Avalanche transistor generators
Abstract Generated abstract
This paper examines low-frequency generator circuits based on avalanche transistors, using the negative-resistance behavior produced by avalanche breakdown in grounded-emitter and grounded-base configurations. It derives operating relations for sawtooth-voltage and sinusoidal-oscillation generators, including oscillation period, dissipated power, discharge current, load constraints, efficiency, and the influence of supply voltage, capacitance, resistance, and temperature. Experimental results for several transistor types are reported and used to confirm the calculated dependencies, identify practical limits such as permissible power and critical capacitance, and suggest component choices. The circuits are presented as simple, stable, and reliable sources for sweep, timing, pulse, and low-frequency sinusoidal laboratory applications, though with limited supply-voltage utilization and efficiency.
Full Text
AVALANCHE TRANSISTOR GENERATORS
G. P. TROFIMOV
(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)
At sufficiently high voltages, the collector characteristics in a circuit with grounded emitter and base exhibit a clearly pronounced falling section [1]. This makes it possible to create simple and compact generators. The transistors used in such generators are called avalanche transistors, since the breakdown mechanism—the appearance of negative resistance—is based on avalanche multiplication of charge carriers.
In works [2, 3, 4], the static and dynamic properties of transistors in the generation of relaxation oscillations were investigated.
The study of the physical properties and capabilities of the avalanche transistor has led to the creation of generators whose operating frequency is tens of gigahertz [5]. However, the avalanche transistor can also be successfully used for generating low-frequency oscillations.
In the present article, several circuits of such generators are considered.
Sawtooth-Voltage Generator
The generator circuit is shown in Fig. 1a. After the voltage \(E\) is switched on, the capacitance \(C\) and the parallel-connected capacitance of the collector junction \(C_k\) are charged. As the collector voltage approaches the breakdown voltage, multiplication of charge carriers occurs. The increasing collector current creates, across the bulk resistance of the base, a voltage drop that unlocks the emitter junction.
Fig. 1a, b
The avalanche-like process of carrier multiplication leads to breakdown of the transistor and to rapid discharge of the capacitance. A considerable excess charge accumulates in the base, maintaining the open state of the transistor. After the capacitances discharge and the excess charge dissipates, the transistor is cut off and the process is repeated.
Table 1
| Transistor type | P12 | P15 | P13 | P16B | P403 | P16 | P103 |
|---|---|---|---|---|---|---|---|
| Breakdown voltage | 43 | 63 | 84 | 81 | 51 | 87 | 64 |
The voltage across the capacitance increases according to the law
\[ U_c = E(1 - e^{-\frac{t}{RC'}}), \tag{1} \]
where \(C' = C + C_k\) is the total charging capacitance. In low-frequency generators one may take \(C' \approx C\). Since the discharge time of the capacitance is small, the oscillation period can be determined from (1)
\[ T = RC \ln\left(\frac{E}{E - U_p}\right), \tag{2} \]
where \(U_p\) is the breakdown voltage, which varies considerably from specimen to specimen and depends on a number of factors.
With an increase in the voltage \(E\), an increase in the oscillation frequency, and at elevated temperatures, the role of thermal breakdown increases and the voltage \(U_p\) decreases. Therefore, when determining the oscillation frequency accurately, it should be determined experimentally.
To obtain a sufficiently linear voltage rise, transistors with a small collector current in the pre-breakdown region should be selected, and the value of \(E\) should be increased, as in a thyratron generator. A substantial improvement in linearity can be achieved by using current-stabilizing elements in the capacitance charging circuit (D-305-type diodes connected in reverse, or high-voltage transistors with current \(I_k(U_{1k}) = \mathrm{const}\) over a wide range of \(U_k\) values).
The discharge time of the capacitance [2, 3] does not depend on the magnitude of the capacitance when it is varied over wide limits. However, at small values of the capacitance \(C\), the operating oscillation frequency increases, which leads to heating of the transistors and the appearance of an additional quantity of free carriers. The latter increases the transistor current and the discharge time decreases. Heating of the transistor also reduces the breakdown voltage. In this case the linearity of the sawtooth voltage improves, since a more linear initial portion of the exponential is used.
The power dissipated in the transistor is due to the capacitance discharge current and to the current from the source \(E\), flowing through the resistance \(R\) and the transistor at the moment of breakdown.
