# RF Signal Chain Design for FMCW Chirped Radar Systems

*If you could hear the output from your chirped radar system, it might sound like a brahminy starling*

In automotive and UAV radar applications, radar signals are amplified throughout the signal chain. Amplification is critical for ensuring the reflected signal can be accurately detected and for maximizing the range and resolution of your radar system. Although there are some ICs that integrate an entire signal chain into a single package, these integrated packages may not meet your particular needs. In such a case, you’ll need to think about designing your own signal chain for a chirped radar system.

## RF Signal Chain Basics for FMCW Chirped Radar Systems

In FMCW chirped radar systems, the frequency sent to the Tx antennas is synthesized with a linear ramp rate (e.g., with a VCO). If you look at the frequency over time, the ideal graph will look like a sine wave. In real systems, the output frequency graph can look much closer to a stairstep waveform when the emitted frequency is synthesized at discrete values.

Range and resolution are two important design points in any chirped radar system. In an FMCW chirp system with linear ramp rate (such as that used in automotive and UAV radar), the equation below shows how to calculate the maximum usable range as a function of your desired SNR value and Tx power output from the antenna:

*Maximum range in FMCW chirped radar systems*

Note that the noise figure (NF) is equal to the logarithm of the Rx SNR divided by the Tx SNR. The range resolution in FMCW radar can also be easily calculated in terms of the chirp bandwidth (e.g., 4 GHz in 77 GHz automotive radar):

*Range resolution in FMCW chirped radar systems*

FMCW chirped radar can be used to determine the speed of an oncoming object by extracting the frequency shift of successive chirps with heterodyne detection. This frequency shift is due to the Doppler effect, which provides a simple way to calculate the speed of target. When combined with directional emission from a phased array antenna, you can also use your radar system to calculate the target’s heading. This aspect is more of a signal processing topic, and as such is outside the scope of this article. Instead, we want to focus on how the particular characteristics of RF amplifiers affect signal integrity in the signal chain.

## Intermodulation Products and Harmonic Distortion

On the Tx side in FMCW radar, the synthesized frequency will not be a single frequency. In frequency synthesis, the circuit or nonlinear element used to generate the desired modulated signal may also generate other higher order harmonics in addition to sidelobes. These components then enter the Tx amplifier. The power amplifier on the Tx side is generally operating near saturation and the output quickly becomes nonlinear in order to produce the desired power output and satisfy your range requirement. This generates intermodulation products, which appear in the output of the amplifier as the frequency is ramped. This is similar to what happens in passive intermodulation.

These higher order harmonics and intermodulation products should be filtered from the signal on the Tx side prior to entering the amplifier stage if possible. Harmonics and intermodulation products will have lower intensity thanks to the finite bandwidth of the amplifier and the antenna. This will reduce the strength of higher order harmonics and intermodulation products that are sent to the antenna and emitted.

These same higher order harmonics and any intermodulation products in the emitted signal will reflect from the target and can be detected at the receiver. This means the Rx side should also contain a filter to remove higher order harmonics and any intermodulation products. Ideally, the bandwidth of any filters should overlap with the chirp bandwidth, although this is not always possible. Any intermodulation products and harmonics effectively increase the noise floor in the signal chain, and particular intermodulation products can interfere with extraction of the beat frequency.

*Example showing how harmonics and intermodulation products can be generated in the RF signal chain. Note that the width of the upper left spectrum due to modulation is omitted for clarity.*

Among the various intermodulation products that can be generated, the 3rd order product (IM3) is the most important for two reasons. First, this particular pair of frequencies tends to fall very close to the frequency of the desired signal and is likely to fall within the bandwidths of downstream components in your signal chain.

Second, the 3rd order intermodulation product will determine the maximum input level of the fundamental harmonic on the receive side. As the fundamental harmonic increases in strength, the 3rd order harmonic also increases in strength, and the two signal levels eventually become equal. This point is known as the 3rd-order intercept point (3OIP), which determines the highest input signal level that can be reliably used in the Rx side while maintaining linearity of the amplifier stage and ensuring the desired signal can be extracted.

Removing higher order harmonics from your input signal on the Tx side is quite easy; just use a very high order bandpass filter. Any residual frequency-modulated higher order harmonics can generate their own set intermodulation products at lower frequencies that are near your desired frequency band. Removing any intermodulation products near your desired band requires very precise filter design, which is not always feasible.

### Harmonic Balance and Load Pull for Nonlinear Amplifier Analysis

In order to maximize power transfer from your amplifier stages to downstream components in RF design, you’ll need to use load-pull analysis for impedance matching for your Tx amplifier’s output impedance in your signal chain. This is particularly important for examining the behavior of an amplifier operating at large input signals (i.e., your Tx amplifier) as typical DC/AC sweeps produce incorrect results at high input signal levels.

If you want to get an idea of how spurious harmonics affect signal integrity in your system, then you need to use a technique like harmonic balance analysis to determine how any higher order harmonics present in an amplifier’s input will appear at the output. Note that, for an amplifier operating in the linear regime (ideally on the Tx side), the output can be determined using the amplifier’s transfer function, which can then be determined by applying a frequency sweep in a SPICE-based simulation.

Harmonic balance analysis is uniquely designed for determining how higher order harmonics present on an input signal in a nonlinear circuit will propagate to the output. We won’t go into the finer points of harmonic balance analysis here, but there are a number of simulation packages you can use for harmonic balance with SPICE or IBIS models.

There are other important design guidelines to consider when working with microwave and mmWave frequencies in general. These include routing and transmission line layout guidelines (see this article for guidelines in 77 GHz automotive radar), manufacturing considerations, and substrate material selection.

The layout, component selection, and simulation tools in Altium Designer give you a broad toolset for working with chirped radar systems. The simulation and modeling tools are very useful for determining the best circuit design and layout choices for your next chirped radar system.

Now you can download a free trial of Altium Designer and learn more about the industry’s best layout, simulation, and production planning tools. Talk to an Altium expert today to learn more.