Transformer Coupled CE Amplifier

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Figure 1 gives the basic circuit of a transformer coupled CE amplifier stage. In figure 1, a current source Is having shunt source resistance Rs drives the amplifier through a transformer TR1. Load resistance RL is fed from the collector output circuit through a transformer TR2. A transformer coupled CE amplifier finds following applications:

  1. As input stage of a multistage simplified and usually driven by a microphone.
  2. As output stage feeding the load impedance and
  3. As intermediate stage

Transformer coupling permits impedance matching thereby resulting in greater power gain. The transformer serves another function of isolating the collector circuit from the dc bias stabilization network of the next stage. For excellent performance, it is necessary to shield the transformer from electrical noise, hum and unwanted pick-ups.

In figure 1, capacitor C allows complete input power to flow into the base circuit. Resistor R1, R2 and Re taken together come in series with the primary of the output transformer TR2.

basic circuit of transformer coupled CE amplifier

For maximum transfer of power from the driving source to the amplifier, the source resistance Rs is required to be matched with the input impedance of the amplifier transferred to the primary side of the input transformer TR1.

Thus, R_s = n^2_1\times Zi       ….(1)

Similarly, for maximum transfer of power from the amplifier output circuit to the load impedance, the output impedance Z0 of the amplifier must be matched with the load impedance RL transferred to the primary side of the output transformer TR2.

Thus, Z_0 = n^2_2\times R_L     …..(2)

In cascade amplifier using transistors, the input and output impedances of different stages will be different. Hence each transformer is required to be designed separately.

Analysis of Transformer Coupled CE Amplifier

As in the case of RC coupled amplifier, here also the entire frequency range may be divided into three frequency ranges namely (a) low frequency range (b) middle frequency range and (c) high frequency range. Figure 2 gives the equivalent circuit of one stage using high frequency hybrid-\pi model for the transistor. Here shunt capacitance C in the input circuit indicates the total effective capacitance. Further, in figure 2, L_1(1-K^2) represents the leakage inductance of the transformer TR1. Similarly L_{11}(1-k^2) represents the leakage inductance of the transformer TR2 while L_{11}K^2 represent the magnetizing inductance. TR1 and TR2 represent ideal transformer.

equivalent circuit of one stage of transformer coupled amplifier

Middle Frequency Range

In the midband, frequency is so small that reactance of shunt capacitance C is very large. Hence C may be omitted. Similarly, the reactance of series inductances L_1(1-k^2) and L_{11}(1-k^2) are so small that these may be neglected. Then the output circuit in the equivalent circuit of figure 3 reduce to that shown in figure 3. In this circuit, resistance R1 and R2 have also been neglected being small in the midband. Further the reactance of magnetising inductance L_{11}K^2 is large in comparison with the impedance R0 and n^2R_L. Hence L_{11}k^2 is also neglected. Since, no reactive element is involved in the equivalent circuit of figure 2, the current gain and voltage gain remain constant in the midband.

equivalent circuit valid for middle frequency range

Low Frequency Range

In low frequency range, frequency being low, we may neglect the impedance R1’ and L_{11}(1-k^2) in the series path but we cannot neglect the impedance of magnetizing inductance L_{11}k^2. Hence the equivalent circuit valid for low frequency range is as shown in figure 4.

equivalent circuit valid for low frequency range

Because of the presence of shunt inductance L_{11}k^2, the gain falls with the decrease of frequency.

The lower 3-dB frequency is then given by,

f_L = \dfrac{1}{2\pi (Time\ constant\ of\ R-L\ circuit)}     …..(3)

= \dfrac{1}{2\pi(L/R)}

Where L = L_1^2 k_2

And R = R_o || (n_2^2\times R_L) = \dfrac{R_o\times n_2^2\times R_L}{R_0 + n_2^2 R_L}       …..(4)

Hence, f_L = \dfrac{1}{\pi}\times \dfrac{R_o \times n_2^2 \times R_L}{(R_o + n_2^2 R_L)L}

In a typical case, n_2^2\times R_L = R_o = 3k\Omega and L = 10 henry.

Then f_L = \dfrac{1}{\pi}\times \dfrac{1.5\times 10^3}{10} = 24 Hz

High Frequency Range

Figure 5 gives the input circuit of the equivalent circuit valid for high frequency range. Here leakage inductance L_1(1-k^2) has been transferred to the secondary side to result in inductance \dfrac{L_1(1-k^2)}{n_1^2}. The magnetizing inductance has not been included in the equivalent circuit since its effect is negligible in high frequency range.

equivalent circuit of high frequency transformer coupled amplifier

Now capacitance C resonates with inductance {L_1(1-k^2)}{n_1^2}. But r_{b1e} being very low, the effect of this resonance is not of significance.

In the high frequency range, voltage V_{b1e} across C reduces as the frequency increases. This time constant of the circuit equals \dfrac{L}{R} where

L = \dfrac{L_1(1-k^2)}{n_1^2}      …..(5)

And under matched condition,

R = r_{bb1} + R_2 + r_{b1e} = \dfrac{R_1 + R_s}{n_1^2}      ……(6)

The higher 3-dB frequency is given by,

f_H = \dfrac{1}{2\pi} \times \dfrac{1}{\dfrac{L}{R}} = \dfrac{R}{2\pi L}     …..(7)

Where L and R are given by Equations 5 and 6 respectively.

In a typical case, L_1 = 9 H, n_1^2 = 9, C = 300 pF, R = 103 \Omega and k = 0.98

Then L = \dfrac{9[1-(0.98)^2]}{9} = 0.04H Hence f_H = \dfrac{10^3}{2\pi \times 0.04}Hz = 4 KHz

In a typical case, resonance of shunt capacitance C and leakage inductance {L_1(1-k^2)}{n_1^2} takes place at a frequency of about 20 KHz. But since Rb’c is small, effect of this resonance is not of much important.

Voltage gain versus frequency curve of transformer coupled CE amplifier is similar to that of RC coupled amplifier except for the possibility of slight increase in gain at the frequency of resonance. Transformer coupled amplifier is generally not used for intermediate stage in a cascade amplifier since it is costly and bulky. It is used as input stage and output stage where it can conveniently provide impedance matching.

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