On the Correction of Flat-Topped Pulse Distortions in Video Amplifiers Using Planar Semiconductor Triodes (PST)
Abstract Generated abstract
This paper analyzes correction of flat-top pulse distortion in wideband video amplifier stages using planar semiconductor triodes, where low input resistance and coupling or emitter bypass capacitances cause low-frequency droop. Using equivalent low-frequency circuits, the author derives transient-response expressions and practical correction conditions for an added RC network in the load circuit, including the influence of emitter stabilization networks. The analysis shows how correction effectiveness depends on resistance ratios, time constants, permissible pulse duration, and parameter spread, and finds that correction in semiconductor-triode amplifiers is generally less effective than in tube amplifiers under comparable conditions. The paper also discusses temperature stability, identifying stabilization of input resistance, chiefly through emitter resistance selection, as important for maintaining correction over temperature changes.
Full Text
ON THE CORRECTION OF FLAT-TOP PULSE DISTORTIONS IN VIDEO AMPLIFIERS USING PLANAR SEMICONDUCTOR TRIODES (PST)
I. N. Pustynskii
(Presented at the 2nd All-Union Conference of the USSR Ministry of Higher Education on Dielectrics and Semiconductors)
Introduction
Video amplifiers are often required to provide amplification over a frequency range from several tens of hertz to several megahertz. The low input resistance of semiconductor triodes (ST) is a cause that makes the reproduction of low frequencies difficult.
The reduction of gain at low frequencies (droop of the pulse top) is due to the presence of the coupling capacitance \(C_n\) and the capacitance \(C_{e2}\), connected in the emitter circuit for shunting the resistance \(R_{e2}\), in the amplified frequency range (Fig. 1). The resistances \(R_{b1}\), \(R_{b2}\), and \(R_{e1} + R_{e2}\) provide the necessary bias to the base of the ST triode and its temperature stabilization. The network \(R_{e1} C_{e1}\) is intended for correction of high frequencies in the amplifier stage.
Fig. 1. Circuit of a video-amplifier stage.
The distortion (droop) of the flat top of a pulse, as in vacuum-tube amplifiers, can be corrected by inserting the network \(R_{\phi} C_{\phi}\) into the load circuit (Fig. 1). The network \(R_{\phi} C_{\phi}\), moreover, improves the decoupling of stages when they are powered from a common source.
Distortion of the Pulse Top
The equivalent circuit of the amplifier stage for low frequencies is shown in Fig. 2. Here triode \(ST_1\) is replaced by a current generator
$i_1 \cdot b$ by the output resistance $R_{\mathrm{out}}$, and the influence of the next stage is represented by the resistance $R_{\mathrm{in}}$, connected in series with the input-referred circuit $R_{e2} C_{e2}$
\[ R_e=R_{e2}(1+b), \qquad C_e=\frac{C_{e2}}{1+b}, \qquad R_b=\frac{R_{b1}\cdot R_{b2}}{R_{b1}+R_{b2}}, \]
\[ R_{\mathrm{in}}\simeq r_b+(r_e+R_{e1})\cdot(1+b), \]
where
$b$ is the current gain of the common-emitter triode with a short-circuited output at low frequency;
$r_b, r_e$ are the base and emitter resistances of the triode, respectively [3].
The transient characteristic for the complete circuit is represented by a very cumbersome expression, which is of no special interest for practical calculations. Therefore it is more convenient to consider the amplifier stage without the circuit $R_e C_e$, and to take its influence on the distortion of the pulse top into account by introducing an equivalent value of the time constant of the transient circuit.
Fig. 2. Equivalent circuit of an amplifier stage at low frequencies.
