Solving Impedance Matching Reflection Problem: Homework Equations & Solutions

  • Thread starter ikurious
  • Start date
XIn summary, to solve the reflection problem caused by mismatched impedances, you can use impedance matching techniques such as using a series resistor and a shunt capacitor. The values of these components can be calculated using specific equations and adjusted if necessary to achieve a desired impedance range. This will minimize reflections and prevent damage to the pulse generator and pulse counter.
  • #1
ikurious
1
0

Homework Statement


Two meters of cable of inductance per unit length 0.169 microH/ft and 30.0 pF/ft are connected in between a pulse generator with a 175 ohm output impedance and a pulse counter with 1 Kohm input impedance. If the output of the generator is a single 5V pulse of duration 0.1ns, what is the amplitude of the pulse when it reaches the detector? What is the amplitude of the voltage amplitude of the reflected pulse when it reaches the detector for the first time? The second time? If the pulse counter can count pulses which have a voltage amplitude between 0.3 and 0.7 V, how many pulses will the detector count?

How would you solve the reflection problem caused by mismatched impedances above?


Homework Equations



A(ref) = A(inc)(Z-Z0)/(Z+Z0)

The Attempt at a Solution



Using above mentioned equation i got 2V as reflected amplitude.

But i am sure how to proceed after that. I am not clear with question being asked.

Thanx for reading
 
Physics news on Phys.org
  • #2
.


Hello,

To solve the reflection problem caused by mismatched impedances, you can use a technique called impedance matching. This involves using a network of components such as resistors, capacitors, and inductors to adjust the impedance of the cable so that it matches the output impedance of the pulse generator and the input impedance of the pulse counter.

In this case, you can use a series resistor and a shunt capacitor to match the impedances. The values of these components can be calculated using the following equations:

Rs = (Z_generator - Z_cable)/2

Cs = 1/(2*pi*f*L)

Where Rs is the series resistor, Z_generator is the output impedance of the pulse generator, Z_cable is the characteristic impedance of the cable (which can be calculated using the given inductance and capacitance per unit length), Cs is the shunt capacitor, f is the frequency of the pulse, and L is the length of the cable.

Once you have calculated the values of Rs and Cs, you can connect them in series with the cable and check the impedance using an impedance meter. If the impedance is still not perfectly matched, you can adjust the values of Rs and Cs until the impedance is within a desired range.

By matching the impedances, you can minimize the reflections and ensure that the full amplitude of the pulse is transmitted to the pulse counter. This will also prevent any damage to the pulse generator or the pulse counter due to mismatched impedances.

I hope this helps. Let me know if you have any further questions or need clarification.
Scientist
 

1. What is impedance matching and why is it important?

Impedance matching is the process of adjusting the impedance of a source to match the impedance of a load, in order to minimize reflections and maximize power transfer. It is important because it ensures efficient and accurate signal transmission in electronic systems.

2. What is the reflection coefficient and how is it related to impedance matching?

The reflection coefficient is a measure of the amount of the incident signal that is reflected back at the interface of two different impedances. It is directly related to impedance matching, as a lower reflection coefficient indicates a better match between the source and load impedances.

3. What are some common techniques for solving impedance matching reflection problems?

Some common techniques include using a matching network (such as a transformer, balun, or stub), using a resistive pad or attenuator, and using a Smith chart to plot and adjust impedance values.

4. How do I calculate the optimum match for a given source and load impedance?

The optimum match can be calculated using the reflection coefficient formula: Γ = (ZL - ZS) / (ZL + ZS), where ZL is the load impedance and ZS is the source impedance. A match is considered optimum when the reflection coefficient is equal to 0, indicating no reflections.

5. Can I use impedance matching for all types of electronic systems?

Yes, impedance matching can be applied to any electronic system where signal transmission is important. This includes systems such as radio frequency (RF) circuits, audio amplifiers, and digital communication systems.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
18
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
905
Replies
8
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
6
Views
4K
  • Advanced Physics Homework Help
Replies
12
Views
3K
Back
Top