However, the latter may be neglected, and the average dissipated power is
\[ P = \frac{CU_p^2}{2T}. \tag{3} \]
Substituting the value of \(T\) from (2) into (3), we obtain
\[ P = \frac{U_p^2}{2R \ln \frac{E}{E - U_p}}. \tag{4} \]
Expression (4) makes it possible to determine the parameters \(R\) and \(E\) for which the dissipated power is less than the permissible value at the specified temperature, i.e.,
\[ P+P_0<P_{\text{perm}}, \tag{5} \]
where \(P_0\) is the power dissipated in the transistor due to the heat current \(I_{k0}\) at the maximum operating temperature. In addition, it follows from (4) that the dissipated power does not depend on the capacitance value. The capacitance value can be found from (2) for a specified value of the oscillation period.
The amplitude of the capacitor-discharge current can be determined [4] from the expression
\[ I_{\mathrm{m}}=\frac{Q_{\mathrm{bm}}D_e}{W_{\mathrm{bm}}}, \tag{6} \]
where \(D_e\) is the effective diffusion coefficient;
\(W_{\mathrm{bm}}\) is the base width of the transistor at the instant of maximum current through the transistor;
\(Q_{\mathrm{bm}}\) is the charge accumulated in the base by the instant of maximum current through the transistor.
At a collector voltage \(U_k\), a charge accumulates in the base
\[ Q_{\mathrm{bm}}=\frac{C+C_k}{n+1} \left[ \left(\frac{U_k}{U_p}\right)^{n+1} - \left(\frac{U_n}{U_p}\right)^{n+1} \right], \tag{7} \]
where \(U_n\) is the voltage at the collector of the transistor at the instant the avalanche process begins, usually \(U_n \le |0.8 \div 0.9|U_p\);
\(C_{kn}\) is the capacitance of the collector junction at voltage;
\(n=3\) for p-n-p transistors;
\(n=5\) for n-p-n transistors.
The base width, taking modulation into account, is determined by the expression
\[ W_{\mathrm{bm}}=W_{\mathrm{b0}}-l_0 \sqrt{\frac{U_{\mathrm{km}}}{\Delta\varphi_0}}, \tag{8} \]
where \(W_{\mathrm{b0}}\) is the initial value of the base width;
\(l_0\) is the width of the p-n junction, \(l_0 \simeq 6\ \mu\);
\(\Delta\varphi_0\) is the height of the equilibrium potential barrier, \(\Delta\varphi_0 \simeq 0.35\ \text{V}\).
\[ U_{\mathrm{km}}=U_p(1-\gamma)^{1/n}, \tag{9} \]
where \(\gamma\) is the emitter efficiency.
The short discharge time of the capacitance makes it possible to create a short-pulse generator (Fig. 1, b). With \(R_e=33\ \Omega\), \(C=680\ \text{pF}\), the amplitude of the output pulses is \(12\ \text{V}\). A drawback of such a relaxation generator is the low utilization factor of the power-supply voltage
\[ m=\frac{U_{\text{out m}}}{E}, \tag{10} \]
where \(U_{\text{out m}}\) is the amplitude of the output pulses. In practice, \(m\) does not exceed 25% at any output.
The sawtooth-voltage generator operates only into a high-impedance load. With a capacitance \(C=2000\ \text{pF}\) (\(R=56\ \text{k}\Omega\), \(E=300\ \text{V}\)), the minimum connectable load is \(\sim 70\ \text{k}\Omega\) (with a 15% decrease in the oscillation amplitude).
Sinusoidal-Oscillation Generator
Adding an inductance \(L\) (Fig. 2) of sufficiently high \(Q\) (15 or more) to the circuit considered makes it possible to create a simple generator of sinusoidal oscillations in the audio-frequency range.
Fig. 2.
During charging of the capacitance, the transistor is practically cut off, and the circuit of Fig. 2 may be regarded as a series circuit \(R—L—r—C\), connected to a constant voltage.
