Impedance

Impedance definition: A circuit’s resistance and reactance combine to present opposition to alternating current. Impedance, denoted by the letter ‘Z’, is a measurement of resistance (R) to the electrical flow.

Impedance is an important concept in the study of electronics, and it is derived from the study of AC analysis. The resistance is measured in ohms. Impedance and resistance are the same in DC systems and are defined as the voltage that is present across any component divided by the current that flows through it (R = V/i). The formula of impedance is 

Where R = Resistance,

 XL = Inductive Reactance, 

XC = Capacitive Reactance.

Ohm’s law

According to Ohm’s Law, I = V/Z

For a pure resistor, 

 Z = R

Therefore, I = V/R

Here I and V are the effective or RMS values. 

Since the phase affects the impedance and the contributions of capacitors and inductors differ in phase from resistive components by 90 degrees, a process like a vector addition (phasors) is used to develop an expression for impedance.

Impedance Combination

The formula used to represent the impedance when a resistor and a capacitor are placed in series is found as stated below.

 Z = (R2 + X2)1/2

Properties of Impedance

• The frequency affects the impedance of a capacitor.
• At lower frequencies (ZC ≥ ∞ and f ≥  zero), a capacitor is bound to behave like an open circuit.
• At higher frequencies (ZC ≥  zero and f ≥  ∞), a capacitor is bound to behave like a short circuit.
• At intermediate frequencies, a capacitor’s impedance is given as ZC. 

Therefore, it can be said that because impedance is influenced by reactance (X) and resistance (R), it is also influenced by frequency (f), and the value of impedance varies with frequency.

Deriving the expression

• Impedance definition: A circuit’s resistance and reactance combine to present opposition to alternating current. The inductive and the capacitive reactance are frequency dependent. It means that the value of this reactance will change with the frequency. Now, suppose your circuit contains the resistive element and some reactive element, then the total resistance offered by the circuit is known as the impedance. 

• And it is denoted by the symbol of Z. The total impedance will be the summation of this resistive element and the reactive element. So, here, in this case, the total impedance will be equal to R+jwL. Now, a lot of times, it is also depicted in the polar form. It means that it has some finite magnitude as well as some finite phase. 

• Now the magnitude of this impedance can be given by this expression.

|Z|= (R2 + X2)1/2

  And the phase of this impedance can be found by this expression – 

 = tan -1(X/R)

• Now, similar to the resistance, this impedance is also a ratio of voltage and current. So for any particular network or circuit, if the impedance is represented like this, it means that the voltage will lead the current by some phase angle. The voltage and current signal ratio will give the magnitude of the impedance.

The Input Impedance

• Also represented as ZIn, the input impedance is seen by anything that is connected to a circuit or device’s input (for example, an amplifier). 

• It is the sum of all the resistance, capacitance, and inductance present inside the circuit or device which is linked to the input.

• In most cases, input impedances should be high, at least ten times that of the circuit (or component) sending the signal to the input.

• This guarantees that the input does not ‘overload’ the signal source, resulting in a significant reduction in signal intensity (voltage).

• The value of ZIn can range from tens of ohms (Ω) to a few thousand ohms (kilo-Ω k) to millions of ohms (Mega-Ω M) for bipolar and FET transistor circuits.

The output Impedance

• The output impedance is also represented as ZOUT. The output impedance is equivalent to a voltage source in series with an output impedance.

• Output impedances should typically be lower, less than a tenth of the load connected to the output.

• Since much of the signal’s voltage is lost inside the circuit, pushing current through the output impedance ZOUT, an output impedance that is too high will be unable to send a sufficiently strong signal to the load.

The Impedance with Low Output

• This case scenario is applicable when ZOUT << ZLOAD.

• Less voltage is lost in this scenario since the source voltage appears across the load.

• This is considered the best arrangement.

The Impedance with High output

• This case scenario is applicable when ZOUT >> ZLOAD.

• Most voltage is lost in this scenario since the output current is driven out through the output impedance.

• This is considered an unsatisfactory arrangement.

The Impedances that are Matched

• The output current is driven by the other half of VSOURCE, which appears across the load and is lost when it sends the output current through the output impedance.

• Since it supplies the highest power to the load, this arrangement is advantageous in particular cases (such as an amplifier that drives a loudspeaker).

• It’s worth noting that feeding the output current through ZOUT wastes an equal amount of power, resulting in a 50 percent efficiency.

CONCLUSION

Impedance works with the help of three major elements, namely inductor, capacitor, and resistor. This article gives an idea about the two types of impedance, i.e. the input impedance and the output impedance, and the kind of resistance they provide.

The relationship between voltage and current for an input that is sinusoidal is impedance. When connecting a loudspeaker to an audio system, the term impedance is usually expressed as a numeral of Ω written next to many sockets – input or output. In various technical areas, the term impedance refers to a resistance to work being done.