Lab Exercise 7: Doppler Radar

Transcription

1 Lab Exercise 7: Doppler Radar Contents 7-1 PRE-LAB ASSIGNMENT INTRODUCTION Speed Discrimination Doppler Antenna Radio Frequency Module Processing Unit EQUIPMENT EXPERIMENT Speed Detection Angle Dependence Multiple Reflections LAB WRITE-UP Objective The objective of this lab is to to investigate the fundamental concepts of Doppler radar. General concepts to be covered: Doppler radar fundamentals Doppler frequency shift Speed determination Multiple reflections 21

2 22 LAB EXERCISE 7: DOPPLER RADAR 7-1 PRE-LAB ASSIGNMENT 1. Read Sections and 10-7 of the Ulaby text. 2. To be entered into your lab notebook prior to coming to lab: Summarize the experimental procedure (1 paragraph per section) of: (a) Section 7-4.1: Speed Detection (b) Section 7-4.2: Angle Dependence (c) Section 7-4.3: Multiple Reflections 7-2 INTRODUCTION At one point or another, we have all experienced the phenomenon known as the Doppler effect. The text defines the Doppler effect as a shift in the frequency of a wave caused by the motion of the transmitting source, the reflecting object, or the receiving system. An example of the Doppler effect is a police siren. When you hear a siren coming towards you and you pull off to the side of the road, have you ever noticed the change in pitch as the siren approaches you? What causes this shift in pitch, which is related to the frequency? This shift in frequency is a prime example of the Doppler shift. You may be asking yourself how can the frequency change? One way to think of it is by the following example: Imagine that you are in a large swimming pool or lake. In the center of this body of water, we start dropping spherical marbles at a constant rate. The dropping of the marbles will cause a circular wave (remember the button driver from Lab #1) to travel outward, away from the source. Each time we drop a marble, we create another wavefront. Since the drop rate is constant, the wavefronts are separated by the same distance. This corresponds to a single frequency being present. Now, lets say you are in the water, but you are not interfering with the waves. If you stand still, the wavefronts will hit at a constant rate, equal to the rate at which the marbles are being dropped. What happens if you start walking or swimming towards the source? The waves are still separated by the same distance, but since you are moving, the waves are hitting you at a faster rate. This corresponds to the frequency increasing. If you turn around and start moving away from the source, the waves will hit you at a slower rate since they have to travel farther to catch up with you. This corresponds to a lower frequency. What if you swam in a circle of constant radius from the source? Since the distance to the source is always fixed, the waves will hit you at the same rate as if you were standing still, hence the frequency is unchanged. The Doppler effect (or Doppler shift as it is sometimes referred to) can be described mathematically in the case of the Doppler radar by Eq f d = 2u λ t cos(θ) (7.1) where f d is the change in frequency (Doppler frequency), u is the velocity of the relative motion, λ t is the wavelength of the transmitted waves, and θ is the angle between the source and the direction of motion. Does the equation conform to what we expect physically? In the water wave example, according to Fig. 7-1, if you are moving towards the source, then θ is in the range 90 θ

3 7-2 INTRODUCTION This makes cos(θ) negative, which would make f d positive. Thus, f d corresponds to an increase in frequency as we expect. If we are moving away from the source then θ is in the range 0 θ 90, which makes f d negative, since cos(θ) is positive. A negative f d means that the frequency is decreased, which is what we expect. What about the case when you swam around in a circle? As indicated in Fig 7-1, when you swam in the circle, your direction of travel was always perpendicular to the radial direction from the source. This corresponds to θ = 90, or f d =0. Hence, there is no change in frequency, which is what we expect. θ (a) Configuration as you swim towards the source (b) Configuration as you swim away from the source (c) Configuration as you swim in a circle of constant radius Figure 7-1: Definitions for θ as you swim (a) towards (b) away (c) in a circle of constant radius about the source Speed Discrimination The Doppler radar is commonly used by law enforcement to catch speeders. We know that the received Doppler shift by the radar is directly proportional to the speed of the object. What happens if there is more than one moving object present in the field of view (fov) of the radar? The returned radar signals are superimposed on each other, so what the radar receives is a linear superposition of all of the Doppler frequencies. How can you tell which Doppler shift belongs to which object? If the velocities of all of the objects are similar, then

4 24 LAB EXERCISE 7: DOPPLER RADAR this becomes a difficult process. If the velocities of the objects are very different, then the task becomes easier. If the velocities of the objects are very different, then we can implement a bank of filters to select the object of interest. For example, if you are trying to monitor the speed of a pedestrian walking along a major road, there will also be cars present. Since the person is moving at a couple of miles per hour and the cars are moving at 55 MPH, the Doppler frequency for the cars will be much higher than the Doppler frequency for the pedestrian. If the signal is passed through a low pass filter that has been designed to pass only the Doppler frequencies that correspond to 0 to 10 MPH, then the response of the pedestrian can be isolated from the response of the car. By using a bank of filters that contain a low pass and several bandpass filters, the Doppler radar can be designed to discriminate based on speed. In the Doppler radar unit that you will be using to make your measurements; however, there are no filters to perform the speed discrimination. Part of this lab exercise is to determine with experimentation the composition of the Doppler frequency with more than one reflector. The Doppler unit you will be using consists of three components: Doppler Antenna The antenna is used to transmit and receive the radio frequency (RF) signal, which for this system is GHz. It is located at the front of the upper module, and has a fairly narrow beamwidth for pointing accuracy Radio Frequency Module The Doppler module supplies the transmitted RF signal to the antenna, and it also performs a mixing operation on the received signal. Typically three frequencies are of interest in a mixer: the RF, the local oscillator (LO) frequency, and the difference frequency (absolute value of RF minus LO). In this system the LO and RF are the same GHz, and therefore the difference frequency is centered at DC, or 0 Hz. Baseband also describes the frequency spectrum of the signal demodulated to DC. Now the only difference between the LO and RF is that which the Doppler shift cuases, and this is what is output from the mixer Processing Unit The processing unit amplifies the baseband signal f d and filters any DC components. The output can be viewed on the oscilloscope for frequency determination. The visible signal is actually the difference between the transmitted GHz and the received signal. Because there is no way to obtain phase information in this system, motion towards and away from the Doppler unit are indistinguishable.

