Application Note:
FMCW Radar Signal with Triangle Waveform
Michael Zito
11/12/11
Abstract: In our project, we will be using a Frequency Modulated
Continuous Waveform Radar. There are four different waveforms that
can be used for an FM chirp. In this note, I will explain why we we are
using a triangle wave chirp and how we build it at the component level.
Figure 1: XR-2206 Chip with FMCW Triangle Wave Implementation
Radars are systems that are used for detecting objects. They accomplish this goal by using
electromagnetic waves to determine a variety of detection parameters. Such parameters include
altitude, speed, range and direction. The project that we choose uses range and Doppler (direction) to
detect objects. But how do you detect objects with electromagnetics? There are many different
configurations in which a radar can exist. Among the many, the few that are most common include
Monopulse Radar, Bistatic Radar, Doppler Radar and Frequency Modulated Continuous Wave Radar.
Among the stated configurations, our project uses a FMCW configuration to determine range and
direction of an object. We will produce this FMCW signal by means of an XR-2206 function generator
chip. Figure 1 represents how we produce our FMCW signal and in this document, I will be explaining
why we have this specific configuration and what exactly our input, output response will be.
Figure 2: Circuit for Sine Wave Generation
FMCW radars are capable of slewing up and down with four different wave configurations. Sine
waves, sawtooth waves, triangle waves or square waves are all possible. However, only a triangle
modulation will give you both range and velocity. Therefore, figure 1 must output a triangle wave to the
system. Referring to the XR-2206 datasheet, they give an example circuit for sine wave generation;
Figure 2. Looking at pins 13 and 14 of figure 2, we notice for a sine wave, S1 must be closed. However,
for a Triangle wave output, S1 must remain open. This is accomplished by removing all of the external
components connecting pins 13 and 14. Additionally, pins 15 and 16 will have no external connections
since we are outputting a triangle wave.
Figure 3: Block Diagram of XR-2206
Chirp Rate Adjust & Frequency Span:
Next, we’ll need to select R and C values for pins 5, 6 and 7. The frequency equation is given
by
, Therefore selecting C = 0.47uF and adjusting R, we can adjust our potentiometer to
achieve a value to make our operating frequency roughly 25 Hz (our requirement is a 40ms period).
The frequency span is proportional to R3 (the potentiometer). According to the data sheet, each kΩ of
R3 will produce approximately 160mV of peak. So we can expect to see about an 8v peak for our
triangle wave. Additionally, we’ll need to control the output level at pin 2; the spec sheet states that at
the output, Pin 2 is approximately the same as the dc bias at pin 3. Pin 3 is biased midway between V+
and ground which would give an output dc level of roughly V+/2. If the voltage rail is not set to 12v,
then our waveforms will become clipped. So, it is important that we ensure a 12v rail.
Ramp Generator:
Now that we have all of our “adjust” and “span” pins set, we must now focus on the pins we
need to power and ground. Pin 1 is used to modulate the output amplitude. Since we are designing a
frequency modulated chirp, we can attach this pin to ground. The timing terminals (pin 7) are internally
biased with respect to pin 12. Therefore, we must set this pin to ground as well. Lastly we must supply
a voltage to the VCC pin. Our positive power supply is set at 12v with to parallel capacitors to control
our ramping.
Figure 4 shows the output at pin 2. Here we adjusted our period of our triangle wave to 10ms
instead of 40ms but as explained earlier, you simply need to adjust the potentiometer for the desired
response. However, you can see that our max peak is roughly 8 volts.
Figure 4: Triangle Waveform Output
Radars that are frequency modulated are great for detecting objects. Specifically, when trying
to confirm an objects range and velocity using a triangle waveform for your chirp will allow you to do so.
Ensuring proper voltage at each pin is key for proper waveforms to be displayed, if not; clipping will
occur. Additionally, S1 will need to be off in order to produce a triangle wave, if not; a square wave
could be produced instead.
References:
1. "Free Online Course Materials | Resource Home | MIT OpenCourseWare." Free Online Course
Materials | MIT OpenCourseWare. Web. 12 Nov. 2011. <http://ocw.mit.edu/resources/res-ll003-build-a-small-radar-system-capable-of-sensing-range-doppler-and-synthetic-apertureradar-imaging-january-iap-2011/index.htm>.
2. EXAR, XR-2206 Monolithic Function Generator Chip Data Sheet, Fremont, CA, June 1997