Case Study 5 They have been working in the

Grid bias modulation consists in feeding the audio modulating voltage in series with the fixed grid bias in the grid circuit of a class C amplifier. Figure 4.8 shows the basic circuit of grid bias modulated amplifier. In this case, we thus have three voltages in series in the grid circuit namely:

i. Fixed grid bias _xx,

ii. Modulating voltage _₄ and iii. Carrier voltage _.

It assumed that modulation frequency ₄ is much smaller than the carrier frequency _x, then from the point of view of the carrier voltage, the modulation voltage _₄ together than constitute the variation grid bias _₄together than constitute the variable grid bias __xx.

Figure4.8. Basic circuit of grid bias modulation.

3.2.6.1.Analysis of Grid Bias Modulation System

We must understand that the analysis of grid bias modulation amplified may be done in a way similar to that of linear series plate modulation.

Now, let the carrier voltage be given by,_ = 4sin _xa (4.36)

122

The modulation voltage is,_₄ = ₄₄Í _xa (4.37)

Total varying grid __xx is given by,__xx = ₄₄Í _xa (4.38) Total grid-to-cathode voltage __x is given by

__x = _+ __xx ¤¥ _xa + ₄₄Í _xa + _xx (4.39)

Let the r.m.s value of tank current for linear modulation characteristic be given by,

U = A(__xx− _x) (4.40)

Where _xis grid-to-cathode voltage for zero tank current.

But the instantaneous tank current varies at frequency _x and is given by,

¤ = U 4sin _xa (4.41)

Where U 4 is the amplitude of the tank current.

Hence ¤ = √2U sin _xa (4.42)

Or¤ = √2A . (__xx− _x) sin _xa (4.43)

= √2A . [₄₄Í ₄+ _xx− _x] sin _xa (4.44) When the modulation voltage_₄is zero, tank current is given by,

¤ = √2A [_xx− _x] sin _xa (4.45)

¤ = U₄sin _xa (4.46)

Where U₄is the amplitude of the tank current with zero modulation voltage and is given by,

U 4 = √2A [xx− x] (4.47)

Equ. (4.44) may be written as

¤ = √2A (__xx − _x) Î1 +^{ÏÏ Ô} ^Ðl

ÐÐ_Ð Ñ sin _xa (4.48)

¤ = U₄Î1 +_ÐÐ^ÏÏ_ÐÍ _xaÑ sin _xa (4.49)

¤ = U₄[1 + HÍ _xa] sin _xa (4.50)

123 Where His the modulation index and is given by

H =^ÏÏ

ÐÐ_Ð (4.51)

Now since the grid bias is no longer constant but consists of a steady component _xx and variable component _₄ the d.c plate current U is no longer constant but varies in accordance with the variation of variable grid bias __xx as given b the relation.

U = A(_xx− _x) (4.52)

The steady value C.D plate current is given by,

U= A(_xx− _x) (4.53)

Substituting the value of __xx as given by Equ. (4.38) intoEqu. (4.52), we get U = A(_xx− ₄₄Í _xa − _xx)

= A(_xx− ₄₄)Î1 +^{ÏÏ Ô} ^Ðl

ÐÐ_Ð Ñ (4.54)

= A(_xx− ₄₄)(1 + HÍ _xa) (4.55)

= U(+HÍ _xa) (4.56)

Tank circuit voltage is the desired A.C output voltage and given by,

= u vU (4.57)

Where X is the reactance of either the inductor or capacitors at the resonant frequency _x Equ. (4.57)may be put as,

= u v A (xx− _x)(1 + HÍ _xa) (4.58) The instantaneous output voltage is given by,

_ = √2X A (_xx− _x)(1 + HÍ _xa) sin _xa 90)

= √2A (xx− _x)(1 + HÍ _xa) cos _xa (4.59) D.C input power. The average input power from the D.C plate source is given by, =₁⁸

Ï±¹^ÏU ¦a (4.60)

Where 4 is the periodic time of the modulating voltage _4. Putting the value of U in Fig (4.60), we get

= 1

₄

±

¹^Ï

U

(1 + H

Í

a)¦a

On integration, we get

= . U (4.61)

Thus the D.C input power from the plate supply source remains constant for all values of modulation indexH. The A.C output power is given by

=₁⁸

Ï±¹^Ï_¤_W¦a =₁⁸

Ï±¹^Ï$. ¤_W¦a (4.62)

Where ¤_W the a.c component of is plate current at fundamental frequency and $ is the impedance of the tank at resonance of the frequency.

124 3.2.6.2.Characteristics of Grid Bias Modulation

As you might want to know, we have features associated with grid bias modulation. Now, the grid bias modulation has the following salient features:

i. The amount of power required from modulating amplifier is small as compared with plate modulation.

ii. For 100% modulation, the peak amplitude of modulated voltage is twice the amplitude of the unmodulated carrier and hence assuming the same permissible peak power for a tube, the maximum carrier amplitude that may be used in grid bias modulated amplifier is half of that permitted in the class C amplifier using the same tube. Thus, the carrier power that is obtainable from the modulated amplifier is roughly one-quarter of that obtainable for the same tube when used as class C modulated amplifier.

iii. Plate circuit efficiency at zero modulation of class C amplifier offers an increase of modulation index. At 100% modulation, the plate circuit efficiency is about 51%.

3.2.6.3.Performance comparison between Linear Series Plate and Grid Bias Modulations

We now want to make some basic comparisons between linear series plate and grid bias modulations.

The following are the identified comparison regarding plate and grid bias modulation.

i. Plate Circuit Efficiency: Grid modulation amplifier has a low plate circuit efficiency of 34 to 51 per cent whereas the series plate modulated amplifier has large plate circuit efficiency of 75%.

ii. Power output in problem: This is small in grid bias modulation but large in plate modulation.

iii. Amount of modulation power: Grid bias modulation requires small modulating power whereas plate modulation requires large amount of modulating power.

Point i and ii above supports the plate modulation whereas iii supports grid bias modulation. As a result of modulation, the overall efficiency considering both the amplifier modulated, is more or less the same in the method of modulation. Further, both the methods are capable of giving almost 100%

modulations with good linearity of modulation

Thus, there is no clear preference of one method over the other. However the circuit adjustments in grid bias modulation are more sensitive to changes in carrier voltage, plate supply voltage and load impedance and hence it is usually very difficult to achieve and maintain perfect linearity of modulation index.

From the consideration of ease of adjustment, high efficiency plate modulation is generally employed in amplitude modulation radio transmitters operating on medium and sort waves. However in spite of difficulty of adjustment, grid bias modulation of last RF power amplifier is used in high power television because of large width (about 7MHz) of the frequency band involved.

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