# Wave amplitude and frequency relationship to impedance

### Impedance in the Frequency Domain | Signal Integrity, Impedance and Electrical Models | InformIT In radio engineering and telecommunications, standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. Impedance mismatches result in standing waves along the transmission line, The SWR can as well be defined as the ratio of the maximum amplitude to. Transverse Sinusoidal Waves • The Intensity, Impedance and Pressure Amplitude of a Wave • Intensity Level and decibel scale • Hearing Loss. Electronics Tutorial about Harmonics and Harmonic Frequency. In an AC circuit, a resistance behaves in exactly the same way as it does in a DC circuit. by “adding” together a series of sine wave frequencies known as “Harmonics”. but also on the phase relationship between the fundamental or base frequency and.

Equation This says the current amplitude will increase with frequency, even if the voltage amplitude stays constant. The higher the frequency, the larger the amplitude of the current through the capacitor. This suggests the impedance of a capacitor will decrease with increasing frequency. The impedance of a capacitor is calculated from: Equation Here is where it gets confusing. This ratio is easily described using complex math, but most of the insight can also be gained from sine and cosine waves. All the important information is here. As the angular frequency increases, the impedance of a capacitor decreases. This says that even though the value of the capacitance is constant with frequency, the impedance gets smaller with higher frequency.

We see this is reasonable because the current through the capacitor will increase with higher frequency and hence its impedance will be less. The phase of the impedance is the phase shift between a sine and cosine wave, which is —90 degrees. When described in complex notation, the —90 degree phase shift is represented by the complex number, —i. For most of the following discussion, the phase adds more confusion than value and will generally be ignored.

A real decoupling capacitor has a capacitance of 10 nF. What is its impedance at 1 GHz? First, we assume this capacitor is an ideal capacitor. This is a very small impedance. If the real decoupling capacitor behaved like an ideal capacitor, its impedance would be about 10 milliOhms at 1 GHz.

Of course, at lower frequency, its impedance would be higher. At 1 Hz, its impedance would be about 16 MegaOhms. Let's use this same frequency-domain analysis with an inductor.

When we apply a sine wave current through an inductor, the voltage generated is: Equation This says that for a fixed current amplitude, the voltage across an inductor gets larger at higher frequency. It takes a higher voltage to push the same current amplitude through an inductor.

This would hint that the impedance of an inductor increases with frequency.

## Electrical impedance

Using the basic definition of impedance, the impedance of an inductor in the frequency domain can be derived as: Equation The magnitude of the impedance increases with frequency, even though the value of the inductance is constant with frequency. It is a natural consequence of the behavior of an inductor that it is harder to shove AC current through it with increasing frequency.

In a real decoupling capacitor, there is inductance associated with the intrinsic shape of the capacitor and its board-attach footprint. A rough estimate for this intrinsic inductance is 2 nH.

We really have to work hard to get it any lower than this.

## Acoustic impedance, intensity and power

What is the impedance of just the series inductance of the real capacitor that we will model as an ideal inductor of 2 nH, at a frequency of 1 GHz? When it is in series with the power and ground distribution and we want a low impedance, for example less than 0.

How does this compare with the impedance of the ideal-capacitor component of the real decoupling capacitor? In the last problem, the impedance of the ideal capacitor element at 1 GHz was 0. The impedance of the ideal inductor component is more than times higher than this and will clearly dominate the high-frequency behavior of a real capacitor. We see that for both the ideal capacitor and inductor, the impedance in the frequency domain has a very simple form and is easily described.

This is one of the powers of the frequency domain and why we will often turn to it to help solve problems. The value of the resistance, capacitance, and inductance of ideal resistors, capacitors, and inductors are all constant with frequency. For the case of an ideal resistor, the impedance is also constant with frequency. However, in the latter case, the feed line still has a high SWR present, with the resulting increased feed line losses unmitigated. The magnitude of those losses are dependent on the type of transmission line, and its length. They always increase with frequency. For example, a certain antenna used well away from its resonant frequency may have an SWR of 6: For a frequency of 3. However the same 6: Certain types of transmissions can suffer other negative effects from reflected waves on a transmission line. Analog TV can experience "ghosts" from delayed signals bouncing back and forth on a long line.

FM stereo can also be affected and digital signals can experience delayed pulses leading to bit errors. Whenever the delay times for a signal going back down and then again up the line are comparable to the modulation time constants, effects occur.

For this reason, these types of transmissions require a low SWR on the feedline, even if SWR induced loss might be acceptable and matching is done at the transmitter. Methods of measuring standing wave ratio[ edit ] Slotted line. The probe moves along the line to measure the variable voltage. SWR is the maximum divided by the minimum voltage Many different methods can be used to measure standing wave ratio. The most intuitive method uses a slotted line which is a section of transmission line with an open slot which allows a probe to detect the actual voltage at various points along the line.

This method is used at VHF and higher frequencies. At lower frequencies, such lines are impractically long. Directional couplers can be used at HF through microwave frequencies. Some are a quarter wave or more long, which restricts their use to the higher frequencies. Other types of directional couplers sample the current and voltage at a single point in the transmission path and mathematically combine them in such a way as to represent the power flowing in one direction.

### Lecture 14 (Waves, Wave Equation and Intensity)

Other types use a single coupler which can be rotated degrees to sample power flowing in either direction. Unidirectional couplers of this type are available for many frequency ranges and power levels and with appropriate coupling values for the analog meter used. A directional wattmeter using a rotatable directional coupler element The forward and reflected power measured by directional couplers can be used to calculate SWR.

The computations can be done mathematically in analog or digital form or by using graphical methods built into the meter as an additional scale or by reading from the crossing point between two needles on the same meter. The above measuring instruments can be used "in line" that is, the full power of the transmitter can pass through the measuring device so as to allow continuous monitoring of SWR. Other instruments, such as network analyzers, low power directional couplers and antenna bridges use low power for the measurement and must be connected in place of the transmitter.