System-Level Tutorial Lesson 7: Simulating a Frequency-Modulated Continuous-Wave (FMCW) Radar System
Contents
What You Will Learn
In this tutorial you will use RF.Spice's black-box virtual blocks to model a Quadrature Amplitude Modulation (QAM) communication system and construct a pair of transmitter and receiver circuits. Then you will use a long lossy transmission line as the channel to connect the transmitter and receiver circuits. You will simulate the transmission of a binary data packet through this communication link.
Overview of the FMCW Radar System
In an FMCW radar system, a chirp signal is launched into the free space using a transmit antenna. A chirp signal is an FM-modulated signal of a known stable frequency whose instantaneous frequency varies linearly over a fixed period of time (sweep time) by a modulating signal. The transmitted signal hits at the target and reflects back to a receive antenna. The frequency difference between the received signal and the transmitted signal increases with delay, and the delay is linearly proportional to the range, that is the distance of the target from the radar. The echo from the target is then mixed with the transmitted signal and down-converted to produce a beat signal which is linearly proportional to the target range after demodulation. The figure below shows the transmitted and received ramp signals:
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The delay τ is equal to the round-trip wave travel time and given by:
[math] \tau = \frac{2R}{c} [/math]
where R is the target range and c is the free-space speed of light. The beat frequency at the output of the receiver is given by:
[math] f_b = \frac{B}{T_s}\tau [/math]
where B is the total frequency deviation of the chirp signal and Ts is the sweep time (chirp period). The target range is thus found from the following equation:
[math] R = \frac{cT_s}{2B} f_b [/math]
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An FMCW radar system with a sawtooth chirp modulation can only measure the target's range but not its velocity if the target is moving. For that purpose, you need a triangular wave chirp modulation as shown in the figure below:
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A moving target causes addition frequency shifting of the echo signal due to the Doppler effect, which can be expressed by the following relationship:
[math] f_{Rx} = f_{Tx} \left( \frac{1+v/{c}}{1-v/c} \right) [/math]
where fTx and fRx are the frequency of the transmitted and received signals respectively, and vr is the relative velocity of the target with respect to the radar system. The frequency shift due to the target's velocity is then given by:
[math] f_d = f_{Rx} - f_{Tx} = 2 f_{Tx}\frac{v_r}{c-v_r} \approx \frac{2v_r}{\lambda_0} [/math]
where and λ0 = c/f is the free=space wavelength, and it was assumed that vr << c.
[math] f_{bu} = f_b - f_d \\ f_{bd} = f_b + f_d [/math]
where fbu and fbd are the beat frequencies during the up-ramp and down-ramp sweeps, respectively. The target range and velocity are then calculated from the following equations:
[math] R = \frac{cT_s}{4B} \left( f_{bd} + f_{bu} \right) [/math]
[math] v_r = \frac{\lambda_0}{4} \left( f_{bd} - f_{bu} \right) [/math]
Exploring FM Modulation
The following is a list of parts needed for this part of the tutorial lesson:
| Part Name | Part Type | Part Value |
|---|---|---|
| V1 | Voltage Source | Waveform TBD |
| X1 | FM Modulator Block | Defaults |
| R1 | Resistor | 100 |
RF.Spice's FM modulator takes an arbitrary input signal and generates a frequency-modulated sinusoidal signal as its output. Place and connect the parts as shown in the figure below.
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In this part of the lesson, you will use different waveforms as the input signal to the FM modulator. You can access the FM Modulator Block from Menu > Parts > Modulation Blocks > FM Modulator Block. The property dialog of this block is shown in the figure below. Set the Carrier Frequency to 10MHz and the Maximum Frequency Deviation to 5MHz.
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You will use the basic voltage source V1 to generate a sinusoidal waveform. Then you will replace it with a Pulse Generator, a Ramp Generator and a Triangular Wave Generator, all of which can be accessed from Menu > Parts > Waveform Generator Blocks > Basic Waveforms. Define each source one by one according to the waveform tables below:
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For each waveform, run a Transient Test of your modulator circuit with the following parameters:
The results are shown in the figures below for all the four different waveforms. Using the graph window's Delta Line Mode, you can measure the period of the FM-modulated waveforms at different time instants. You will find that when the input signal is zero, the period is 100ns (corresponding to 10MHz). When the input signal reaches +1V or -1V, the modulated output frequency increases to 15MHz or decreases to 5MHz, respectively.
