# Bandwidth and frequency relationship to impedance

### Q Factor and Bandwidth of a Resonant Circuit | Resonance | Electronics Textbook

The "impedance bandwidth" is just the ordinary bandwidth of the antenna. Normally this is defined as the range of frequencies over which the return loss is . Bandwidth is the difference between the upper and lower frequencies in a continuous band of A graph of a band-pass filter's gain magnitude, illustrating the concept of −3 dB bandwidth at a For either, a set of criteria is established to define the extents of the bandwidth, such as input impedance, pattern, or polarization. In electronics, impedance matching is the practice of designing the input impedance of an In simple cases (such as low-frequency or direct-current power transmission) Such an impedance bridging connection also minimizes distortion and Impedance matching networks are designed with a definite bandwidth, take.

This maximum-voltage connection is a common configuration called impedance bridging or voltage bridging, and is widely used in signal processing. In such applications, delivering a high voltage to minimize signal degradation during transmission or to consume less power by reducing currents is often more important than maximum power transfer.

In older audio systems reliant on transformers and passive filter networks, and based on the telephone systemthe source and load resistances were matched at ohms. One reason for this was to maximize power transfer, as there were no amplifiers available that could restore lost signal.

Another reason was to ensure correct operation of the hybrid transformers used at central exchange equipment to separate outgoing from incoming speech, so these could be amplified or fed to a four-wire circuit. Most modern audio circuits, on the other hand, use active amplification and filtering and can use voltage-bridging connections for greatest accuracy.

## Q Factor and Bandwidth of a Resonant Circuit

Strictly speaking, impedance matching only applies when both source and load devices are linear ; however, matching may be obtained between nonlinear devices within certain operating ranges. Impedance-matching devices[ edit ] Adjusting the source impedance or the load impedance, in general, is called "impedance matching". There are three ways to improve an impedance mismatch, all of which are called "impedance matching": Given a source with a fixed voltage and fixed source impedance, the maximum power theorem says this is the only way to extract the maximum power from the source.

Given a transmission line source with a fixed source impedance, this "reflectionless impedance matching" at the end of the transmission line is the only way to avoid reflecting echoes back to the transmission line. Devices intended to present an apparent source resistance as close to zero as possible, or presenting an apparent source voltage as high as possible. This is the only way to maximize energy efficiency, and so it is used at the beginning of electrical power lines. Such an impedance bridging connection also minimizes distortion and electromagnetic interference ; it is also used in modern audio amplifiers and signal-processing devices.

There are a variety of devices used between a source of energy and a load that perform "impedance matching". To match electrical impedances, engineers use combinations of transformersresistorsinductorscapacitors and transmission lines.

These passive and active impedance-matching devices are optimized for different applications and include balunsantenna tuners sometimes called ATUs or roller-coasters, because of their appearanceacoustic horns, matching networks, and terminators.

Transformers[ edit ] Transformers are sometimes used to match the impedances of circuits. A higher value for this figure of merit corresponds to a more narrow bandwith, which is desirable in many applications.

### nickchinlund.info - Bandwidth

More formally, Q is the ratio of power stored to power dissipated in the circuit reactance and resistancerespectively: This formula is applicable to series resonant circuitsand also parallel resonant circuits if the resistance is in series with the inductor.

This is the case in practical applications, as we are mostly concerned with the resistance of the inductor limiting the Q. This is correct for a large value of R in parallel with C and L. Our formula is correct for a small R in series with L. In a parallel resonant circuit, current through L or C is Q times the total applied current. Series Resonant Circuits A series resonant circuit looks like a resistance at the resonant frequency.

The impedance is also at a minimum at resonance. Figure below Below the resonant frequency, the series resonant circuit looks capacitive since the impedance of the capacitor increases to a value greater than the decreasing inductive reactance, leaving a net capacitive value. Above resonance, the inductive reactance increases, capacitive reactance decreases, leaving a net inductive component.

At resonance the series resonant circuit appears purely resistive. Below resonance it looks capacitive. Above resonance it appears inductive. Current is maximum at resonance, impedance at a minumum. Current is set by the value of the resistance. Above or below resonance, impedance increases. Impedance is at a minumum at resonance in a series resonant circuit.