Writing the circuit equation and differentiating it with respect to time, we obtain
\[ L\frac{d^2 i}{dt^2}+(R+r)\frac{di}{dt}+\frac{i}{C}=0. \tag{11} \]
Solving equation (11), we find the instantaneous value of the voltage amplitude on the capacitance
\[ U_{\mathrm{cm}}=-E+E\frac{\omega_0}{\omega'}\cos(\omega' t-\beta')e^{-\delta' t}, \tag{12} \]
where
\[
\omega_0=\frac{1}{\sqrt{LC}}
\]
is the natural angular frequency of oscillation of the circuit;
\[
\delta'=\frac{R+r}{2L}
\]
is the damping coefficient;
\[
r
\]
is the active resistance of the inductance;
\[
\omega'=\sqrt{\omega_0^2-(\delta')^2}
\]
is the angular frequency of oscillations;
\[ \beta'=\operatorname{arctg}\frac{\delta'}{\omega'},\qquad 0<\beta<\frac{\pi}{2}. \]
Since the voltage at the transistor collector cannot exceed the breakdown voltage \(U_{\mathrm{p}}\), the part \(L—r—C\) of the whole circuit may be considered as switched on at this voltage. In this case equation (12) takes the form
\[ U_{\mathrm{cm}}=-U_{\mathrm{p}}+U_{\mathrm{p}}\frac{\omega_0}{\omega}\cos(\omega t-\beta)e^{-\delta t}, \tag{13} \]
where
\[
\delta=\frac{r}{2L}
\]
is the damping coefficient in the circuit
\[ r—L—C; \]
\[
\omega=\sqrt{\omega_0^2-\delta^2}
\]
is the angular frequency of oscillations;
\[ \beta=\operatorname{arctg}\frac{\delta}{\omega},\qquad 0<\beta<\frac{\pi}{2}. \]
The equation of discharge of the capacitance is analogous to (13). Thus, the circuit generates undamped sinusoidal oscillations
\[ U_{\mathrm{cm}}=-U_{\mathrm{p}}+U_{\mathrm{p}}\frac{\omega_0}{\omega}\cos(\omega t-\beta), \tag{14} \]
where the voltage \(U_{\mathrm{p}}\) changes sign after a half-period of the oscillations.
In this circuit, during discharge of the capacitance \(C\), multiple breakdown of the transistor occurs because of the presence of the capacitance \(C_{\mathrm{k}}\). The period of the relaxation—
oscillations \(T_k\) is not constant, since the discharge current of the capacitance \(C\) decreases and the reaction of the inductance to this current changes. Therefore, in the middle of the discharge time the period is minimal.
The power dissipated in the transistor in the case of a sinusoidal-oscillation generator increases to
\[ P_{\sim}=\frac{C U_{\text{p}}^{2}}{2T}\cdot \frac{1}{2}\frac{T}{T_k}=P\cdot k, \tag{15} \]
where \(k\) is the number of transistor breakdowns during the discharge time of the capacitance \(C\); \(T\) is the period of the sinusoidal voltage oscillations. The minimum connected load is
\[ R_{\text{n}}>10X_c, \tag{16} \]
where \(X_c=\frac{1}{\omega C}\) is the reactance of the capacitance at the generated frequency \(\omega\).
The power delivered to the load is
\[ P_{\text{n}}=\frac{U_{\text{p}}^{2}}{4R_{\text{n}}}. \tag{17} \]
Since \(R_{\text{n}}\) is large, the power in the load does not exceed a few tens of mW.
The utilization factor of the supply voltage in the generator under consideration is
\[ m=\frac{U_{\text{p}}}{E}. \tag{18} \]
Since, in order to obtain a small nonlinear-distortion factor \(\kappa_2\), the value of \(E\) must be increased, the factor \(m\) in practice does not exceed 20–25%.
The efficiency of the generator is
\[ \eta=\frac{P_{\text{n}}}{P_{\text{src}}}, \tag{19} \]
where \(P_{\text{src}}=\frac{E^2}{R}\) is the power consumed by the circuit from the power supply.
Substituting the values of \(P_{\text{n}}\) and \(P_{\text{src}}\) into (19) and taking (18) into account, we obtain
\[ \eta=\frac{1}{4}\frac{R}{R_{\text{n}}}\cdot m. \]
Usually \(R_{\text{n}}=(2\div 4)R\). Therefore the value of \(\eta\) does not exceed \(1.5\div 3\%\).
Adding external resistances \(R_b=(300\div 800)\ \Omega\) to the base circuit makes it possible to reduce the value of \(E\) by a factor of 2 with an unchanged nonlinear-distortion factor \(\kappa_2\).
Experimental Results
a) Sawtooth-voltage generator. An oscillogram of the sawtooth voltage obtained in the circuit using a P12 transistor is shown in Fig. 3. The experimental curves in Figs. 4 and 5 confirm the dependences described earlier, which are typical for all the transistors investigated. Table 1 gives averaged breakdown-voltage values for several types of transistors. In the...
depending on the circuit parameters, primary or secondary breakdown may occur [1].
