A Parallel Scheme for Correcting High-Frequency Distortions in Transistor Video Amplifiers

I. N. Pustynskii

(Presented by the scientific seminar of the Radio Engineering Faculty)

Introduction

This article considers a parallel correction circuit with simultaneous allowance for the inertia of the transistor and the capacitance of its collector circuit, in contrast to work [1], where the analysis is carried out only for one or another particular case.

Figure 1 shows a single-stage video amplifier based on a semiconductor triode (ST) and its equivalent circuit, where

\[ \beta=\frac{\beta_0}{1+j\omega\tau_\beta} \]

is the base-current transfer coefficient,

\[ \tau_\beta \]

is the base-current transfer time constant,

\[ R_b=R_2 \parallel R_1 \parallel R_3 \]

is the equivalent generator resistance, and the \(R_T C_T\) circuit is intended for temperature stabilization.

Determination of the Correcting Inductance from the Condition of Ensuring an Optimal Frequency or Phase Characteristic. Experimental Verification

The voltage gain of the stage (Fig. 1) is equal to

\[ K_u=K_{u0}\frac{1+j\Omega a_1}{1+j\Omega b_1+(j\Omega)^2 b_2}, \tag{1} \]

where

\[ a_1=m,\qquad b_1=1+q,\qquad b_2=m,\qquad \Omega=\omega\frac{\tau_{HK}}{a_{hbe}},\qquad \tau_{HK}=C_k R_H(1+\beta_0), \]

\[ m=\frac{L a_{hbe}}{R_H^2 C_k(1+\beta_0)} \]

is the correction parameter,

\[ q=\frac{\tau_i}{\tau_{HK}} \]

is the coefficient of the relative inertia of the transistor in the stage,

\[ a_{hbe}=1+\frac{r_e(1+\beta_0)}{R_b+r_b} \]

is the feedback coefficient at midrange frequencies.

\[ K_{u0}=-\frac{\beta_0 R_n}{(R_b+r_b)\alpha_{nbe}}. \]

Formula (1) was obtained under the assumptions:

\[ 1+\beta \simeq \frac{1+\beta_0}{1+j\omega\tau_\beta}, \qquad \frac{r_e(1+\beta)}{\beta z_k}\ll 1,\qquad (\alpha_{nbe}-1)\ll(1+\beta_0),\qquad \frac{R_n(1+\beta_0)}{r_k}\ll 1, \]

which is usually the case.

Fig. 1.

From the modulus of the frequency-distortion coefficient we determine the condition for the optimum frequency response \(a_1^2=b_1^2-2b_2\), from which we find that

\[ m_u=-1+\sqrt{1+(1+q)^2}, \tag{2} \]

i.e.,

\[ L=m_u R_n^2\,\frac{C_k(1+\beta_0)}{\alpha_{nbe}}. \]

In this case the normalized cutoff frequency is equal to

\[ \Omega_{gr\cdot k}=\frac{1}{\sqrt{2}}\sqrt{\,1+\sqrt{1+\frac{4}{m_u^2}}\,}, \tag{3} \]

and without correction

\[ \Omega_{gr\cdot bk}=\frac{1}{1+q}, \]

i.e., the gain in amplification area is equal to

\[ Q_u=\frac{1+q}{\sqrt{2}}\cdot \sqrt{\,1+\sqrt{\,1+\frac{4}{\left[\sqrt{1+(1+q)^2}-1\right]^2}}\,}. \tag{4} \]

When a capacitance \(C_n \simeq (0.1\div 0.3)\dfrac{C_k(1+\beta_0)}{\alpha_{nbe}}\) is present in the load, in the first approximation it may be assumed that

\[ \tau_{nk}\simeq \left[C_k(1+\beta_0)+C_n\alpha_{nbe}\right]R_n \]

and

\[ L=m_u R_k^2\left[\frac{C_k(1+\beta_0)}{\alpha_{nbs}}+C_n\right]. \]

From expression (1) we find that the phase shift of the circuit is

\[ \varphi=-\arctan \Omega \frac{1+q-m+m^2\Omega^2}{1+\Omega^2mq}. \tag{5} \]

Taking the derivative with respect to \(\Omega\) and equating in it the coefficients of \(\Omega^2\) in the numerator and denominator, we obtain the condition for the optimum phase characteristic

\[ m_\varphi^3+3m_\varphi(1+q)-(1+q)^3=0. \tag{6} \]

To speed engineering calculations, the dependence \(m_\varphi=f(q)\) is shown graphically in Fig. 2. For \(q \ll 1\), \(m_\varphi=0.322\) (as in the tube circuit), and for \(q \gg 1\), \(m_\varphi \simeq q\).

Fig. 2.

To verify the calculation formulas (2) and (3), an experiment was carried out with a P403 triode, which had the following parameters: \(\beta_0=62\), \(r_b=100\ \text{ohms}\), \(r_e=12\ \text{ohms}\), \(r_k=157\ \text{kohms}\), \(C_k=5\ \text{pF}\), \(\tau_e=0.247\ \mu\text{s}\).

The results of calculation and experiment are given in Table 1, from which it is evident that the formulas obtained are entirely acceptable for engineering calculations.

The greatest discrepancy between calculation and experiment is observed at the smallest \(R_b\) and \(R_n\), since in this case the passband becomes considerable and, apparently, the capacitance of the emitter junction begins to have an effect, because \(L_{\text{exp}}<L_{\text{calc}}\).

Conclusion

1. As is evident from formula (2), for \(q \ll 1\), \(m_u=0.414\) (as in the tube circuit), while for \(q \gg 1\), \(m_u \simeq q\) and

\[ L=\frac{\tau_e R_n}{\alpha_{nbe}}. \]

These special cases

Table 1

agree fairly well with the results obtained in [1].

1. If, in a tube amplifier, the gain in amplification area for the parallel correction circuit (at $m=m_u$) is 1.72, then in a transistor amplifier this circuit gives a considerably larger gain, since here $q>0$, and for $q \gg 1$ we have $Q_u \simeq q$ (see formula (4)).

REFERENCES

1. K. S. Rzhevkin, E. S. Andrianov, Correction of amplifiers using semiconductor triodes. Radiotekhnika i elektronika, No. 9, 1957.