Difference between revisions of "System-Level Tutorial Lesson 7: Simulating a Frequency-Modulated Continuous-Wave (FMCW) Radar System"

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{{projectinfo|Tutorial| Simulating a Frequency-Modulated Continuous-Wave (FMCW) Radar System |SysTUT3 41.png|In this project, you will build a QAM modulator and demodulator pair using virtual blocks and will use them to simulate a communication link.|
+
{{projectinfo|Tutorial| Simulating a Frequency-Modulated Continuous-Wave (FMCW) Radar System |SysTUT7 9.png|In this project, you will build and test FMCW radar systems with the capability of target range and velocity detection.|
  
−
*Communication Link
+
*Radar System
−
*Modulator
+
*FMCW Radar
−
*Demodulator
+
*Chirp Signal
−
*Communication Channel
+
*FM Modulation
−
*Binary Dara
+
*Target Range
−
*Carrier Frequency
+
*Target Velocity
−
*QAM Modulation
+
*Beat Frequency
−
|All versions|{{download|http://www.emagtech.com/content/project-file-download-repository|System-Level Tutorial Lesson 7|[[RF.Spice A/D]] R15}} }}
+
|All versions|{{download|http://www.emagtech.com/downloads/ProjectRepo/SystemLesson7.zip System-Level Lesson 7}} }}
  
 
=== What You Will Learn ===
 
=== 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.
+
In this tutorial you will use RF.Spice's black-box virtual blocks to model an FMCW radar system. You will explore FMCW radar systems with both sawtooth and triangular chirp modulations and see how the target range and velocity information are extracted from the output beat signals.
  
 
== Overview of the FMCW Radar System ==
 
== Overview of the FMCW Radar System ==
Line 64: Line 64:
 
<math> f_d = f_{Rx} - f_{Tx} = 2 f_{Tx}\frac{v_r}{c-v_r} \approx \frac{2v_r}{\lambda_0} </math>
 
<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 &lambda;<sub>0</sub> = c/f is the free=space wavelength, and it was assumed that v<sub>r</sub> << c.
+
where and &lambda;<sub>0</sub> = c/f is the free=space wavelength, and it was assumed that v<sub>r</sub> << c. For example, at an operating frequency of f<sub>0</sub> = 10GHz, &lambda;<sub>0</sub> = 30mm. A moving car target driving at a speed of 20m/s (or 72km/hr) towards the radar generates a frequency shift of f<sub>d</sub> = 1.33kHz. When driving away from the radar, the same car produces a Doppler shift of -1.33kHz.
 +
 
 +
The Doppler frequency shift f<sub>d</sub> caused by a moving target is superposed with the frequency shift of the echo signal due to reflection from a stationary target. When the target is approaching the radar, f<sub>d</sub> is positive and it slightly lifts up the reflected ramp signal. When the target is moving away from the radar, f<sub>d</sub> is negative and it slightly lowers down the reflected ramp signal. This leads to generation of two different frequency beat signals during the up-ramp and down-ramp sweeps:
  
 
<math> f_{bu} = f_b - f_d \\
 
<math> f_{bu} = f_b - f_d \\
Line 74: Line 76:
  
 
<math> v_r = \frac{\lambda_0}{4} \left( f_{bd} - f_{bu} \right) </math>
 
<math> v_r = \frac{\lambda_0}{4} \left( f_{bd} - f_{bu} \right) </math>
 +
 +
In the above equations, the sweep time T<sub>s</sub> is half the period of the ramp's triangular wave function.
  
 
== Exploring FM Modulation ==
 
== Exploring FM Modulation ==
Line 102: Line 106:
 
|}
 
|}
  
−
[[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.  
+
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.  
  
 
<table>
 
<table>
Line 232: Line 236:
 
</table>
 
</table>
  
−
For each waveform, run a Transient Test of your modulator circuit with the following [[parameters]]:
+
For each waveform, run a Transient Test of your modulator circuit with the following parameters:
  
 
{| border="0"
 
