# Understanding RF & Microwave Specifications - Part II

Publish Date: Oct 18, 2008 | 23 Ratings | 3.87 out of 5 |  PDF

## Overview

This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series teaches you a specific topic of common measurement applications by explaining the theory and giving practical examples. This tutorial covers the second part of RF and microwave specifications.

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page, or for more RF tutorials, refer to the NI RF Fundamentals Main subpage.

### 1. Voltage Standing Wave Ratio (VSWR)

Voltage standing wave ratio (VSWR) is the ratio of reflected-to-transmitted waves. Any impedance mismatches along a transmission line causes the propagating signals to partially reflect. The impedance difference determines the reflection magnitude. The length of a mismatched section determines the lowest signal frequencies that reflect from the section. VSWR is a measure of that signal reflection.

When an incident sine wave enters the switch module, some of the signal reflects down the line. This reflected wave interferes with the incident wave. VSWR is the ratio of maximum to minimum amplitude in the resulting interference wave, as shown in the following formula:

where p is the reflection coefficient. Reflections can also be represented as a logarithmic ratio of the reflected signal to the input signal. This ratio is called return loss:

 RL (dB) = 10 log (PIN/PREFLECTED) = 20 log (VIN/VREFLECTED) = –20 log (VREFLECTED/VIN) = –20 log |p|

### 2. Frequency Response (Flatness)

Frequency response is the gain and phase response  of a circuit or other unit under test (UUT) at all frequencies of interest. Although the formal definition of frequency response includes both the gain and phase, in common usage, the frequency response often implies only the gain (magnitude).

The frequency response , shown below, is defined as the inverse fast Fourier transform (FFT) of the impulse response of a system.

Frequency response measurements require the excitation of the UUT with energy at all relevant frequencies. The fastest way to perform the measurement is to use a broadband excitation signal to excite all frequencies simultaneously, and then use FFT techniques to measure the frequency response magnitude at all these frequencies at the same time. Noise and non-linearity is best minimized by using random noise excitation, but short impulses or rapid sweeps (chirps) may also be used.

When the resolution bandwidth of interest is less than about 100 kHz, the fastest way to measure the frequency response functions is to use FFT-based techniques.

The book Random Data: Analysis & Measurement Procedures by Julius S. Bendat and Allan G. Piersol (Wiley-Interscience, 2000), is considered a definitive work on the error estimation techniques for the various classes of measurements. In our definition, we used the mathematical conventions and symbols Bendat and Piersol use.

### 3. Modulation Error Ratio (MER)

The modulation error ratio (MER) is a measure of the signal-to-noise ratio (SNR) in a digitally modulated signal. Like SNR, MER is usually expressed in decibels (dB). MER over number of symbols N is defined as:

where
is the I component of the j-th symbol received
is the Q component of the j-th symbol received
is the ideal I component of the j-th symbol received and
is the ideal Q component of the j-th symbol received.

### 4. Error Vector Magnitude (EVM)

Error vector magnitude (EVM) is a measurement of demodulator performance in the presence of impairments. The measured symbol location obtained after decimating the recovered waveform at the demodulator output are compared against the ideal symbol locations. The root-mean-square (RMS) EVM and phase error are then used in determining the EVM measurement over a window of N demodulated symbols.

As shown in Figure 1 below, the measured symbol location by the demodulator is given by w. However, the ideal symbol location (using the symbol map) is given by v. Therefore, the resulting error vector is the difference between the actual measured and ideal symbol vectors, that is, e=wv. The error vector e for a received symbol is graphically represented as follows:

Figure 1. Graphical Representation of Error Vector

In Figure 1,
v is the ideal symbol vector,
w is the measured symbol vector,
wv is the magnitude error,
θ is the phase error,
e=wv) is the error vector, and
e/v is the EVM.

This quantifies, but does not necessarily reveal, the nature of the impairment. To remove the dependence on system gain distribution, EVM is normalized by |v|, which is expressed as a percentage. Analytically, RMS EVM over a measurement window of N symbols is defined as

where
is the I component of the j-th symbol received,
is the Q component of the j-th symbol received,
is the ideal I component of the j-th symbol received,
is the ideal Q component of the j-th symbol received.

EVM is related to the MER and ρ, where ρ measures the correlation between the two signals. EVM and MER are proportional.

### 5. Third-Order Intercept (TOI)

The third order intercept (TOI) point is the theoretical level at which the third-order harmonic distortion component has the same power level as the fundamental tone. In practice, an amplifier compresses the signal, and the TOI point may never be reached in practice. This is a useful expression of the maximum signal level for RF circuits. The higher the TOI, the better.

### 6. Relevant NI Products

Customers interested in this topic were also interested in the following NI products:

### 7. Conclusions

This document is meant to provide a brief overview of the basics of RF and microwave specifications. Learn more about RF and microwave specifications in part I of this document.

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page, or for more RF tutorials, refer to the NI RF Fundamentals Main subpage.

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