#research/waveform-analysis # The Cathode and Anode Waveform shapes are generated directly from the Shockley-Ramo Theorem - Pixelated Anode Case ![[Pasted image 20230116164256.png]][^1] ![[sample-waveforms.png]] An example set of waveforms from a given radiation event measured with the H3DD_UMv4 digital ASIC. Shown are the anode collecting pixel, cathode, and Trigger +4 neighbor waveforms. (I made this one!) This might be a bit of a review for me since I passed our group's Shockley-Ramo Test, but all the same, I had a thought or two that I wanted to write down to make sure I understood this for the eventual event-reconstruction process of my [[Radiography]] project. From the [[Shockley-Ramo Theorem]], we can determine the output waveform from a photon event entering our [[CdZnTe (CZT) Detectors]] detectors. In our group we have detectors with pixelated anodes and planar cathodes. When we use the idea of a weighting potential, we can observe how the charge flows across equipotential lines for the anode and the cathode: ## The Anode  Since the anode is pixelated, we only use a single pixel with the weighting potential. the equipotential lines will curve outward from the pixel, clustering very close to the anode. ## The Cathode The cathode is planar, so the holes moving toward the cathode will create a linear response as they reach the cathode. This, again, has to do with the equipotential lines of the weighting potential as dictated by the [[Shockley-Ramo Theorem]].Because the cathode is planar, no matter the x,y position of the charge carier, its distance away from the cathode, z, is the same. Because there is a linear increase, it makes sense that the cathode waveform response itself would be more linear. ## Waveform shape While the waveform shape remains similar, it will vary based on the depth of interaction of the event, which is how we can determine where in the crystal the photon interaction may have occurred. This is determined ultimately by the [[Cathode-to-Anode Ratio]]. ## More Cases There are cases where instead of a pixelated anode we might have a [[Frisch Grid]], or something similar. To review the mechanics of the [[Shockley-Ramo Theorem]], either visit its page or read [[@heReviewShockleyRamo2001]]. [^1]: [[@petrykAlgorithmsElectronicsProcessing|Dr. Mattew Petryk's Thesis]]