# Calculating Bandwidth for RF/Photonic Components based on Velocity mismatch

The bandwidth of a device such as a modulator or photodetector is an important figure. When designing a modulator or photodetector for high frequencies, much attention is paid to matching the velocity of the optical waves and the RF waves.

By finding the propagation time difference between the optical and RF waves, we model this in the time domain as a rect function. Note that for the rect function, the difference in propagation time is the tau variable. Performing the Fourier transform on the rect function will give us a sinc function. The 3dB cutoff point of this sinc function in the frequency domain gives us the device bandwidth. Note the MATLAB algorithm used below. The 3dB bandwidth is calculated using a simple manipulation of the frequency vector indices.

v_optical = ; %simulated optical velocity [define]

v_RF = ; %simulated RF velocity [define]

l_device = ; %device length [define]

f_max = ; %max frequency of vector (should be higher than bandwidth) [define]

f_num = ; %number of frequencies in vector [define]

tau = abs((l_device/v_optical)-(l_device/v_RF)) ; %propagation time difference

W = linspace(0,f_max,f_num); %frequency vector

S = tau*sinc(W*tau/2); %sinc function in frequency domain

Qs = find(20*log10(S)<=(20*log10(S(1))-3)); %intermediate calculation for index of 3db cutoff

BW_3dB= f_max*(Qs(1))/f_num %This is the result

# IMD3: Third Order Intermodulation Distortion

We’ll begin a discussion on the topic of analog system quality. How do we measure how well an analog system works? One over-simplistic answer is to say that power gain determines how well a system operates. This is not sufficient. Instead, we must analyze the system to determine how well it works as intended, which may include the gain of the fundamental signal. Whether it is an audio amplifier, acoustic transducers, a wireless communication system or optical link, the desired signal (either transmitted or received) needs to be distinguishable from the system noise. Noise, although situationally problematic can usually be averaged out. The presence of other signals are not however. This begs the question, which other signals could we be speaking of, if there is supposed to be only one signal? The answer is that the fundamental signal also comes with second order, third order, fourth order and higher order distortion harmonic and intermodulation signals, which may not be averaged from noise. Consider the following plot:

We usually talk about Third Order Intermodulation Distortion or IMD3 in such systems primarily. Unlike the second and fourth order, the Third Order Intermodulation products are found in the same spectral region as the first order fundamental signals. Second and fourth order distortion can be filtered out using a bandpass filter for the in-band region. Note that the fifth order intermodulation distortion and seventh order intermodulation distortion can also cause an issue in-band, although these signals are usually much weaker.

Consider the use of a radar system. If a return signal is expected in a certain band, we need to be able to distinguish between the actual return and differentiate this from IMD3, else we may not be able to trust our result. We will discuss next how IMD3 is avoided.

The basic principle of an RF over Fiber link is to convey a radio frequency electrical signal optically through modulation and demodulation techniques. This has many advantages including reduced attenuation over long distances, increased bandwidth capability, and immunity to electromagnetic interference. In fact, Rf over fiber links are essentially limitless in terms of distance of propagation, whereas coaxial cable transmission lines tend to be limited to 300 ft due to higher attenuation over distance.

The simple RFoF link comprises of an optical source, optical modulator, fiber optic cable and a receiver. The RF signal modulates the optical signal at its frequency (f_opt) with sidebands at the sum and difference of the RF frequency and optical signal frequency. These beat against the carrier in the photodetector to reproduce and electrical RF signal. The above picture shows amplitude modulation and direct detection method. Also, impedance matching circuitry is generally included to match the ports of the modulator to the demodulator as well as amplifiers.

Before designing an RFoF link, it must be essential to bypass a transmission line in the first place. Will the system benefit from having a lower size and weight or immunity to electromagnetic interference? Is a wide bandwidth required? If not, this sort of link may not be necessary. It also must be determined the maximum SWaP of all the hardware at the two ends of the link. Another important consideration is the temperature that the link will be exposed to (or even pressure, humidity or vibration levels) that the link will be exposed to. The bandwidth of the RF and distance of propagation must be considered, finally.

The Following Figures of Merit can be used to quantify the RFoF link:

Gain

In dB, this is defined as the Signal out (in dBm) – Signal in (dBm) or 10log(g) where g is the small signal gain (gain for which the amplitude is small enough that there is no amplitude compression)

Noise Figure

For RADAR and detection systems where the input signal strength is unknown, Noise Figure is more important than SNR. NF is the rate at which SNR degrades from input to output and is given as N_out – kTB – Gain (all in dB scale).

Dynamic Range

It is known that the Noise Floor defines the lower end of dynamic range. The higher end is limited by spurious frequencies or amplitude compression. The difference between the highest acceptable and lowest acceptable input power is the dynamic range.

For example, if defined in terms of full compression, the dynamic range would be (in dB scale) : S_in.max – MDS. where MDS is the minimum detectable signal strength power.

Scattering Parameters

Scattering parameters are frequency dependent parameters that define the loss or gain at various ports. For two port systems, this forms a 2×2 matrix. In most Fiber Optic links, the backwards isolation S_12 is equal to zero due to the functionality of the detectors and modulators (they cannot perform each other’s functions). Generally the return losses at port 2 and 1 are what are specified to meet the system requirements.

# High Speed Waveguide UTC Photodetector I-V Curve (ATLAS Simulation)

The following project uses Silvaco TCAD semiconductor software to build and plot the I-V curve of a waveguide UTC photodetector. The design specifications including material layers are outlined below.

# Simulation results

The structure is shown below:  Forward Bias Curve: Negative Bias Curve: Current Density Plot: Acceptor and Donor Concentration Plot: Bandgap, Conduction Band and Valence Band Plots: # DESIGN SPECIFICATIONS

Construct an Atlas model for a waveguide UTC photodetector. The P contact is on top of layer R5, and N contact is on layer 16. The PIN diode’s ridge width is 3 microns. Please find: The IV curve of the photodetector (both reverse biased and forward bias).

The material layers and ATLAS code is shown in the following PDF: ece530proj1_mbenker