrical components can be connected in parallel.

In Figure 17.a. parallel connections of ohmic resistors and inductive resistances (coils) are shown, which make up one total incomplete impedance ZRLT, resistive-inductive type.

In Figure 17.b. parallel connections of ohmic resistors and capacitive resistances of capacitors are shown, which form one total incomplete impedance ZRCT, capacitive-resistive type.

In Figure 17.c. parallel connections of inductive and capacitive resistances – reactances (coils and capacitors) are shown, which also form one incomplete impedance ZLCT, but therefore form one complete – pure reactance XT, inductive – capacitive type.

In Figure 17.d. parallel connections of ohmic, inductive and capacitive resistances (ohmic resistors, coils and capacitors) are shown, which make up one complete electrical impedance ZT or ZRLCT.

F. Combined impedance connections

In the case of mixed or combined connections of different types of electrical components connected in series or parallel, there are hundreds and thousands of combinations, of which I will show a few basic ones here.

Components (resistors, windings and capacitors) can be connected to each other in parallel groups of the same components but also of the same or different values ​​of resistance, inductance or capacity, and the groups are further connected in series with one or more of the same components.

Also, electrical components can be connected to each other in parallel groups with several different components, of the same or different values ​​of resistance, inductance or capacity, and groups connected in a series with one or more different components, again of the same or different values.

In Figure 18.a. Coils are shown using component graphic symbols of the same values ​​of inductance, i.e. inductive resistance, i.e. inductive reactance in a combined connection. Groups with parallel coils are connected in series with serially connected coils also of the same inductance value.

It should be emphasized here,

yes, even though the coils have the same inductance values ​​L, their impedances, i.e. inductive reactances have different values ​​due to the way they are connected to each other, which can be seen in Figure 18.b. Total inductive reactive resistance XLT ie inductive impedance ZLT is shown in Figure 18.c.

In Figure 19.a. Coils of different values ​​of inductance or inductive resistance are shown, i.e. inductive reactance in a combined connection. Groups with parallel windings connected in a series (string) with two, three or more coils  of different values ​​of inductance L.

In Figure 19.b. the equivalent calculation scheme of this group of inductive reactances after calculating their values ​​as well as the total reactance of the entire combination of inductances is presented.

In Figure 20.a. shown are capacitors of the same values ​​of capacity C, i.e. capacitive resistance, i.e. capacitive reactance in the combined connection, two and three of the same value of capacitor C connected to each other in parallel and then in series with one, two or more series capacitors.

In Figure 20.b. the equivalent calculation scheme of this group of capacitive reactances after calculating their values ​​as well as the total reactance of the entire combination of capacitances is presented.

In Figure 21.a. capacitors of different values ​​of capacity C, i.e. capacitive resistance, ie. capacitive reactance in the combined connection, two and three different values ​​of capacitor C connected in parallel and then in series with one, two or more series capacitors .

In Figure 21.b. the equivalent calculation scheme of this group of capacitive reactances after calculating their values ​​as well as the total reactance of the entire combination of capacitances is presented.

Figure 22.a. shows a combination of ohmic resistors R of different resistance values ​​and inductive coils of different inductance values ​​L. Shown are two parallel groups connected in series, with two series groups of resistors and coils of different resistance values ​​R and inductance L. Of course, there can be more than two components.

In Figure 22.b. the equivalent calculation scheme of this group of impedances after calculating their values ​​is shown, as well as the total impedance of the entire combination of these two electrical elements. The total impedance of the whole combination can be seen in Figure 22.c. Everything else is completely clear from the picture.

Figure 23.a. shows a combination of ohmic resistors R of different resistance values ​​and capacitors of different capacitance values ​​C. Shown are two parallel groups connected in series, with two series groups of resistors and capacitors of different resistance values ​​R and capacitance C. Of course, there can be more than two in groups components.

In Figure 23.b. the equivalent calculation scheme of this group of impedances after calculating their values ​​is shown, as well as the total impedance of the entire combination of these two electrical elements. The total impedance of the whole combination can be seen in Figure 22.c. Everything else is completely clear from the picture.

Figure 24.a. shows a combination of coils of different values ​​of inductance L and capacitors of different values ​​of capacitance C. Shown are two parallel groups connected in series, with two series groups of coils of different values ​​of inductance L and capacitor C. Of course, there can be more than two components in the groups.

In Figure 24.b. the equivalent calculation scheme of this group of impedances is shown, that is, in this case, the reactance after calculating their values, as well as the total reactance of the entire combination of these two electrical elements. It should be noted that certain reactances can be of a positive or negative character, depending on which of the two predominates. The same applies to the total reactance of this combination. The total impedance of the whole combination can be seen in Figure 24.c. Everything else is completely clear from the picture.

Figure 25.a. shows a combination of resistors, coils and capacitors of different values ​​of resistance R, inductance L and capacitance C. Three parallel groups are shown; RL, RC and LC which are connected in series with coil, capacitor and resistor, again of different values ​​of inductance L and capacitance C and ohmic resistance R. Of course, there can be more than two components in groups. In Figure 25.b. the equivalent calculation scheme of individual reactances of this combination is shown in Figure 25.c. calculation scheme of impedances, of which there are five in this combination, and at the end, picture 25.d. the total impedance of the whole combination with all three electrical elements, which means that ZT is the total impedance. Everything else is completely clear from the picture.

And at the end of this consideration of electrical impedances we have Figure 26.

Figure 26.a. shows a combination of resistors, coils and capacitors with different values ​​of resistance R, inductance L and capacitance C. Two parallel RLC and two series RLC groups are shown. It is clear here that it is about four complete electrical impedances because they are made up of three main electrical components of resistor R, voltage of inductance L and capacitor of capacity C. In Figure 26.b. the equivalent calculation scheme of individual reactances of this combination is shown in Figure 26.c. the calculation scheme of the impedances of which there are four in this combination, and at the end, picture 26.d. the total impedance of the whole combination with three electrical elements each, which means that ZT is the total impedance. Everything else is completely clear from the picture.

And, let’s conclude!

Plain, clear, simple, understandable for everyone from student to professional.