In the last tutorial, we saw that an Attenuator is a purely resistive four terminal device designed to attenuate all frequencies by an equal amount without distortion. Attenuators provide “attenuation”, that is a reduction in magnitude of any electrical parameter of a signal when passing along any transmission path to a lower level. The amount of attenuation is a ratio of Output/Input.

There are many different ways in which resistors can be arranged in attenuation circuits, and one such circuit we looked at previously was the “T”-type attenuator. Another popular type of attenuator design commonly used in electrical and electronic circuits is the Pi Attenuator also known as a π attenuator as shown below.

Pi Attenuator Circuit – Unbalanced

The physical configuration of the resistors normally sets the name of the attenuator circuit, with the “pi attenuator” above being so named because in its unbalanced form it resembles the shape of the Greek letter “p” (Pi) which has two vertical bars connected at the top by a third bar forming the resistive shape. There are two sub-classes of pi attenuator network, balanced and unbalanced. An unbalanced pi attenuator uses a common ground connection (as shown above) and are mainly used to reduce the signals in coaxial transmission lines, while a balanced pi attenuator has an additional resistor in this ground connection making them ideal attenuators in twisted pair and line balanced transmission lines. A balanced Pi Attenuator circuit is usually referred to as a balanced “O-type attenuator”.

Pi Attenuator – Equal Impedances

If the input and output impedances are equal, that is Zin = Zout, then the attenuator is symmetrical making the calculation of pi attenuators a lot easier. In the case of a symmetrical pi attenuator, it is usually placed in series between the signal source and the load to provide the required amount of attenuation. Then let us consider that a “Pi Attenuator” is required to provide a specified 6dB attenuation of a 50Ω radio frequency transmission line.

The formulas given for calculating the Pi attenuator circuit for equal input and output impedances are:

Pi Attenuator Equations for Equal Impedances

Using the table of the “K factors” from the previous “T”-type attenuation tutorial below, we can see that the “K” factor value for calculating 6dB attenuation loss is given as 1.9953. This value corresponds to the voltage ratio derived from the given attenuation expressed in decibels.

Attenuator Loss Table

Then the resistor values of R1, R2 and R3 required for 6dB of attenuation matching a 50Ω source and load are calculated as follows:

Giving us the following “symmetrical Pi attenuator” circuit:

Note that the same pi attenuator design will have different resistor values for one a used on a 50Ω network than one that is being matched to a 75Ω or 600Ω network.

Pi Attenuator – Unequal Impedances

Thus far we have calculated the resistor values of an unbalanced symmetrical “Pi attenuator circuit” using some simple maths. But when pi attenuators are used as impedance-matching devices between a source impedance and a different load impedance (Zin ≠ Zout), they may not be symmetrical resulting in different equations being used to match the attenuator.

The formulas given for calculating the resistive values of a Pi attenuator circuit for unequal impedances are:

Pi Attenuator Equations for Unequal Impedances

We can see that the equations for calculating the attenuators three resistor values are much more complex between unequal impedances due to their effect on the resistive network. However, with careful calculation we can find the value of the three resistances for any given network impedance and attenuation as follows:

Non-symmetrical Pi Attenuator Question

An unbalanced non-symmetrical Pi attenuator circuit is required to attenuate a signal between a radio transmitter with an output impedance of 75Ω and a power signal strength meter of impedance 50Ω by 6dB. Calculate the values of the required resistors.

Resistor R1 Value

Resistor R2 Value

Resistor R3 Value

Giving us the following nonsymmetrical Pi attenuator circuit:

The accuracy of the calculated pi attenuator is determined by the accuracy of the component resistors with the values given in the enclosed brackets representing the nearest preferred value at 1% tolerance. Which ever tolerance of resistor is selected to construct a Pi attenuator circuit, 1%, 5% or even 10% they MUST all be non-inductive resistors and not Wirewound! types. Also as we are using resistors in the attenuation network these non-inductive resistors MUST be able to safely dissipate the required amount of electrical power as calculated using Ohms Law.

Zinc Carbon Cell

The carbon zinc dry cell is a very common type of cell. Because its low cost.  It is also called the Leclanche cell, named after the inventor.  Example of Zinc carbon cell is shown in figure (a). while figure (b) illustrates internal construction for the cell.  Voltage output for the carbon zinc cell is 1.4 to 1.6 V, with a normal value of 1.5 V.  Suggested current range is up to 150 mA for the D size, which has a height of 2 ½ in, and a current range of up to 1500 mA.

(a) Carbon Zinc Cell Examples

(b) Internal View of carbon Zinc Dry Cell. This is size D, with height of 2 ½ in.

The electrochemical system consists of a zinc anode and a manganese dioxide cathode in a moist electrolyte.  The electrolyte is a combination of ammonium chloride and zinc chloride is solved in water.  For the round cell construction, a carbon rod is used down the center, as shown in figure (b).  The rod is chemically inert.  However, it serves as a current collector for the positive terminal at the top.  The path for current inside the cell includes the carbon rod as the positive terminal, the manganese dioxide, the electrolyte and the zinc can which is the negative electrode.  As additional functions of the carbon rod, it prevents leakage of the electrolyte but is porous to allow the escape of gases which accumulate in the cell.