The normalized transient characteristic for the circuit (Fig. 2) without the circuit $R_e C_e$ has the form
\[ h(t)=\frac{1}{\gamma-\alpha}\left[(a_0-\alpha)e^{-\alpha t}-(a_0-\gamma)e^{-\gamma t}\right], \tag{1} \]
where
\[ a_0=\frac{1+d}{d\cdot \tau_H} \tag{1a} \]
\[ \tau_H=R_H\cdot C_\phi \tag{1b} \]
\[ \alpha=\frac{a_1-\sqrt{a_1^2-4aa_2}}{2a} \tag{1v} \]
\[ \gamma=\frac{a_1+\sqrt{a_1^2-4aa_2}}{2a} \tag{1g} \]
\[ a=d\,\tau_H\tau_n\left[1+k_1\left(1+\frac{R_1}{R_{\mathrm{out}}}\right)\right] \tag{1d} \]
\[ \tau_n=C_n\cdot R_1 \tag{1e} \]
\[ R_1=\frac{R_b\cdot R_{\mathrm{in}}}{R_b+R_{\mathrm{in}}} \tag{1zh} \]
\[ a_1=d\tau_H\left(1+\frac{R_H}{R_{\mathrm{out}}}\right) +\tau_n\left[1+k_1(1+d)\left(1+\frac{R_1}{R_{\mathrm{out}}}\right)\right] \tag{1z} \]
\[ a_2=1+(1+d)\frac{R_H}{R_{\mathrm{out}}} \tag{1i} \]
\[ d=\frac{R_\phi}{R_H} \tag{1k} \]
\[ k_1=\frac{R_H}{R_1} \tag{1l} \]
Despite the external similarity of the equivalent circuits of amplifier stages using planar triodes and tubes, the expressions for their transient characteristics differ considerably from one another [2]. This is due to די
because the inequalities \(R_g \gg R_n\) and \(R_g \gg R_n + R_\phi\), valid for tube amplifiers, lose their force in amplifiers using PTs (especially when \(R_{e1}=0\)).
Formula (1), after expanding the exponentials in power series, takes the form
\[ h(t)=1+t\{a_0-(\gamma+\alpha)\}-\frac{t^2}{2!}\,[a_0(\gamma+\alpha)-(\gamma^2+\alpha\gamma+\alpha^2)]+ \]
\[ +\frac{t^3}{3!}\,[a_0(\gamma^2+\alpha\gamma+\alpha^2)-(\gamma+\alpha)(\gamma^2+\alpha^2)]-f(t,\gamma,\alpha)^n=1+\delta, \tag{2} \]
where
\[ f(t,\gamma,\alpha) \]
is the part of the expansion containing terms of higher orders;
\(\delta\) is the relative deviation of the transient response.
For \((\gamma+\alpha)t<1\), the correction condition is the relation
\[ a_0-(\gamma+\alpha)=0, \tag{3} \]
i.e.,
\[ \tau_n=\tau_p\,\frac{R_{\mathrm{out}}}{R_{\mathrm{out}}+R_n}. \tag{3a} \]
When \(R_{\mathrm{out}} \gg R_n+R_\phi\) and \(R_{\mathrm{out}} \gg R_1\), which usually occurs,
\[ \tau_n=\tau_p \tag{4} \]
and
\[ \delta \approx -\frac{t_u^2}{2\tau_n^2 d(1+k_1)} \left(1-\frac{1}{3}\frac{t_u}{\tau_n}\right), \tag{5} \]
where \(t_u\) is the duration of a single pulse.
If
\[ \frac{t_u}{\tau_n}<0.3, \]
then
\[ \delta \approx -\left|\frac{t_u^2}{2\tau_n^2 d(1+k_1)}\right|. \tag{6} \]
In this case the error of the determination does not exceed 10%.
The effectiveness of the correction is determined by the ratio
\[ \sigma=\frac{t_{u\,\mathrm{corr}}}{t_{u\,\mathrm{without\ corr}}} =\sqrt{\frac{2d}{\delta(1+k_1)}}, \tag{7} \]
where \(t_{u\,\mathrm{corr}}\), \(t_{u\,\mathrm{without\ corr}}\) are the permissible pulse durations for given values of \(\tau_n\) and \(\delta\) when correction is used and without it, respectively.
As is evident from expression (7), the effectiveness of low-frequency correction in video amplifiers using PPTs is \(\sqrt{1+k_1}\) times smaller than in video amplifiers using tubes [2]. If in practice the deviation from equality (4) is 10–15% or more, then the determining factor is already the second term of expansion (2), and
\[ \delta \approx \frac{t_u}{\tau_n(1+k_1)} \left(\frac{\tau_n}{\tau_n}-1\right). \tag{8} \]
In this case the correction efficiency is
\[ \sigma \simeq \frac{1}{1-\dfrac{\tau_n}{\tau_\mu}}, \]
i.e., it will be the same as in the case of tube amplifiers [2].
