Fundamentals

Resolution of Discrete Fourier Transform

In the previous post we had introduced the Discrete Fourier Transform (DFT) as a method to perform the spectral analysis of a time domain signal. We now discuss an important property of the DFT, its spectral resolution i.e. its ability to resolve two signals with similar spectral content. Initially one might think that increasing the sampling frequency would increase the spectral resolution but this totally incorrect. In fact if the sampling frequency is increased, keeping the number of time domain samples to be the same, the resolution actually decreases. So how do we calculate the spectral resolution. One simple way is […]

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Fundamentals

Discrete Fourier Transform

Discrete Fourier Transform or DFT is a mathematical operation that transforms a time domain signal to frequency domain. It is usually implemented using the Fast Fourier Transform (FFT). The computational complexity of the DFT is N2 whereas its (N)log2N for the FFT, where N is the number of samples of the the time domain signal. Mathematically, the DFT is written as and this operation can be easily implemented in MATLAB as shown below. clear all close all fm=100; fs=1000; Ts=1/fs; N=1024; t=0:Ts:(N-1)*Ts; x=cos(2*pi*fm*t); W=exp(-j*2*pi/N); n=0:N-1; for k=0:N-1 X(k+1)=sum(x.*(W.^(k*n))); end plot((0:k)/N,abs(X)) xlabel (‘Normalized Frequency’) ylabel (‘X’) The DFT of the cosine […]

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LTE, WCDMA

Inside Qualcomm Snapdragon S4

We have previously looked at the antennas inside a cell phone. Now we look at another important component of a cell phone; the mobile station modem (MSM). One of the most popular MSM in cell phones today is the Qualcomm Snapdragon S4. The details of this MSM are given in the table below. As can be seen from the above table this small chipset (can easily fit on a fingertip) packs a punch as far as processing power is concerned. It supports a number of wireless standards from GSM/GPRS to LTE and from CDMA 2000 to TD-SCDMA. One of its […]

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Antennas, LTE, WiMAX

Antennas on Samsung Galaxy S

We have previously discussed the theory of Planar Inverted F Antennas (PIFA), now let us look at a practical example. Shown below is the rear view of a Samsung Galaxy S phone with six antennas. The description of these antennas is given below. 1. 2.6 GHz WiMAX Tx/Rx Antenna 2. 2.6 GHz WiMAX Antenna Rx Only (as a diversity antenna) 3. WiFi/Bluetooth Tx/Rx Antenna 4. Cell/PCS CDMA/EVDO Tx/Rx Antenna 5. Cell/PCS CDMA/EVDO Rx Only (as a diversity antenna) 6. GPS Antenna Rx Only The figure above shows the top conducting plane of the PIFAs. The bottom conducting plane (ground plane) is […]

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Antennas, LTE, WiMAX

Planar Inverted F Antenna (PIFA)

A Planar Inverted F Antenna or PIFA is a very common antenna type being used in cell phones. In fact a cell phone would have multiple PIFAs for LTE, WiMAX, WiFi, GPS etc. Furthermore, there would be multiple PIFAs for diversity reception and transmission. A PIFA is composed of 5 basic elements. 1. A large metallic ground plane 2. A resonating metallic plane 3. A substrate separating the two planes 4. A shorting pin (or plane) 5. A feeding mechanism The resonant frequency of the PIFA can be calculated from the relationship between the wavelength of the antenna and the […]

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Antennas

E and H Field of a Patch

The Electric and Magnetic Field variations within a patch are sometimes a bit confusing and difficult to visualize. The figure below shows the E and H Field variations within a rectangular patch of length L and width W. E and H Field of a Patch As can be seen the E-field varies along the length of the patch with minimum at the centre and maximum at the edges (maximum positive and maximum negative). The H-field also varies along the length is in a direction perpendicular to the E-field. The H-field is maximum at the center and minimum at the edges. […]

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Antennas

Patch Antenna Design using Transmission Line Model

A microstrip antenna can be designed using either the transmission line model or the cavity model (more complex models also exist that suit a particular design). We here demonstrate the transmission line model since it is fairly simple to implement and results in antenna designs with reasonably good performance in terms of return loss and efficiency. The design starts with selecting the operating frequency, selecting a substrate with the required permittivity, and defining the width of the substrate. Thick substrates with low permittivity result in antenna designs with high efficiency and large bandwidths. Thin substrates with high permittivity lead to a smaller […]

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Antennas

E-field of a Patch Antenna

A Microstrip Patch Antenna or simply a Patch Antenna is a very common antenna type used in cell phones and many other electronic devices. It basically consists of two metallic plates separated by a dielectric layer. The metallic plates are usually made of copper or some other highly conductive material. Another important feature of this antenna is the feeding mechanism, which is also made of a highly conductive material. A Microstrip Patch Antenna fed by a 50 ohm transmission line and a quarterwave transformer is shown below. The E-field and H-field generated by the Patch Antenna can be calculated by using […]

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Antennas

Some Commonly Used Antenna Terminology

Antenna Pattern Antenna Pattern or Radiation Pattern is a three dimensional description of how the antenna radiates energy in to the space around it. All practical antennas are directional i.e. they radiate more energy in certain directions and lesser energy in other directions. Although the Radiation Pattern is a three dimensional quantity it can be described in two perpendicular planes known as the principal planes. Usually one of these planes is horizontal (azimuth plane) and the other is vertical (elevation plane). Gain As discussed previously antennas do not radiate uniformly in all directions. Antenna Gain is the ratio of the […]

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