Difference between revisions of "System-Level Tutorial Lesson 7: Simulating a Frequency-Modulated Continuous-Wave (FMCW) Radar System"
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The controlled source E1 is dependent on the voltage at Node 4, i.e. the antenna load, and creates an exact replica of it that is fed into the echo block. Node 6 indeed represents the receive antenna, or the receiver's entry point. The received signal is amplified by the low-noise amplifier '''Gain Block''' LNA with a gain of 5e+3. This signal is then mixed with the other half of the split chirp signal using the '''Multiplier Block''' MIX. The down-converted signal is then amplified once more by the '''Gain Block''' AMP with a gain of 50 and is passed through a generic lowpass filter block with a cutoff frequency of 2MHz. | The controlled source E1 is dependent on the voltage at Node 4, i.e. the antenna load, and creates an exact replica of it that is fed into the echo block. Node 6 indeed represents the receive antenna, or the receiver's entry point. The received signal is amplified by the low-noise amplifier '''Gain Block''' LNA with a gain of 5e+3. This signal is then mixed with the other half of the split chirp signal using the '''Multiplier Block''' MIX. The down-converted signal is then amplified once more by the '''Gain Block''' AMP with a gain of 50 and is passed through a generic lowpass filter block with a cutoff frequency of 2MHz. | ||
Revision as of 04:01, 12 October 2015
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 is amplified by the power amplifier Gain Block PA with a gain of 5e+3 and then 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 and a Radar Echo Block X3. This block simulates the effect of signal reflection from a target. It cause a delay of its input signal (transmitted signal) as well as its attenuation. The figure below shows the property dialog of the Radar Echo Block. Set the target range equal to 1500m, the frequency fo to 1GHz and keep the default value of σ = 1m2 for the targets radar cross section (RCS).
The controlled source E1 is dependent on the voltage at Node 4, i.e. the antenna load, and creates an exact replica of it that is fed into the echo block. Node 6 indeed represents the receive antenna, or the receiver's entry point. The received signal is amplified by the low-noise amplifier Gain Block LNA with a gain of 5e+3. This signal is then mixed with the other half of the split chirp signal using the Multiplier Block MIX. The down-converted signal is then amplified once more by the Gain Block AMP 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. You can zoom in the graph to see the details of the transmitted and received signals. The figure below shows the results with a scale time axis limited to the interval [19.98μs, 20μs]:
Using the equations given at the beginning of this tutorial lesson, you will find the range of your target to be 1.5km, you would have expected from your specified delay of 10μs. [math] R = \frac{cT_s}{2B} f_b = \frac{(3\times 10^8)(100\times 10^{-6})}{2(10\times 10^6)} \left( 10^6 \right) = 1500\text{m} [/math] Modeling an FMCW System with Triangular Chirp ModulationThe following is a list of parts needed for this part of the tutorial lesson:
RF.Spice A/D doesn't offer a sine wave chirp generator with triangular modulation. But you can build one using an FM modulator block just as you did in the first part of this tutorial lesson.
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