# Simplified Derivative-Based Carrierless PPM Using VCO and Monostable Multivibrator
## 7 Conclusions  
This work introduces a simplified carrierless pulse position modulation (PPM) technique based on differentiating the input signal prior to modulation. The proposed system comprises a differentiator, voltage-controlled oscillator (VCO), and monostable multivibrator to form a compact analog transmitter that generates a PPM waveform without requiring a carrier or synchronization reference. This structure was motivated by the observation that existing carrierless PPM demodulators--whether based on integration, PLLs, or quasi-FM-PWM methods--consistently yield the derivative of the transmitted message.  
Theoretical analysis demonstrated that PPM inherently encodes the derivative of the signal under various processing schemes. Building on this, the proposed modulation method intentionally differentiates the message signal at the outset, streamlining the architecture by aligning modulation and demodulation characteristics. The signal path and behavior were validated through MATLAB (MATLAB Version R2024b Update 5 (24.2.0.2871072)) simulations and hardware-level circuit experiments. In all tested demodulation configurations, the recovered signals closely match the time-derivative of the input message, as confirmed by waveform comparison and correlation metrics.  
The integration of the output to retrieve the original message was not performed in this study to ensure alignment with the objective of demonstrating the simplified derivative-based modulation scheme. This approach also aimed to confirm the consistent recovery of the signal derivative across multiple demodulation methods. Signal-to-noise ratio (SNR) analyses for the three demodulator types are presented and shown to be applicable to the proposed system. The influence of non-ideal hardware characteristics--such as VCO jitter, differentiator noise amplification, and monostable timing drift--is discussed qualitatively.  
Future work will focus on integrating full message recovery, modeling hardware non-idealities, and benchmarking the system against conventional carrierless PPM approaches.  
We have five codes for the Supplementary Materials which can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15116272/s1](https://www.mdpi.com/article/10.3390/app15116272/s1)]([https://www.mdpi.com/article/10.3390/app15116272/s1](https://www.mdpi.com/article/10.3390/app15116272/s1)), Code S1: PWM Signal Generation and Analysis for Section 5.1.1.(A), Code S2: PPM Signal Synthesis Through Signal Processing for Section 5.1.1.(B), Code S3: Signal Conditioning and Final Processing for Section 5.1.1.(C), Code S4: Noise Resistance Analysis for Section 5.1.2., Code S5: Simulation for Non Ideal Analysis and Bandwidth as well as Slew Rate for Section 6.1.  
Conceptualization, J.K., P.W., A.S., and P.T.; data curation, C.K.-i.; methodology, J.K., P.W., C.K.-i., and P.T.; formal analysis, J.K., P.W., A.S., and P.T.; investigation, A.S. and C.K.-i.; software, C.K.-i.; resources, C.K.-i.; validation, J.K., A.S., and P.T.; visualization, C.K.-i., writing--original draft, J.K., P.W., A.S., C.K.-i. and P.T.; writing--review and editing, J.K., P.W., A.S., and P.T.; supervision, J.K. and P.W.; Funding acquisition, P.W. All authors have read and agreed to the published version of the manuscript.  
This work was financially supported by King Mongkut's Institute of Technology Ladkrabang through the Research Fund under Grant Number KREF016727.  
Not applicable.  
Data Availability Statement: Data is contained within the article or Supplementary Materials.  
The authors express their gratitude to King Mongkut's Institute of Technology Ladkrabang for providing facility support.  
The authors declare no conflicts of interest. The authors also declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.