Electronic Equations 3: Content :
The Basics of quadrupole parameters for electronic components
Analog electronics units and components can be considered as a black boxes of whose contents we do not know. They are defined by their input and output data. This black boxes are called n-Port . At Fig.1,2,3 we see a 2 port to explain the parameters. The definition can be done with the following 4 parameters which are of course complex values:
The complex Quadrupole parameters at the same frequency, can be converted into one another:
Series connection of Quadrupoles
Two quadrupoles in series. Fig.1 can be computed, to be one quadrupole, if the H or S parameter of the block are known. Y-parametres must first changed into H or S parameters and vice versa:.
Electronic Tubes basic’s, understanding, application, formulas.
There are still many friends of electronic vacuum tubes. The behaviour of vacuum tubes in a circuit can be calculated with the formulas of Barkhausen, but can not be analysed with modern CAD programs, because these programs do not have data blocks of tubes installed. There are mainly 4 kind of tubes used , which have different curves. Fig.1(without filament):
Fig.1 Electronic-tubes and their curves
Electronic tubes have a very high-ohm input grid and its output resistance is in the kOhm range. The tube general formulas without parasitic's , are:
How to analyse vacuum tubes using CAD Programs
Here is a very simple way to analyse tubes with an analysis program, if the program has an Y parameter quadrupole block.(n-port ). The things we need are the y parameters versus frequency of the tube, which must be written in a CAD-Y 2 Port Block. The Y parameters of vacuum tubes are :
This Values can be computed from Capacitance’s and Resisters found in tube Catalogues. Catalogue values are resistor and capacitor values >>>Y = 1/ R . To analyse in a CAD program, we nee values over the frequency working range.
Fig.1 Tube Data
Fig.1 Tube 2 Port
Typical Value are:
In the following formulas, the regular quadrupole formulas are enhanced due of the gain slope S.
Y11, Y22, Y12 , Y 22 are values to be written in a CAD Y- Block like Fig.2Fig.2 Y- Block
Y parameter of tubes in Cathode common circuits
To analyze a circuit without a Cad Block we can use :
Y parameter of tubes in Grid common circuits
To analyze a circuit without a Cad Block we can use :
Y parameter of tubes in Anode common circuits
To analyse a circuit without a Cad Block we can use :
------------------------------------------------------------------------------------------------------------------Analysing the tube with CAD
The Y values Y11, Y22 , Y12, Y21, depending on the frequency, must be written in a CAD Y Block, for instance as a touchstone format . The blue text must be written as a ASC2 DOS text-file.
frequency Y11 Y11angle Y21 Y21angle Y12 Y12angle Y22 Y22angle
OR FIRST COMPUTE THE Y PARAMETERS INT0 S-PARAMETRS AND ANALYSE THE S -PARAMETER-BLOCK USING ‘APPCAD’
How to analyse unknown Transistors with CAD programs
If we want to analyze circuits with transistors, whose data’s are not available in the program , You can write the Data’s of the transistor in a 2-Port Block. But one must know, the quadrupole data’s of the transistor.We write the transistor 2 Port values in a standard S , Y or H block. This are values from catalogue , where sometimes other names are used. Static H Parameters can be read directly from the Data sheet..
Read bidirectional transistor h parameters directly from the datas-heet.
When the transistor cross frequency is ten times higher than the operating frequency, one can use static H parameters for circuit analysis. H Parameters can be read directly from the Data sheet.. Fig. We find these data from the slope of the curve at the working point.
Fig. H parameter emitter common circuit in the data sheet.
The h-parameter are defined as :
Transistor H parameter equations.
To compute the behavior of a circuit with h parameters, we use the 2 Port of Fig1.
Fig.1 Loaded H- parameter 2 port.
Knowing the H- parameters of a transistors, we have a lot of formulas for design. First, we should know that H parameters are complex values having a real part and a imaginary part. For the emitter common circuit we have the following Formulas:
Transistor Y-parameter equations
:Knowing the Y-parameters of a transistor, we have a lot of formulas for design. First, we should know that Y-parameters sometimes have other names and are complex values having a real part and a imaginary part. For the emitter common circuit we have the following Formulas:
To compute the behavior of a circuit with Y parameter, we use the 2 Port of Fig.
:Fig1 Loaded Y-2 Port (Common Emitter)
Rsource and Rload are the real parts of Zsorce and Zload.