{| border="0"
Line 315: Line 319:
 
|-
 
|-
 
! scope="row"| X3  
 
! scope="row"| X3  
−
| Ideal Delay Block
+
| Radar Echo Block
−
| Defaults, delay = 10u
+
| Defaults, range = 1500m, fo = 1GHz
 +
|-
 +
! scope="row"| X4
 +
| Generic Lowpass Filter Block
 +
| Defaults, Cutoff = 2Meg
 
|-
 
|-
 
! scope="row"| E1  
 
! scope="row"| E1  
 
| Voltage-Controlled Voltage Source
 
| Voltage-Controlled Voltage Source
−
| Defaults, gain = 1e-4, controlled by v(3,0)
+
| Defaults, gain = 1, controlled by v(4,0)
 
|-
 
|-
−
! scope="row"| A1
+
! scope="row"| PA
 
| Gain Block
 
| Gain Block
 
| Defaults, gain = 5e+3
 
| Defaults, gain = 5e+3
 
|-
 
|-
−
! scope="row"| A2
+
! scope="row"| LNA
−
| Multiplier Block
+
| Gain Block (must be made unique)
−
| Defaults
+
| Defaults, gain = 5e+3
 
|-
 
|-
−
! scope="row"| A3
+
! scope="row"| AMP
 
| Gain Block (must be made unique)
 
| Gain Block (must be made unique)
 
| Defaults, gain = 50
 
| Defaults, gain = 50
 
|-
 
|-
−
! scope="row"| X4
+
! scope="row"| MIX
−
| Generic Lowpass Filter Block
+
| Multiplier Block
−
| Defaults, Cutoff = 2Meg
+
| Defaults
−
|-
+
−
! scope="row"| X5
+
−
| Ideal Comparator Block
+
−
| Defaults, Gain
+
 
|-
 
|-
 
! scope="row"| Rant
 
! scope="row"| Rant
Line 351: Line 355:
 
|}
 
|}
  
−
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 100&mu;s (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.   
+
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 100&mu;s (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.   
  
 
<table>
 
<table>
Line 361: Line 365:
 
</table>
 
</table>
  
−
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 50&Omega; 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 10&mu;s. 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.   
+
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 50&Omega; 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 &sigma; = 1m<sup>2</sup> for the targets radar cross section (RCS).   
 +
 
 +
<table>
 +
<tr>
 +
<td>
 +
[[File:SysTUT7 21.png|thumb|550px|The property dialog of the Radar Echo Block.]]
 +
</td>
 +
</tr>
 +
</table>
 +
 
 +
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.   
  
 
<table>
 
<table>
Line 371: Line 385:
 
</table>
 
</table>
  
−
Run a Transient Test of your modulator circuit with the following [[parameters]]:
+
Run a Transient Test of your modulator circuit with the following parameters:
  
 
{| border="0"
 
{| border="0"
Line 392: Line 406:
 
|-
 
|-
 
! scope="row"| Preset Graph Plots
 
! scope="row"| Preset Graph Plots
−
| v(2), v(6), v(7), v(9)
+
| v(1), v(7), v(9), v(10)
 
|}
 
|}
  
−
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&mu;s. Therefore, f<sub>b</sub> = 1MHz.
+
Some of the results are shown in the figure below. v(1) is the transmitted chirp signal, and v(7) is the amplified received signal. The blue signal v(10) is the output beat signal, which has a measured period of 1.009&mu;s. Therefore, f<sub>b</sub> = 1MHz.  
  
 +
{{Note|Radar system simulations usually involve time scales of different orders. They typically require a large transient time interval with a very fine time step ceiling.}}
  
−
As you can see from the figure, the voltage signal v(7) at the output of the peak detector (plotted in dark blue) is a good reconstructed replica of the baseband 300MHz sinusoidal signal. Compare this signal to the envelope of the input AM-modulated signal plotted in yellow. You can use the "Delta Line Mode" of the graph window to measure the period or clock rate of the binary output, which is about 3.34ns consistent with the signal frequency of fs = 300MHz.   
 
−
 
 
 
<table>
 
<table>
 
<tr>
 
<tr>
 
<td>
 
<td>
−
[[File:SysTUT7 15.png|thumb|750px|The graph of the analog input voltage (yellow), output of the QAM block v(4), output of the peak detector v(7) and the digital output of the QAM Demodulator circuit.]]
+
[[File:SysTUT7 15.png|thumb|750px|The graph of the transmitted signal (light blue), received signal (yellow), and the output beat signal (dark blue).]]
 
