Diode detectors for RF measurement Part 1: Rectifier ...

1 1. Diode detectors for RF measurement Part 1: Rectifier circuits, theory and calculation procedures. By David W Knight1. Version2 (not yet finished), 1st Jan. 2016. D. W. Knight, 2005-2008. 2013-2016. Please check the author's website to make sure you have the most recent version of this document and its accompanying files: . Abstract This article addresses the subject of RF signal detection from the point of view of those who design and calibrate impedance matching bridges and other measuring instruments operating in the HF and VHF radio ranges. The principal discussion relates to the simple Diode peak-detector; and covers the different possible circuit configurations, the associated theory, and the numerical methods needed for data analysis.

2 Circuit techniques used to linearise the Diode detector output are to be discussed in a separate document. Analysis of the detector transfer characteristic for sinusoidal input shows that the AC-induced error term involves the zero-order modified Bessel function of the first kind (I0). This result is not new, but it is often disregarded. The dynamic contribution is quite unlike the error that occurs for DC input, regardless of any compensatory modification of circuit parameters; which means that linearity correction schemes using a reference Diode to produce a DC amplifier with a complementary gain law can never be perfect. It is also shown however, that the AC error is independent of frequency provided that the smoothing capacitor is 'large'.

3 This means that the tracking detector system, which involves automatic self-calibration against a low-frequency precision Rectifier , is theoretically sound. By considering the power dissipated in the detector, it is shown that the input impedance can be calculated using first and zero-order modified Bessel functions of the first kind (I0 and I1). This allows the determination of detector transfer -functions that take source impedance into account. When this facility is combined with the ability to calculate the dynamic component of the peak detection error, a measurement of DC output taken with a calibrated voltmeter can be converted into a measurement of AC input without the need for an AC reference. The computation procedures required are not simple, but they are described in detail and given as Basic algorithms readily adaptable to any programming environment.

4 1 Ottery St Mary, Devon, England. 2 Revision history: Version (2016-01-01): Minor additions & corrections. References added. Added section Comments on guard-ring structure in section Re-rendered formulae using OO math. Version (2014-10-18): Eliminated perfect decoupling capacitors from equivalent circuits (redundant, confusing). Added section - temperature dependence of IS . Section - series-parallel to series transformation, general form with macros. Section - shunt Diode Rectifier with parasitics. Section 15 - content added. Problems with numerical instability still unresolved. 2. Diode detectors for RF measurement Part 1: Rectifier circuits, theory and calculation procedures. Table of Contents 1. Series- Diode half-wave Rectifier .

5 6. Circuit behaviour and basic design principles ..6. Diode peak inverse voltage ..8. Input chokes ..9. Large signal input impedance ..9. Separation of port resistance and source impedance ..12. Actual input voltage ..13. Inductively loaded AM Demodulated signal frequency 2. Shunt- Diode Rectifier ..17. Sampling floating voltages ..19. 3. Voltage-doubler Rectifier ..21. Doubler input impedance ..22. 4. Bridge Rectifier ..23. 5. Bi-phase Rectifier ..27. 6. Diode static voltage vs. current characteristic ..29. Variation of saturable leakage current with Diode 7. Signal Diode data ..34. 8. Diode circuit model ..36. Diode stacking ..36. 9. Back diodes ..37. 10. Vacuum thermionic diodes ..38. 11. A brief history of Diode detectors .

6 39. 12. Simple Diode voltmeter dynamic characteristics ..44. AC-DC transfer function ..44. Peak to average current ratio ..53. Detector power dissipation and input impedance ..55. Diode power dissipation ..57. Fast unrestricted computation of input impedance ..61. Using Diode dynamic resistance to estimate input impedance ..62. 13. Calculation procedures for the simple Diode voltmeter ..64. Modified Bessel function, first kind, zero order ..64. Polynomial used in the asymptotic form, first kind, zero order ..66. Determining output voltage from peak input voltage ..67. Determining peak input voltage from output voltage ..70. Derivative of the asymptotic form polynomial, first kind, zero order ..73. Inverse modified Bessel function, first kind, zero order.

7 74. Modified Bessel function, first kind, first order ..76. Polynomial used in the asymptotic form , first kind, first order ..77. Ratio of modified Bessel functions, first order / zero order ..78. Determining output voltage from source off-load voltage ..79. 3. Determining source off-load voltage from output voltage ..82. 14. Generalised half-wave detector model ..83. Series Diode Rectifier with port resistance and parasitics ..83. Series-parallel to series transformation ..93. Shunt Diode Rectifier with port impedance and parasitics ..95. 15. Detector with Diode series resistance ..98. Instantaneous Diode current ..99. Average Diode current by numerical integration ..101. Output voltage from peak input voltage ..108. Comparison of numerical integration and transformation methods.

8 110. Peak input voltage from output voltage ..111. 99. Work in progress ..113. Note on detector modelling routines The program routines given in the text are available from the accompanying spreadsheet file: To access, edit or copy the code, open the file using Apache Open Office3 and select the top menu item: ' Tools / Macros / Organise Macros / OpenOffice Basic '. Then navigate to the library ' / Standard / detector_funcs '. See the OO Basic Guide4 for a description of the programming language. The StarOffice Basic programming guide5 can also provide useful additional detail because it relates to the language from which OO Basic evolved. 3 4 5 4. Introduction The Diode detector finds widespread use as a high-frequency voltmeter; its principal advantage, apart from the simplicity of the circuit, being the ability to provide a bandwidth of several hundred MHz with minimal attention to physical layout.

9 This property means that detectors can be connected directly to the output ports of bridges and other measuring devices, thereby eliminating the need for down conversion or high-speed sampling. The essential preconditions are that the signal amplitude should be tailored to lie somewhere in the range from about V to 10 V RMS, and that the source network should have a moderate load-driving capability. The difficulty with the Diode detector however, is that there is a big difference between using it to make a crude RF level indicator, and using it to make an accurate measuring instrument. This is primarily because the circuit behaves in an extremely non-linear manner for small signals and becomes only approximately linear as the signal voltage approaches the point at which the Diode will be destroyed.

10 Correction is not straightforward, and widely-used linearisation schemes involving a DC amplifier with a complementary gain law are not completely successful because the behaviour under AC excitation is not the same as under static conditions. The matter of turning the Diode detector into an accurate broadband voltmeter is nevertheless well worth pursuing; not least because the perfect solution, an active Rectifier or 'superdiode' circuit, is typically restricted to an upper frequency limit of about 50 kHz. In this article, we will consider the Diode detector on two ways: firstly, as a measuring device in its own right; and secondly, as a circuit module for inclusion in more elaborate instruments. In the latter case, we will assume that the implementation involves linearisation (or some other re- mapping) of the rectified output, using either digital or analogue methods.