# The relationship between bandwidth and transmission rates of hepatitis

Multilevel Encoding: Data rate = 2 × Bandwidth × log 2 M. Example: M=4 Thermal Noise. ❑ Due to thermal agitation of electrons in the media and devices. How data is transmitted is there in this slide:) second the term bandwidth can also refer to the number of bits per second that a channel, a link. and how to optimize, and to make the data and predictions available o Validation/correlation of how network speed, file system, caching, operating system.

Finally, on changing the constellation size to 4 points squaring the number of signal levels relative to the first transmissionthe transmission also takes about 20 seconds, but uses only 1 MHz, when transmitting at 2 Mbps: You will have to make your reservation in advance. To reserve WITest, visit http: Then, use the reservation calendar to reserve one or two consecutive hours for this experiment. For further information, refer to this tutorial on the reservation system.

Then, click on "Control Panel". Use the calendar interface to request time on sb2, sb3 or sb7. Set up testbed At your reserved time, open a terminal and log in to the console of the testbed that you have reserved.

This is usually your regular GENI username with a geni- prefix, e. If you are using WITest, log in to witestlab. Then, you must load a disk image onto the testbed nodes. From the testbed console, run: If you are using WITest note that there is no space around the comma: This process can take minutes. Don't interrupt it in middle - you'll just have to start again, and it will only take longer. If it's been successful, then once the process finishes running completely you should see output similar to: Then, turn on your nodes with the following command: Prepare your receiver Open a new terminal window, and run the following command to tunnel the ShinySDR ports between your laptop and the receiver node: If you are using WITest note: Then, in that terminal window which should now be logged in to your testbed consolelog on to the receiver node: If you are using WITest: Configure your Shiny window as follows: Click on the "hamburger" icon in the top left corner to open the menu, if it isn't already open.

Un-select the "Frequency DB" display to hide that display if it is showing. Select the "Radio Config" display if it isn't showing. Note the "Gain" slider in the "Radio Config" section.

## Transmission Line Analysis

You may have to increase the gain later if you aren't able to see the transmission in the ShinySDR window. The entire forward wave is reflected with its voltage and current negated. Because the voltage of the reflected wave is negated, the net voltage on the load is zero.

Because the current is negated, and it was in the first place assumed to be going in the opposite direction to that of the forward wave, the current flowing into the load is twice the current of the forward wave. The voltage on the load is double the forward wave's voltage, and the current into the load is zero. Transmission Line Stubs When a forward wave reflects off the load at the far end of a transmission line, the reflected wave returns to the near end.

When it arrives at the near end, it adds to the forward wave, and so alters the ratio of voltage to current at the near end. Thus the reflection alters the impedance of the transmission line, as seen by any voltage source connected to the near end.

### Nyquist formula: relating data rate and bandwidth

The value of the load impedance, ZL, determines the reflection coefficient, while the length, L, of the transmission line determines the phase of the reflected wave at the near end. It turns out that we can create any impedance we like at the near end by our choice of ZL and L. We call such a line a transmission line stub. We can use a stub to introduce an impedance into a circuit instead of using capacitors, inductors, and resistors.

## Nyquist formula: relating data rate and bandwidth

Stubs with open-circuit and short-circuit terminations are often used in radio-frequency matching networks. In the figure below, we derive the impedance at the near end in terms of L, ZL, and the characteristics impedance of the line, ZT. In our derivation, we represent voltages, currents, and phase shifts with complex exponentials.

Transmission Line Stub Impedance. The numerator represents the sum of the forward and reflected voltages at the near end, while the denominator represents the difference between the forward and reflected currents at the near end. The following table gives some example stub impedances for various stub lengths and load impedances. The stub length, L, is in units of wavelength. The characteristic impedance, ZT, we assume is resistive.

The load impedance, ZL, has a real and imaginary part. We calculate the real and imaginary parts of the reflection coefficient, Gamma. We calculate the real and imaginary parts of the reflection coefficient R. We obtained our table with our stub impedance calculation spreadsheet, available here. We use "1e10" as an open-circuit load. And "inf" result means an open circuit stub impedance. Conclusion Our discusion answers the most important questions about the behavior of transmission lines. We show that it is the attenuation of higher frequencies by the skin effect that causes the degradation of voltage transitions on long transmission lines, not the dispersion of higher frequencies.

Indeed, the dispersion alone would cause the opposite effect: The amplitude of the 1-GHz signal, however, will be attenuated by a factor of six hundred by the time it gets to the other end, while the 1-kHz signal will arrive at almost the same amplitude as it entered. The late-arrival of the low-frequency component of a signal gives rise to settling times of order microseconds at the far end of hundred-meter cables. The attenuation of higher frequencies is dominated by the skin effect, which serves to increase the effective resistance of the transmission line in proportion to the square root of the frequency.

Once we get above MHz, the surface polish of the conductor begins to limit the performance of a cable, which explains why the best high-frequency coaxial cables use polished silver conductors. Because an imperfectly-terminated transmission line causes power to be reflected back to the source, the impedance seen looking into such a line is not equal to the characteristic impedance of the line, but some function of the reflection coefficient at the far end, and the length of the line.

If we are working at one particular frequency, or a narrow range of frequencies, we can use a finite transmission line, or stub to create any impedance we like. We can use such stubs as matching networks.