</td>
 
</td>
 
</tr>
 
</tr>
 
</table>
 
</table>
 +
 +
The figure below shows the input and output signals of the lowpass filter, i.e. the mixer's down-converted output signal and the filtered output beat signal:
 +
 
<table>
 
<table>
 
<tr>
 
<tr>
 
<td>
 
<td>
−
[[File:SysTUT7 16.png|thumb|750px|The graph of the analog input voltage (yellow), output of the QAM block v(4), output of the peak detector v(7) and the digital output of the QAM Demodulator circuit.]]
+
[[File:SysTUT7 22.png|thumb|750px|The graph of the input and output signals of the lowpass filter.]]
 
</td>
 
</td>
 
</tr>
 
</tr>
 
</table>
 
</table>
 +
 +
In this simulation, the stop time was 20&mu;s to cover both the transmitted and received signals adequately. On the other hand, the periods of the signals were on the order of 1ns. Therefore, a step ceiling of 50ps was chosen. From the above figure, you can see that the received signal starts at t = &tau; = 10&mu;s. 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 [19.99&mu;s, 20&mu;s]: 
 +
 
 
<table>
 
<table>
 
<tr>
 
<tr>
 
<td>
 
<td>
−
[[File:SysTUT7 17.png|thumb|750px|The graph of the analog input voltage (yellow), output of the QAM block v(4), output of the peak detector v(7) and the digital output of the QAM Demodulator circuit.]]
+
[[File:SysTUT7 16.png|thumb|750px|The zoomed-in graph of the transmitted and received signals and the mixer output in the interval [19.99&mu;s, 20&mu;s].]]
 
</td>
 
</td>
 
</tr>
 
</tr>
 
</table>
 
</table>
  
−
== Putting the Transmitter and Receiver Together With the Channel ==
+
Using the equations given at the beginning of this tutorial lesson, you will find the range of your target to be 1.5km, you had set in the radar echo block.
 +
 
 +
<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 Modulation ==
  
 
The following is a list of parts needed for this part of the tutorial lesson:
 
The following is a list of parts needed for this part of the tutorial lesson:
Line 436: Line 459:
 
! scope="col"| Part Value
 
! scope="col"| Part Value
 
|-
 
|-
−
! scope="row"| A1
+
! scope="row"| V1
−
| Digital Source
+
| Triangular Wave Generator
−
| Data TBD
+
| Defaults, fo= 20KHz
 
|-
 
|-
−
! scope="row"| A2
+
! scope="row"| X1
−
| 1-Bit DAC Conversion Bridge
+
| FM Modulator Block
−
| Defaults, out_high = 5, t_rise = 100p, t_fall = 100p
+
| Defaults, fc = 1GHz, f_del = 10MHz
 
|-
 
|-
−
! scope="row"| X1
+
! scope="row"| X2
−
| Wilkinson Power Divider
+
| FM Modulator Block
−
| Defaults, fc = 1GHz
+
| Defaults, fc = 1.001GHz, f_del = 10MHz
 
|-
 
|-
−
! scope="row"| X2, X5
+
! scope="row"| X3
−
| QAM Modulator Block
+
| Ideal Signal Splitter
−
| Defaults, fc = 3GHz, ac = 5V
+
| Defaults (k = 0.5)
 
|-
 
|-
−
! scope="row"| XTL1
+
! scope="row"| X4
−
| Generic T-Line
+
| Radar Echo Block
−
| Defaults: Z0 = 50, eeff = 1, alpha = 0.5dB/m, len = 10,000mm
+
| Defaults, range = 1500m, fo = 1GHz
 
|-
 
|-
−
! scope="row"| R1 - R2
+
! scope="row"| PA
−
| Resistor
+
| Gain Block
−
| 50
+
| Defaults, gain = 5e3
 
|-
 
|-
−
! scope="row"| VREF
+
! scope="row"| A1
−
| DC Voltage Source
+
| Gain Block (copy of PA)
−
| 2V
+
| Defaults, gain = 5e3
 
|-
 
|-
−
! scope="row"| X3
+
! scope="row"| LNA
−
| Ideal Buffer Block
+
| Gain Block (must be made unique)
−
| Defaults
+
| Defaults, gain = 5e3
 
|-
 
|-
−
! scope="row"| X4
+
! scope="row"| AMP
−
| Resistive Power Divider
+
| Gain Block (must be made unique)
−
| Defaults, len_in = 2mm, len_out = 2mm
+
| Defaults, gain = 100
 