5 7-3 EQUIPMENT EQUIPMENT Item Part # Doppler unit Doppler power supply Roll track Ball, 2 Oscilloscope HP 54645A Power cords Power supply HP E3620A Speaker Variable speed fan Various cables 7-4 EXPERIMENT Speed Detection The purpose of this experiment is to determine the relationship between relative velocity and f d. A 2 ball will be released from 6 various heights along an inclined plane and roll towards the Doppler unit. The output Doppler shift will be observed on the oscilloscope for each of the data points, and then the frequency will be converted into a relative velocity. Because the initial potential energy of the ball equates to the kinetic energy of the ball in motion, the final speed of the ball is known for each case, and the measured speed from the Doppler unit is compared to the known velocity. Setup This experiment uses the Doppler unit, roll track, ball, oscilloscope, probe, and appropriate power supply connections. Set the roll track on the right side of the bench so that the ball will roll from right to left. Set the Doppler unit on the left side directly facing the track so the ball will roll directly into the antenna. Connect the output of the Doppler unit directly to the oscilloscope. Procedure 1. Adjust the oscilloscope display (5 or 10 msec per division and a volts per division of 1 or 2) so that the waveform is clearly visible. 2. Place the ball at a known height along the inclined track. Height is measured as the displacement vertically between the flat bottom of the track and the bottom of the ball. 3. Stand away from the balls path at least 3 to limit your noise contribution. Have one person ready to press the run/stop key on the oscilloscope and another ready to release the ball.

6 26 LAB EXERCISE 7: DOPPLER RADAR 4. Check to make sure the scope is updating (not in stop mode). Release the ball and press the run/stop key as the ball reaches the midpoint of the horizontal track. 5. Measure and record the frequency of the Doppler output either with cursors or with the frequency softkey under the time menu. 6. Following the same procedure from step 2, repeat to obtain at least three (3) good data points for the given height. 7. Repeat again from step 2 for a total of four (4) distinct heights. Measured Data Height (cm) Trial #1 Trial #2 Trial #3 Analysis 1. Average the measured frequencies for each height and convert to velocity in m/sec using Eq Calculate the horizontal velocity of the ball given the height using conservation of energy equations. 3. Plot the measured velocity versus the calculated velocity and compute the error for each of the heights. Questions 1. What is the relationship between fd and relative velocity for your results? Does this agree with Eq. 7.1? 2. What are the causes for the spread (error) in your data at each height? Angle Dependence Setup This experiment uses a protractor along with all the equipment from Procedure 1. Select a single moderate height to release ball for all measurements. 2. Orient Doppler unit so that the antenna is always directed at the center of the horizontal track. 3. In increments of 20, measure and record fd from Rotate the Doppler unit at approximately a two feet radius from the center of the horizontal track. The oscilloscope should also be stopped as the ball passes the center of the track.

7 7-4 EXPERIMENT To measure the angle, first set the track parallel to the table. Then for each measurement, align the desired angle on the protractor to be parallel with the faint horizontal lines on the bench. The Doppler unit can then be set perpendicular to the protractor. Measured Data Angle Trial #1 Trial #2 Trial # Analysis 1. Average the measured frequencies for each height and convert to velocity in m/sec using Eq Normalize the averaged velocities by dividing each by the maximum value. 3. Plot the normalized points, cos(θ) and cos 2 (θ), versus θ on the same plot. Questions 1. What relationship between θ and the measured velocity does your data best follow? Is this what you expected? 2. Thinking of the velocities of the Doppler unit and the ball as vector quantities, what mathematical relationship between vectors helps to illustrate this relationship? What does this mean physically? Multiple Reflections This experiment is open-ended, meaning that you are free to design your own experiments to test the Doppler radar. You should in your experimentation determine physically what happens to the output signal when there is more than one moving reflector. You are required to describe the procedure that you used along with data and analysis. Also you should sketch at least one plot of multiple reflections. The following is a list of suggested measurements that you can make. Measurements of a variable speed fan Measurements of human motion Measurements of more than one ball, or combinations of ball and other object How you accomplish this is up to your group. It may be easier as you get started to have reflections at very different speeds. Please keep safety in mind when designing your experiments, and get your experiments approved by the lab instructor before making measurements.

8 28 LAB EXERCISE 7: DOPPLER RADAR Questions 1. Describe mathematically what happens when there is more than one moving reflector. How does this make distinguishing one signal from another more difficult? 2. Assume that you are given the task of designing an outdoor alarm sensor to detect human motion. The challenge is to trigger the alarm only for human motion, and not for a small animal or for a car passing by. Propose (at a system level) and give specifications for such a system. You need not be too technical about implementation, however you should minimally include: Appropriate human speeds and corresponding frequencies of interest Method for selecting frequency spectrum of interest Method for selecting amplitude of interest Draw block system level diagram 7-5 LAB WRITE-UP For each section of the lab, include the following items in your write-up: Overview of the procedure and analysis. Measured data. Calculations (show your work!). Any tables and printouts. Comparisons and comments on results. A summary paragraph describing what you learned from this lab.