Allowance for the effect of the \(R_{e2} C_{e2}\) network on the distortion of the flat top of the pulse
The \(R_{e2} C_{e2}\) link is included in those cases when the resistance \(R_{e1}\) is far from sufficient to ensure the specified temperature stabilization in the stage. It is not difficult to calculate that the relative droop of the pulse top due to this network is
\[ \delta_e \simeq \frac{t_u(1+b)}{C_{e2}R_1(1+k_1)} . \tag{9} \]
The total deviation without the correcting link, in the presence of the \(R_{e2} C_{e2}\) network, is
\[ \delta=\delta_n+\delta_e \simeq -\,\frac{t_u}{\tau_n(1+k_1)} -\frac{t_u(1+b)}{C_{e2}R_1(1+k_1)} , \tag{10} \]
where \(\delta_n\) is the deviation of the pulse top due to the transient circuit. To correct the total droop, an \(R_\phi C_\phi\) network is required such that
\[ \tau_\mu = \frac{\tau_n C_{e2}}{C_{e2}+C_n(1+b)} =\tau_{n\,\mathrm{eqv}}, \tag{11} \]
since the rise of the pulse top due to the filter is
\[ \delta_\phi=\frac{t_u}{\tau_\mu(1+k_1)} . \tag{12} \]
Sometimes it is necessary to dispense with the inclusion of the \(R_{e2} C_{e2}\) network when amplifying pulses of long duration, because of the considerable dimensions of the capacitor. In this case temperature stabilization is effected to some degree by means of the resistance \(R_{e1}\), which provides high-frequency correction.
Ensuring correction stability
The most unstable parameter of the circuit entering into the correction condition (4) is the resistance \(R_{\mathrm{in}}\), since it depends to a considerable extent on temperature [1]. Consequently, to ensure more stable correction when the temperature changes, \(R_{\mathrm{in}}\) should be stabilized. This can be done in the following way.
Suppose there are characteristics of a triode of the P1B type, taken at various temperatures (Fig. 3) [1]. Choose the operating point A corresponding to the characteristic for \(t=+20^\circ\mathrm{C}\). It is required to ensure constancy of \(R_{\mathrm{in}}\) over the range of temperature variation from \(+50^\circ\mathrm{C}\)
to \(-50^\circ\mathrm{C}\). At point A the triode has a definite
\[ R_{\text{in}} \simeq \frac{dU_b}{dI_b}. \]
On the characteristics at \(+50^\circ\mathrm{C}\) and \(-50^\circ\mathrm{C}\) we find points B and V at which the triode has the same \(R_{\text{in}}\) as at \(t=+20^\circ\mathrm{C}\). To move the operating point from V to B it is necessary to reduce the voltage between base and emitter by \(\Delta U_b\). This can be accomplished by inserting in the emitter circuit a resistance equal to
\[ R_e=\frac{\Delta U_b}{\Delta I_b+\Delta I_k}\simeq \frac{\Delta U_b}{\Delta I_k}. \]
If the points A, B, and V do not lie on one straight line, the stabilization of \(R_{\text{in}}\) will be incomplete.
Usually the value of \(R_{e1}\) is chosen as a compromise, on the basis of the requirement of providing high-frequency correction and constancy of \(R_{\text{in}}\). On average \(R_{e1}\) is equal to several hundred ohms.
Fig. 3. Characteristics of the planar triode P1B, taken at different temperatures with \(U_k = 10\) volts [1].
Conclusions
- As in tube amplifiers, in amplifiers using PT the correction of flat-top distortions is the more effective the larger
\[ d=\frac{R_{\varphi}}{R_n} \]
and the smaller \(\delta\)—the relative deviation (see 7).
-
Correction is more effective for a smaller value of \(k_1\).
-
With a spread in the parameters of the circuit, the deviation \(\delta\) changes less noticeably for large values of \(d\) and \(k_1\), since
\[ \frac{d\delta}{d\tau_n} \quad \text{and} \quad \frac{d\delta}{d\tau_{\ell}}, \]
as is evident from expressions (6) and (8), are inversely proportional to the quantities \(1+k_1\) and \(d\).
- To ensure more stable correction when the temperature changes, it is necessary chiefly to stabilize \(R_{\text{in}}\).
References
-
Semiconductor Devices and Their Applications, collection of articles edited by Ya. A. Fedotov, issue 1, Sovetskoe Radio Publishing House, 1956.
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A. I. Sokolik and T. M. Atakhanyan, “Reproduction of a rectangular pulse by an amplifier with an RC filter in the anode circuit of the tube,” Radiotekhnika, No. 11, 1956.
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R. Shea, Semiconductor Triodes and Their Applications, Gosenergoizdat, 1957.