|-
 
|-
−
! scope="row"| A1
+
! scope="row"| MIX
−
| Limiter Block
+
| Multiplier Block
−
| Defaults, gain = 5, out_lower_limit = -1V, out_upper_limit = 1V
+
| Defaults
 
|-
 
|-
−
! scope="row"| X6
+
! scope="row"| X5
−
| Ideal Full-Wave Rectifier Block
+
| Generic Lowpass Filter Block
−
| Defaults, gain = 5
+
| Defaults, Cutoff = 12Meg
 
|-
 
|-
−
! scope="row"| X7
+
! scope="row"| Rant
−
| Ideal Comparator Block
+
−
| Defaults, gain = 10
+
−
|-
+
−
! scope="row"| R1
+
 
| Resistor
 
| Resistor
 
| 50
 
| 50
 
|-
 
|-
−
! scope="row"| R2
+
! scope="row"| RL
 
| Resistor
 
| Resistor
−
| 60
+
| 50
−
|-
+
−
! scope="row"| R2
+
−
| Resistor
+
−
| 80
+
−
|-
+
−
! scope="row"| C1
+
−
| Capacitor
+
−
| 10p
+
−
|-
+
−
! scope="row"| A4
+
−
| 1-Bit ADC Conversion Bridge
+
−
| Defaults, in_high = 2, t_rise = 100p, t_fall = 100p
+
−
|-
+
−
! scope="row"| Out1
+
−
| Digital Output
+
−
| N/A
+
 
|}
 
|}
  
−
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 Z<sub>0</sub> = 50&Omega;, eeff = 1 and alpha = 0.5dB/m. At a length of 10m, the total single attenuation due to the channel will be 5dB.               
+
[[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. You will do this by feeding a triangular wave generator V1 with a frequency of 20kHz (and a period of 50&mu;s) as the modulating signal to the FM Modulator block X1 with a carrier frequency fc = 1GHz and a maximum frequency deviation of 10MHz. As the input triangular wave oscillates between -1V and +1V, the output frequency of the FM modulator will oscillate between 990MHz and 1010MHz. Therefore, B = 20MHz and T<sub>s</sub> = 25&mu;s.    
−
 
+
−
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.  
+
  
 
<table>
 
<table>
 
<tr>
 
<tr>
 
<td>
 
<td>
−
[[File:SysTUT3 42.png|thumb|550px|The property dialog of the Limiter Block.]]
+
[[File:SysTUT7 25.png|thumb|750px|The schematic of the FMCW radar transmitter-receiver circuit using triangular chirp modulation.]]
 
</td>
 
</td>
 
</tr>
 
</tr>
 
</table>
 
</table>
  
−
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. 
+
Place and connect all the parts as shown in the above figure. The circuit of this part is similar to the circuit of the previous part, except for the fact that you need to introduce a Doppler frequency shift in the echo signal. To model this additionally frequency-shifted echo signal, you introduce a second FM modulator X2 which is fed by the same triangular waveform V1 but with a slightly shifted carrier frequency of 1.0001GHz. For the purpose of this tutorial and to demonstrate a practical simulation, we assume that the Doppler frequency shift is f<sub>d</sub> = 100kHz. This translates to a target velocity of v<sub>r</sub> = f<sub>d</sub>&lambda;<sub>0</sub>/2 = 15km/s, which is extremely high. But remember that typical vehicular speeds would only produce a Doppler shift of few hundreds of Hertz at 1GHz. The VCVS source E1 creates an exact replica of V1 at the input of FM modulator X2 that is amplified by the '''Gain Block''' A1, which is a copy of the gain block '''PA''' placed before the transmit antenna load '''Rant'''. The output of A1 then passes through a '''Radar Echo Block''' of the same parameters as the previous part and with a target range of 1500m. In this way, the signal at Node 9 at the output of the radar echo block gives a good representation of the echo signal received at the aperture of the receive antenna. 
−
 
+
   
−
<table>
+
Run a Transient Test of your modulator circuit with the following parameters:
−
<tr>
+
−
<td>
+
−
[[File:SysTUT3 40.png|thumb|750px|The schematic of the COMM link including the transmitter and receiver circuits and the cable channel.]]
+
−
</td>
+
−
</tr>
+
−
</table>
+
−
 
+
−
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:
+
  
 
{| border="0"
 