To change from common emitter to basec. or collectorc. circuit, the following formulas are valid:
Comparsion of y-parameters of vacuum tubes with transistors
The comparison of a vacuum tube with a transistor is possible if the two-port of the transistor and the 2-port of the tube are equivalent. This requires a transistor 2 - Port with the gain slope S. We obtain the equivalent circuit of Figure 2 with new Y-parameters Y1,Y2,and Y3 :
New Quadrupole Y- parameters including tubes gain steepness S .
With this new 2 port, we can use tube circuit Formulas in transistor circuits:
This values now can be compared with the tube 2 port:
Fig.1 tube 2-port Fig.2 Transistor 2-Port
Neutralization of transistor reaction
The stability of an loaded Transistor amplifier depends on the value of the Collector basis admittance. This reaction of “bad” transistors can be neutralized using a feedback admittance.Fig.1
Fig.1 Neutralized transistor 2-port ((Emitter common)
We have the following Formulas with a “new” transistor and new y-parameters:
Fig.2 “New” transistor due of neutralization
Formulas for transistor resonant amplifiers with y parameters
Fig.1 Two stage transistor amplifier
To find the gain formulas for a resonator loaded transistor amplifier, we must use the formulas for series connection of quadrupoles. Fig.1 shows the blocks of a resonator loaded 2 transistor amplifier . This would be the work of a computer program. For simple circuits we can use the following gain formulas:
Fig.2 Y parameter and resonator
Fig.3 Y parameter and bandpass
Transistor Gain, using S- Parameter equation.
Transistor Amplifier design at higher frequencys, are best realized using the S parameter Formulas .But even at low frequencies ,S-Parameter(Scattering Parameter) are very helpfull. For the case of matched input of a transistor, the gain is: Transistor S-Values
Electronic signals which carry communication content, go through circuits, filters, long distance cables and communication satellite networks . If the phase response of a signal path is not proportional to frequency response, phase and runtime distortions of the signal, will occur. The consequence is that language twitters and images are blurred.
The runtime of the phase is called tp.
tp = b/(omega).
Electronic communication signals consists of many frequencies therefore his run time is called : “group’s run time = tg” , tg is computed with the following differential equation :
tg = db/d(omega).
Fig.1 shows the example of the phase constant of a circuit and its differential quotient
Fig.1 Groups Run Time tg and Phase Constant b versus Frequency
Fig.1b Data bit’s in a communication system:
Delay Equalizer basics of RF-communication electronics.
Delay Equalizer are electronic circuits or layouts or microwave wave-guides, which keep the
running time on a constant value, over the bandwidth of a communication system, to avoid distortions. See Fig.1
Fig.2 Poles and zeros definition
The general transmission equation using the Hurwitz Polynom is :
The definitions are:
In the special case of the run-time equalizer, we get :
The result of the transmission equation F(s) is gain an phase.
Groups run time is as we have already seen: tg = db/d(omega). With the help of a computer program, we can calculate phase and runtime depending on the frequency. As an example at Fig.3 to 6, gruops runtime depending on alpha and beta is shown in the 10 MHz range .The numbered parameter courves at Fig.3-6 are:
#of courve, Alpha , Beta, Phase
Fig.3 -6 Groups runtime tau(omega) versus alpha and beta in the 10 MHz range.
Step by step development of groupdelay equalizers.
The following practical way of developing a group’s runtime Equalizer, is helpful and proven:
.Fig.7 shows as an example the groups run time compensation of a filter
Fig.7 Implementation of a groups run time Equalizer
RF circuits equalizer with discrete components, see the following chapter:
Lumped circuits of runtime Equalizers
There are many circuits for runtime equalizers with discrete components
The circuits and formulas to get basic values are shown in Fig.8-13.This basic basic values are without dimensions and must be multiplied using Lb and Cb.
Omega(b) is the free choice frequency of reference and will be the runtime peak of the equalizer runtime courve. Rb = Free choice of input and output impedance. For Fig.9, we need a perfect coupled transformer having k=1; At RF frequencies the stray inductance of the transformer should be considered, while analyzing the circuit. Factor m is arbitrary.
Fig.8 Equalizer #1; 2. order equalizer
Fig.9 Equalizer #2 ; 4. order equalizer
Fig.10 Equalizer #3; 4. order equalizer
Fig.11 Equalizer #4; 4. order equalizer
Fig-12 Equaliser #5; 4. order equalizer
Practical Example of groups runtime equalizer .
>>>> Go to groups run time equalizer
Readings for runtime equalizers.