The relationships given above can be used to calculate a circuit with the required output-pulse parameters. Increasing \(E\) improves the shape of the output voltage; however, a considerable increase in \(E\), while not providing any substantial gain in improving the waveform, merely requires the creation of a special power supply. It is recommended to choose the value
\[ E = (3 \div 5)\,U_n . \]
Fig. 3.
The resistance \(R\) is chosen on the basis of the permissible dissipation power (5).
Fig. 4. Dependences of the parameters of the sawtooth voltage on the source voltage \(E\) (P16 transistor, \(R = 30\ \text{k}\Omega\), \(C = 680\ \text{pF}\)); \(\varepsilon\) is the nonlinearity coefficient.
Fig. 5. Dependences of the parameters of the sawtooth voltage on the capacitance (P16 transistor, \(R = 30\ \text{k}\Omega\), \(E = 300\ \text{V}\)).
The capacitance \(C\) is chosen on the basis of the specified value of the oscillation period and, on the high side, is limited by the irreversible-breakdown current. The critical capacitance for the transistor types investigated lies in the range of \(20 \div 40\) thousand pF.
The resistance \(R_{\mathrm{e}}\) must not exceed \(70 \div 80\ \Omega\), since otherwise the pulse shape is distorted and the discharge time increases.
Because of the small average dissipated power, the upper limit of the operating temperature is \(45 \div 50^\circ\mathrm{C}\).
The parameters of the output voltage were determined using an IO-4 oscilloscope.
Fig. 6. Dependences of the parameters of the sinusoidal voltage on the supply voltage \(E\) (transistor P12, \(R = 39\ \text{k}\Omega\), \(L = 290\ \text{mH}\), \(C = 680\ \text{pF}\)).
Plot labels: \(U_{\mathrm{st}}(E)\), \(K_2(E)\); axes: \(U_{\mathrm{st}},\ \mathrm{V}\); \(K_2,\ \%\); \(E,\ \mathrm{V}\).
Fig. 7. Dependences of the parameters of the sinusoidal voltage on capacitance (transistor P12, \(R = 39\ \text{k}\Omega\), \(L = 290\ \text{mH}\), \(E = 220\ \text{V}\)).
Plot labels: \(K_2(C)\), \(U_{\mathrm{st}}(C)\), \(F(C)\); axes: \(K_2,\ \%\); \(U_{\mathrm{st}},\ \mathrm{V}\); \(F,\ \text{kHz}\); \(C\).
b) Sinusoidal-oscillation generator. Figures 6 and 7 show the experimental dependences of the output-voltage parameters on \(C\) and \(E\).
An increase in \(R\) usually leads to a decrease (Figs. 6 and 7) in the amplitude and frequency of the oscillations and to an increase in \(K_g\) (at \(E=\mathrm{const}\)). The nonlinear-distortion coefficient was determined using an S6-1 nonlinear-distortion meter; the frequency was monitored with an ICh-6 frequency meter.
The frequency of the generated oscillations is very stable over time and when the voltage \(E\) is varied by \(\pm 10\%\). An increase in frequency is possible by reducing the value of \(L\), with a corresponding reduction in the range of capacitance values used. Thus, at \(L=25\) mH and \(C=100\) pF, the oscillation frequency was \(50\) kHz at \(U_{\mathrm{cm}}\approx 22\) V and \(K_g<2\%\).
In a circuit with parameters \(E=180\), \(C=2000\) pF, \(L=290\) mH, and \(R=39\) kΩ, connecting an active load \(R_{\mathrm{n}}=82\) kΩ leads to a 20% decrease in the oscillation amplitude with an unchanged coefficient \(K_g\).
The temperature dependence of the parameters of the sinusoidal voltage is shown in Fig. 8.
Fig. 8. Dependences of the parameters of the sinusoidal voltage on temperature (transistor P12, \(R=39\) kΩ, \(L=290\) mH, \(C=680\) pF, \(E=150\) V).
The circuit is calculated analogously to the calculation of the sawtooth-voltage generator.
Conclusion
The generator circuits considered have a number of advantages (simplicity of the circuit with a large oscillation amplitude, stability of the output-voltage parameters, reliability, etc.). Sawtooth-voltage generators may find application as horizontal-sweep generators in oscilloscopes, in time-measurement circuits, and in pulse technology. Generators of sinusoidal oscillations, in combination with a cathode follower, can be used as laboratory generators of low-frequency sinusoidal oscillations.
The generators are easily controlled by the base voltage. The cutoff voltage is \(1\text{–}1.5\) V.
The author expresses deep gratitude to Associate Professor, Candidate of Technical Sciences M. S. Roitman for his assistance and consultation.
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