{| border="0"
Line 547: Line 536:
 
|-
 
|-
 
! scope="row"| Stop Time
 
! scope="row"| Stop Time
−
| 55n
+
| 60u
 
|-
 
|-
 
! scope="row"| Linearize Step
 
! scope="row"| Linearize Step
−
| 10p
+
| 100p
 
|-
 
|-
 
! scope="row"| Step Ceiling
 
! scope="row"| Step Ceiling
−
| 10p
+
| 100p
 
|-
 
|-
 
! scope="row"| Preset Graph Plots
 
! scope="row"| Preset Graph Plots
−
| a1(digital), v(6), v(7), out1(digital)
+
| v(1), v(13)
 
|}
 
|}
  
−
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.
+
The results are shown in the figure below. v(1) is the transmitted triangular ramp signal, and v(13) is the two-frequency output beat signal.
  
 
<table>
 
<table>
 
<tr>
 
<tr>
 
<td>
 
<td>
−
[[File:SysTUT3 41.png|thumb|750px|The graph of the digital input and output binary sequences of the QAM Modulator-Demodulator combo circuit, plotted together with the voltages at the input v(6) and output v(7) of the transmission line channel.]]
+
[[File:SysTUT7 26.png|thumb|750px|The graph of the input triangular ramp signal and the output beat signal of the FMCW radar transmitter-receiver circuit using triangular chirp modulation.]]
 
</td>
 
</td>
 
</tr>
 
</tr>
 
</table>
 
</table>
 +
 +
In order to analyze the above results, zoom in the time axis and limit its scale to two intervals: [22&mu;s, 23&mu;s] during the up-ramp and [42&mu;s, 43&mu;s] during the down-ramp. The zoomed-in graphs are shown below. 
 +
 +
<table>
 +
<tr>
 +
<td>
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[[File:SysTUT7 27.png|thumb|750px|The zoomed-in graph of output beat signal v(13) during the time interval [22&mu;s, 23&mu;s].]]
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</td>
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</tr>
 +
</table>
 +
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<table>
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<tr>
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<td>
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[[File:SysTUT7 28.png|thumb|750px|The zoomed-in graph of output beat signal v(13) during the time interval [42&mu;s, 43&mu;s].]]
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</td>
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</tr>
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</table>
 +
 +
Read the periods of the output beat signal at the middle of the two zoomed-in time intervals:
 +
 +
{| border="0"
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|-
 +
| valign="top"|
 +
|-
 +
{| class="wikitable"
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|-
 +
! scope="col"| Time Instant
 +
! scope="col"| Ramp Direction
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! scope="col"| Output Period
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! scope="col"| Output Beat Frequency
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|-
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| t = 22.5&mu;s
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| up-ramp
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| 126.5ns
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| f<sub>bu</sub> = 7.905MHz
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|-
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| t = 42.5&mu;s
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| downp-ramp
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| 123.4ns
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| f<sub>bd</sub> = 8.103MHz
 +
|}
 +
 +
From the two beat frequencies during the up-ramp and down-ramp, you can calculate the target range and its velocity:
 +
 +
<math> R = \frac{cT_s}{4B} \left( f_{bd} + f_{bu} \right) = \frac{(3\times 10^8)(25\times 10^{-6})}{4(20\times 10^6)} (8.103 + 7.905)\times 10^6 = 1500.75\text{m}  </math>
 +
 +
<math> v_r = \frac{\lambda_0}{4} \left( f_{bd} - f_{bu} \right) = \frac{0.3}{4}(8.103 - 7.905)\times 10^6 = 14850\text{m/s} </math>
 +
 
<p>&nbsp;</p>
 
<p>&nbsp;</p>
−
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+
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Latest revision as of 15:37, 4 November 2015

Tutorial Project: Simulating a Frequency-Modulated Continuous-Wave (FMCW) Radar System
SysTUT7 9.png

Objective: In this project, you will build and test FMCW radar systems with the capability of target range and velocity detection.

Concepts/Features:

  • Radar System
  • FMCW Radar
  • Chirp Signal
  • FM Modulation
  • Target Range
  • Target Velocity
  • Beat Frequency

Minimum Version Required: All versions

'Download2x.png Download Link: System-Level Lesson 7

What You Will Learn

In this tutorial you will use RF.Spice's black-box virtual blocks to model an FMCW radar system. You will explore FMCW radar systems with both sawtooth and triangular chirp modulations and see how the target range and velocity information are extracted from the output beat signals.