In this part of the tutorial lesson, you will build and test an FMCW system with a sawtooth chirp modulation. RF.Spice A/D provides three types of chirp generator devices. All three are based on sawtooth modulation but each provides a different output waveform. They are sinusoidal chirp generator, triangular wave chirp generator and square wave chirp generator. For this project, you will use the first type, which can be access from Menu > Parts > Waveform Generation Blocks > Chirp Generators > Sine Wave Chirp Generator. Set the Chirp Period to 100μs (i.e. a 10kHz chirp), and set the values of the two parameters freq_low and freq_high to 1GHz and 1.01GHz, respectively. Therefore, B = 1.01GHz - 1GHz = 10MHz.
Place and connect all the parts as shown in the figure below. The signal of the chirp generator is split into two equal parts using an Ideal Splitter Block, one of which goes to a 50Ω matched antenna load called RL. The received signal at the receiver antenna is modeled here using a voltage-controlled voltage source (VCVS) E1, which is dependent on the voltage at Node 3. i.e. the antenna load, with a proportionality constant of 1e-4. The highly attenuated signal also goes through an Ideal Delay Block with a specified delay of 10μs. This dealy time corresponds to a target range of R = cτ/2 = 1.5×103m = 1.5km. In other words, Node 5 represents the receive antenna, or the receiver's entry point. The received signal is amplified at the low-noise amplifier (LNA), which is modeled by a Gain Block A1 with a gain of 5000. This signal is then mixed with the other half of the transmitted signal using the Multiplier Block A2. The down-converted signal is amplified once more by A3 with a gain of 50 and is passed through a generic lowpass filter block with a cutoff frequency of 2MHz.
Run a Transient Test of your modulator circuit with the following parameters:
The results are shown in the figure below. v(2) is the equal to the transmitted signal, and v(6) is the amplified receiver signal. The blue signal v(9) is the output beat signal, which has a measured period of 1.009μs. Therefore, fb = 1MHz.
In this simulation, the stop time was 20μs to cover both the transmitted and received signals adequately. On the other hand, the periods of the signals were on the order of 1ns. Therefor, a step ceiling of 50ps was chosen. From the above figure, you can see that the received signal starts at t = τ = 10μs.
Putting the Transmitter and Receiver Together With the ChannelThe following is a list of parts needed for this part of the tutorial lesson:
In this part of the tutorial lesson, you will put the QAM modulator and demodulator circuits of the previous parts together with a channel to simulate a communication link. In a wireless system, the channel is the free space between the transmit and receive antennas. One way of modeling the free-space channel in RF.Spice A/D is to use a dependent voltage source at the input of the receiver that is driven by the voltage at the output of the transmitter. The proportionality constant can be set to a very small number representing the free-space path loss. For this project, however, you will use a wired channel or cable represented by a lossy transmission line segment. In that case, the receiver can be directly connected to the output port of the T-Line segment. You will use a TEM line with Z0 = 50Ω, eeff = 1 and alpha = 0.5dB/m. At a length of 10m, the total single attenuation due to the channel will be 5dB. You are now ready to put it all together. This time you will send the QAM-modulated output of the transmitter circuit you built earlier through the transmission line channel and will feed it as the input of your receiver circuit. This signal will replace the AM-modulated voltage source you used in the previous section to feed your QAM demodulator circuit. For this part of the project, you will place an Ideal Buffer Block for isolation between the transmission line and the rest of the receiver circuit. The Limiter Block will both amplify and clip the signal from the top and bottom. Set the gain to 5 and set the lower and upper limits of the output voltage to -1V and +1V, respectively. Also define a gain of 5 for the Ideal Full-Wave Rectifier Block.
Place and connect all the parts as shown in the figure below. Note that the part values of the peak detector's lowpass filter have changed from the previous part. Also, the reference voltage of the Ideal Comparator Block has been decreased to 2V.
As the transmitted signal propagates through the transmission line, besides phase change or time delay, it also gets attenuated by 5dB over its whole length. The QAM-modulated signal signal arrives at the input of the receiver after a time delay equal to: [math] \Delta t = \frac{L}{c} = \frac{10m}{3\times 10^8 m/s} = 33.3ns [/math] To plan your Transient Test, keep in mind that the input binary sequence has a total duration of 20ns, of which the last 4ns are zeros (silent). In addition, the channel causes a time delay of 33.3ns. So choose the following parameters to run a Transient Test of your QAM data communications link:
The results are shown in the figure below. The plots in light and dark blue represent the voltage signals at the input and output of the long lossy transmission line. As you can from the figure, the demodulated signal at the digital output represents a fairly good replica of the input binary sequence.
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