Colpitt’s oscillator output voltage calculation using ” describing functions”

Colpitt’s oscillator is a popular oscillator circuit which is constructed from an inductor, two capacitors, some resistors, and an active device such as a bipolar or a MOSFET, and generally some trial and error !!! Of particular difficulty is the calculation a priori, of the output voltage of the oscillator. However, a technique using the describing function of a bipolar ( or MOSFET or JFET, IGFET etc) makes it possible to calculate the output voltage to a close estimate. ( Perhaps some optimizing needs to be done). For the uninitiated here is a simple definition of a describing function. Assume you have a non linear device which you would need to analyze, using linear tools. How would you do it? In the time domain it is definitely non linear but if you switch to the frequency domain linear analysis tools can be applied. How? Hit the non linear system with a sinusoid of a particular amplitude and frequency. Since the system is non linear it will generate, at its output, a number of sinusoids. Lets pick the output sinusoid that matches our input frequency and all its associated characteristics ( phase etc). This becomes a describing function. Ignore the rest of the outputs. Then linear analysis tools can be applied to this describing function and results obtained. Please visit our website for more technical info and other information.

Signal Processing Group status for October 2021

Signal Processing Group is alive and well and operating as usual. Contact us for analog, RF, Microwave product design, ASICs as well as modules. We can now do 3D modeling using Shapr3d and Solidworks, so we can produce enclosures. Latest work on RFMW is a K band amplifier. Other RFPA’s are a S band amplifier, Find us on Digikey as well where we have started to sell our products starting with a wideband 1dB NF LNA and a wideband RF detector. Many more products to follow. Take a look at our blog for valuable tech. info as well.
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HFSS as a tool to extend EM analysis of RFMW circuits and systems.

Having designed RFMW circuits, ASICs, RFICs and modules for a long time and used most simulators to do the analysis ( the latest in line being ADS and Microwave Office) we added the ANSYS tool HFSS to the repertoire. Although it does not seem to be used as widely as the SPICE based simulators we found it to be of great value in our analysis and a great help in deriving parameters not produced by either of the two aforementioned CAD tools. It provides EM analysis, power analysis, fields and radiation analysis which is a real help in our RFMW design efforts. The philosophy of the tool is slightly different from the usual tools. However, if you want to reduce the risk on your design to a irreducible minimum then HFSS and some of the other ANSYS tools can come in real handy. More on the HFSS tool analysis in this blog to follow. Please visit our website for more analog, RFMW ASIC and module information.

Calculate the gain of a MOSFET in saturation in the strong inversion region given the drain current and the effective gate voltage

The product of the MOSFET transconductance ( KP/KN) and the aspect ratio ( W/L) is being labeled as the gain of the operating MOSFET. A simple calculator to do this is now available for a first order estimate on the Signal Processing Group website. Please check the “complementary” item menu in the SPG website for this and other items of interest.

Calculate the current in the saturation region of a MOSFET in strong inversion

In analog CMOS design the MOSFET is usually operated in saturation where the IDS – VDS curves are close to being flat. The slight slope leads to the definition of the channel length modulation parameter. A simple calculator has been released by Signal Processing Group to allow a first order calculation of this current as starting points of a design. Please visit the SPG website and look under the “calculators” menu item.

Calculate the body effect parameter for a MOSFET in strong inversion

The body effect parameter comes into play for analog CMOS design when the source and substrate is not connected to the same node but have a reverse bias voltage across them. It affects the threshold voltage of the MOSFET and thereby is critical to the operation of the MOSFET. Signal Processing Group has released a simple calculator to evaluate this parameter given the substrate doping and the gate capacitance. The solution is based on a first order model and is primarily useful as a starting point for design. Please visit the Signal Processing Group website for this and other very useful information.

Calculate the surface potential of a MOSFET in strong inversion

The surface potential in a strongly inverted MOSFET is one of the component parameters in the calculation of current in strong inversion ( or for that matter in weak inversion) of a MOSFET. It is used in the calculation of the threshold voltage. It depends strongly on the surface concentration of the MOSFET and the intrinsic concentration of the substrate ( ni). Signal Processing Group has released a simple calculator for first order calculations of this important quantity. Please visit the Signal Processing Group website and look under the ” calculators” menu item to find this calculator as well as many others.