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:

The transmitted and received ramp waveforms in an FMCW system with sawtooth chirp modulation.

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]

The simplified block diagram of an FMCW radar system.

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:

The transmitted and received ramp waveforms in an FMCW system with triangular chirp modulation.

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. For example, at an operating frequency of f0 = 10GHz, λ0 = 30mm. A moving car target driving at a speed of 20m/s (or 72km/hr) towards the radar generates a frequency shift of fd = 1.33kHz. When driving away from the radar, the same car produces a Doppler shift of -1.33kHz.

The Doppler frequency shift fd caused by a moving target is superposed with the frequency shift of the echo signal due to reflection from a stationary target. When the target is approaching the radar, fd is positive and it slightly lifts up the reflected ramp signal. When the target is moving away from the radar, fd is negative and it slightly lowers down the reflected ramp signal. This leads to generation of two different frequency beat signals during the up-ramp and down-ramp sweeps:

[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]

In the above equations, the sweep time Ts is half the period of the ramp's triangular wave function.

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.

A simple FM modulator circuit.

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.

The property dialog of the FM Modulator Block.

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:

V1: Sinusoid
Offset Voltage 0
Peak Amplitude 1V
Frequency 0.5MHz
Delay Time 0
Damping Factor 0

  

V1: Pulse (Square Wave)
Initial Voltage -1
Peak Voltage 1
Delay Time 0
Rise Time 1n
Fall Time 1n
Pulse Width 1u
Pulse Period 2u

  

V1: Ramp (Sawtooth)
Ramp Period 0
Output Lower Limit -1V
Output Lower Limit 1V
Ramp Type 0 (Up-Ramp)

  

V1: Triangular Wave
fo 0.5MHz
Duty Cycle 0.5
Peak Output Amplitude 1V

For each waveform, run a Transient Test of your modulator circuit with the following parameters:

Start Time 0
Stop Time 4u
Linearize Step 1n
Step Ceiling 1n
Preset Graph Plots v(1), v(2)

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.

The graph of the input and output waveforms of the FM modulator circuit with a sinusoidal input.
The graph of the input and output waveforms of the FM modulator circuit with a pulse (square wave) input.
The graph of the input and output waveforms of the FM modulator circuit with a ramp (sawtooth wave) input.
The graph of the input and output waveforms of the FM modulator circuit with a triangular wave input.

Modeling an FMCW System with Sawtooth Modulation

The following is a list of parts needed for this part of the tutorial lesson:

Part Name Part Type Part Value
X1 Ramp Generator Defaults, Chirp Period = 100u, freq_low = 1GHz, freq_high = 1.01GHz
X2 Ideal Signal Splitter Defaults (k = 0.5)
X3 Radar Echo Block Defaults, range = 1500m, fo = 1GHz
X4 Generic Lowpass Filter Block Defaults, Cutoff = 2Meg
E1 Voltage-Controlled Voltage Source Defaults, gain = 1, controlled by v(4,0)
PA Gain Block Defaults, gain = 5e+3
LNA Gain Block (must be made unique) Defaults, gain = 5e+3
AMP Gain Block (must be made unique) Defaults, gain = 50
MIX Multiplier Block Defaults
Rant Resistor 50
RL Resistor 50

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.

The property dialog of the Sine Wave Chirp Generator.

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 property dialog of the Radar Echo Block.

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 schematic of the FMCW radar transmitter-receiver circuit using sawtooth chirp modulation.

Run a Transient Test of your modulator circuit with the following parameters:

Start Time 0
Stop Time 20u
Linearize Step 50p
Step Ceiling 50p
Preset Graph Plots v(1), v(7), v(9), v(10)

Some of the results are shown in the figure below. v(1) is the transmitted chirp signal, and v(7) is the amplified received signal. The blue signal v(10) is the output beat signal, which has a measured period of 1.009μs. Therefore, fb = 1MHz.

Attention icon.png Radar system simulations usually involve time scales of different orders. They typically require a large transient time interval with a very fine time step ceiling.
The graph of the transmitted signal (light blue), received signal (yellow), and the output beat signal (dark blue).

The figure below shows the input and output signals of the lowpass filter, i.e. the mixer's down-converted output signal and the filtered output beat signal:

The graph of the input and output signals of the lowpass filter.

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. Therefore, 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 [19.99μs, 20μs]:

The zoomed-in graph of the transmitted and received signals and the mixer output in the interval [19.99μs, 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 had set in the radar echo block.