In operation of the cell, the ammonia release hydrogen gas which collects around the carbon electrode.  This reaction is called polarization, and it can reduce the voltage output.  However, the manganese dioxide releases oxygen, which combines with the hydrogen to form water.  Then manganese dioxide functions as a depolarizer.  Powdered carbon is also added to the depolarizer to improve conductivity and retain moisture.

Carbon zinc dry cells are generally designed for an operating temperature of 70°F.  Higher temperatures will enable the cell to provide greater output.  However, temperatures of 125°F or more will cause rapid deterioration of the cell.

The chemical efficiency of the carbon zinc cell increases with less current drain.  Stated another way, the application should allow for the largest battery possible, within practical limits.  In addition, performance of the cell is generally better with intermittent operation.  The reason is that the cell can recuperate between discharges, probably by the effect of depolarization.

As an example of longer life with intermittent operation, a carbon zinc D cell may operate for only a few hours with a continuous drain at its rated current.  Yet the same cell could be used for a few moths or even a year with intermittent operation of less than 1 hour at a time with smaller values of current.

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Alkaline Cell

Alkaline cell is also manganese zinc cell type; it is shown in figure (a).  It is available either as a primary or secondary cell but the primary type is more common.  Output of alkaline cell is 1.5 V as carbon zinc cell but the alkaline cell lasts much longer.

The electrochemical system consists of a powdered zinc anode and a manganese dioxide cathode in an alkaline electrolyte.  The electrolyte is potassium hydroxide, which is the main difference between the alkaline and Laclanche cells.  Hydroxide compound are alkaline with negative hydroxyl (OH) ions, while an acid electrolyte has positive hydrogen (H) ions.  Voltage output from the alkaline cell is 1.5 V.

The alkaline cell has many applications because of the ability to work with high efficiency with continuous high discharge rates.  Depending on the application, an alkaline cell can provide up to seven times the service of a Leclanche cell.  As examples, in a transistor radio an alkaline cell will normally have twice the service life of a general purpose carbon zinc cell in toys the alkaline cell typically provides seven times more service.

(a) Construction of Alkaline Cell

The outstanding performance of the alkaline cell is due to its low internal resistance.  Its ri is low because of the dense cathode material, the large surface area of the anode in contact with the electrolyte, and the high conductivity of the electrolyte.  In addition, alkaline cells will perform satisfactorily at low temperatures

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It isn’t a very good circuit for voltage detection. While you have calculated for one value of hfe, what about other extremes? And Vbe variation? And temperature variations?

A couple of possible improvements would be to add a resistor from the base to ground. You should make the base current a lot lower than the current through the potential divider. An additional option to consider would be adding a diode or two in series with the base, or even a zener. Some combination should be possible which gives a reliable, simple circuit even with component and temperature variations.

Keith

Hello Vishal fabrication is done many a ways. if you have acess to milling machine you download the gerber files from your design and use the station to which the milling machine is connected and mill your board. or the primitive but the effective way is to etch your board using acidic solutions a laser printer.

to get a good understanding of how to etch your printed board(tone transfer method). refer to videos on youtube

Circuit Skills: Circuit Board Etching – YouTube

Like these and i hope you will find them useful.

Regards
Elchiquito

Hello,

The closed loop small signal feedback transfer function of a smps with a transconductance error amplifier includes a term which depicts the output divider attenuation ratio?

However, if a normal voltage error amplifier is used then the term involving the output divider ratio is not needed becasue it is taken care of by the transfer function of the voltage error amplifier……(the transfer function of the normal voltage erorr amplifier is Z(fdbk)/Z(in) where Z(in) is the upper divider resistor.

…is the above correct?

9×9 pixels =total 81 pixels. you are right.

but how do you want to access individual pixel?

straight by numbering each pixel individually ? then from 0 to 80(tot 81 pixels) , you require 7 bits to address individual pixel.

but when you use row and column address for referring individual pixel ,
row requires 4 bits and col require 4 bits.(tot 8 bits)

since it is easy to refer individual pixel by (row and col ) addressing , we usually use that method.

Hi…
Can any one help me how to calculate W/L ratio using gm/Id methodology???
any usefull Document for that???

Thanking you….

Hi all,

It would be very helpful if somebody review my explanation about the operation of this ideal voltage doubler based on charge pump shown in the following figure:

ideal_charge-pump_voltage_doubler.jpg

In Phase-1 (when Φ=1): S₁ and S₃ are closed and S₁ is open – the capacitor is connected between the V_DD and the ground.

The capacitor charges up to voltage V_DD and the output (floating) is V_DD

In Phase-1 (when Φ=0): S₁ and S₃ are open and S₁ is closed – the capacitor’s bottom plate is connected to V_DD and top plate to the floating output node.

Initially output voltage is 2V_DD as the voltage across the capacitor is V_DD. But the capacitor will start charging up in the opposite direction so steady state value at output is 0. But it will be not observable in time-domain plot because there is no resistive path so the capacitor charges up to the opposite polarity instantaneously. If I connect a resistance (R) at the output node then it can be seen that the the output discharges from 2V_DD to 0 with RC time-constant.

Am I correct? If not please explain.

Sam.

Hi everybody ;

I need some informations about transformation optics that I will apply to the application of cloaking using metamaterials but I don’t have books, if someone could send me articles or books I will be very thankful …

Nina