[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 Modulation

The following is a list of parts needed for this part of the tutorial lesson:

Part Name Part Type Part Value
V1 Triangular Wave Generator Defaults, fo= 20KHz
X1 FM Modulator Block Defaults, fc = 1GHz, f_del = 10MHz
X2 FM Modulator Block Defaults, fc = 1.001GHz, f_del = 10MHz
X3 Ideal Signal Splitter Defaults (k = 0.5)
X4 Radar Echo Block Defaults, range = 1500m, fo = 1GHz
PA Gain Block Defaults, gain = 5e3
A1 Gain Block (copy of PA) Defaults, gain = 5e3
LNA Gain Block (must be made unique) Defaults, gain = 5e3
AMP Gain Block (must be made unique) Defaults, gain = 100
MIX Multiplier Block Defaults
X5 Generic Lowpass Filter Block Defaults, Cutoff = 12Meg
Rant Resistor 50
RL Resistor 50

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. You will do this by feeding a triangular wave generator V1 with a frequency of 20kHz (and a period of 50μs) as the modulating signal to the FM Modulator block X1 with a carrier frequency fc = 1GHz and a maximum frequency deviation of 10MHz. As the input triangular wave oscillates between -1V and +1V, the output frequency of the FM modulator will oscillate between 990MHz and 1010MHz. Therefore, B = 20MHz and Ts = 25μs.

The schematic of the FMCW radar transmitter-receiver circuit using triangular chirp modulation.

Place and connect all the parts as shown in the above figure. The circuit of this part is similar to the circuit of the previous part, except for the fact that you need to introduce a Doppler frequency shift in the echo signal. To model this additionally frequency-shifted echo signal, you introduce a second FM modulator X2 which is fed by the same triangular waveform V1 but with a slightly shifted carrier frequency of 1.0001GHz. For the purpose of this tutorial and to demonstrate a practical simulation, we assume that the Doppler frequency shift is fd = 100kHz. This translates to a target velocity of vr = fdλ0/2 = 15km/s, which is extremely high. But remember that typical vehicular speeds would only produce a Doppler shift of few hundreds of Hertz at 1GHz. The VCVS source E1 creates an exact replica of V1 at the input of FM modulator X2 that is amplified by the Gain Block A1, which is a copy of the gain block PA placed before the transmit antenna load Rant. The output of A1 then passes through a Radar Echo Block of the same parameters as the previous part and with a target range of 1500m. In this way, the signal at Node 9 at the output of the radar echo block gives a good representation of the echo signal received at the aperture of the receive antenna.

Run a Transient Test of your modulator circuit with the following parameters:

Start Time 0
Stop Time 60u
Linearize Step 100p
Step Ceiling 100p
Preset Graph Plots v(1), v(13)

The results are shown in the figure below. v(1) is the transmitted triangular ramp signal, and v(13) is the two-frequency output beat signal.

The graph of the input triangular ramp signal and the output beat signal of the FMCW radar transmitter-receiver circuit using triangular chirp modulation.

In order to analyze the above results, zoom in the time axis and limit its scale to two intervals: [22μs, 23μs] during the up-ramp and [42μs, 43μs] during the down-ramp. The zoomed-in graphs are shown below.

The zoomed-in graph of output beat signal v(13) during the time interval [22μs, 23μs].
The zoomed-in graph of output beat signal v(13) during the time interval [42μs, 43μs].

Read the periods of the output beat signal at the middle of the two zoomed-in time intervals:

Time Instant Ramp Direction Output Period Output Beat Frequency
t = 22.5μs up-ramp 126.5ns fbu = 7.905MHz
t = 42.5μs downp-ramp 123.4ns fbd = 8.103MHz

From the two beat frequencies during the up-ramp and down-ramp, you can calculate the target range and its velocity:

[math] R = \frac{cT_s}{4B} \left( f_{bd} + f_{bu} \right) = \frac{(3\times 10^8)(25\times 10^{-6})}{4(20\times 10^6)} (8.103 + 7.905)\times 10^6 = 1500.75\text{m} [/math]

[math] v_r = \frac{\lambda_0}{4} \left( f_{bd} - f_{bu} \right) = \frac{0.3}{4}(8.103 - 7.905)\times 10^6 = 14850\text{m/s} [/math]

 

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