Measurement Amplifiers for Automatic Control Systems
Abstract Generated abstract
This paper examines AC voltage measurement amplifiers for automatic control systems, focusing on the need for high stage gain, low phase distortion, and stable operation under temperature variation. It proposes replacing the conventional active load resistance in transistor stages with a nonlinear controlled resistance whose static and dynamic resistances vary so as to help compensate changes in transistor current gain and collector reverse current. Using small signal four-terminal network analysis with h-parameters, the authors derive expressions for gain, input resistance, and output resistance, and describe an amplifier module incorporating an emitter follower for impedance transformation. Experimental characteristics indicate improved temperature stability while maintaining phase-frequency behavior comparable to a conventional rheostat amplifier stage, enabling deeper negative feedback where gain margin permits.
Full Text
MEASUREMENT AMPLIFIERS FOR AUTOMATIC CONTROL SYSTEMS
E. S. Batalin, M. S. Roitman
(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)
Among the many requirements imposed on AC-voltage measurement amplifiers for various special-purpose applications, several basic ones may be singled out; these determine the limits of possible use of a given amplifier or of a given class of amplifier circuits.
Obtaining the maximum possible gain per stage with minimal phase distortion is one such requirement.
If there is a reserve of gain with the appropriate form of the phase-frequency characteristic, deep intrastage and interstage negative feedbacks can be introduced; these are one of the principal means of stabilizing amplifier parameters and of changing them in accordance with specific technical requirements.
A generally known method of increasing the magnitude of the gain coefficient is to increase the load resistance. When this measure is implemented in rheostat transistor measurement amplifiers, two substantial difficulties arise: the instability of the stage operating mode increases sharply, up to a complete loss of operability, and efficiency decreases.
These shortcomings can be overcome by using, as the load, not simply an active resistance but an element with certain special properties.
Such a load element must:
a) have a small static resistance (resistance to direct current) and a large dynamic resistance (resistance to alternating current);
b) change its resistance to direct current when the latter changes slowly, with the calculation that the voltage drop due to the direct current across the load element remains constant;
c) make it possible to control the nature of the dependence of the dynamic resistance on the surrounding conditions, adapting it to compensate for changes in the transistor parameters.
It is quite obvious that a load satisfying such requirements must contain a nonlinear controlled resistance.
A load element possessing, to a considerable degree, the listed properties is shown in Fig. 1. It is a two-terminal network containing a transistor with additional resistances and capacitors—
resistor. In what follows we shall call such a two-terminal network, for short, a “nonlinear controlled resistance” (NCR).
Figures 2 and 3 show the dependences of the static resistance and of the modulus of the dynamic resistance of the NCR on the ambient temperature for various values of the parameters of the elements comprising it.
Fig. 1. Circuit of a “nonlinear controlled resistance.”
A change in the ambient temperature is one of the main causes of instability of the parameters of a transistor amplifier.
Figure 4 shows the dependence on ambient temperature of the modulus of the current gain coefficient $\beta$ and of the reverse current of the collector junction $I_{k0}$ of P 13—15 transistors.
For other types of semiconductor triodes, the dependence of $\beta$ and $I_{k0}$ on temperature has a similar form.
Comparing the curves shown in Figs. 2, 3, and 4, it is easy to see what possibilities for temperature stabilization of the amplifier stage are provided by replacing the active load resistance with a nonlinear controlled resistance.
The decrease, with increasing temperature, of the dynamic resistance of the NCR compensates for the increase of $\beta$, while the decrease of the static resistance of the NCR, simultaneously with the increase of $I_{k0}$, prevents a significant change in the dc voltage at the collector of the triode whose load is the NCR. By properly selecting the parameters of the passive elements included in the NCR circuit, it is possible to stabilize the amplifier gain over a temperature range.
Fig. 2. Dependence of the static resistance of the NCR on temperature.
The amplifier stage in which the load is an NCR is shown in Fig. 5. Here and below, for brevity, it is called simply an “amplifier.”
Figure 6 shows the dependence of the gain coefficient of such an amplifier on the ambient temperature when the parameters of its constituent elements are varied. These graphs confirm the conclusion reached about the increase in the temperature stability of an amplifier in which an NCR is used as the load.
Fig. 3. Dependence of the modulus of the dynamic resistance of the NUS on temperature.
Inset table for the left plot:
| \(R_b = 220\,\text{k}\Omega\) | 1 | 2 | 3 |
|---|---|---|---|
| \(Z_0,\ \text{k}\Omega\) | 0 | 0.51 | 1 |
Inset table for the middle plot:
| \(R_b = 300\,\text{k}\Omega\) | 1 | 2 | 3 |
|---|---|---|---|
| \(Z_0,\ \text{k}\Omega\) | 0 | 0.51 | 1 |
Inset table for the right plot:
| \(R_b = 510\,\text{k}\Omega\) | 1 | 2 | 3 |
|---|---|---|---|
| \(Z_0,\ \text{k}\Omega\) | 0 | 0.51 | 1 |
Fig. 4. Dependence of the current gain coefficient and the reverse current of the collector junction of P13-15 transistors on ambient temperature.
Fig. 5. Circuit of an amplifier stage with an NUS.
Inset table for the left plot:
| 1 | 2 | |
|---|---|---|
| \(Z_0,\ \text{k}\Omega\) | 0 | 1 |
| \(R_b\) | \(820\,\Omega\) | \(240\,\Omega\) |
Inset table for the right plot:
| 1 | 2 | 3 | Note | |
|---|---|---|---|---|
| \(R_{b1},\ \text{k}\Omega\) | 1.5 | 1.2 | 1 | \(Z_0 =\) |
| \(R_b,\ \Omega\) | 470 | 680 | 680 | \(150\,\Omega\) |
Fig. 6. Dependence of the gain coefficient of a transistor amplifier with an NUS on temperature.
Expressions for calculating the principal parameters of the amplifier when operating in the linear mode can be obtained using four-terminal-network theory and the small-signal \(h\)-parameters.
The dynamic resistance of the NUS is defined as the output resistance of a transistor connected in a common-emitter circuit, provided that its input is short-circuited. The transistor is encompassed by negative current feedback arising because of the presence of the resistance \(r_0\). The value of the dynamic resistance of the NUS under these conditions is expressed by the formula
\[ R_{\mathrm{dyn}}=\frac{h_{11.\mathrm{e}}}{D_{h.\mathrm{e}}}\cdot a_1, \tag{1} \]
where
\[ D_{h.\mathrm{e}}=h_{11.\mathrm{e}}h_{22.\mathrm{e}}-h_{21.\mathrm{e}}h_{12.\mathrm{e}}. \]
\[ a_1= \frac{ 1+\dfrac{r_0}{h_{11.\mathrm{e}}}(1+h_{21.\mathrm{e}}) }{ 1+r_0\dfrac{h_{22.\mathrm{e}}}{D_{h.\mathrm{e}}} }; \]
Here and below we assume that the amplifier operates in the mid-frequency range and that the parameters of all elements included in the circuit are expressed by real numbers.
The voltage gain of the amplifier under consideration is equal to
\[ K= \frac{h'_{21.\mathrm{e}}\cdot R_{\mathrm{dyn}}} {h'_{11.\mathrm{e}}+D'_{h.\mathrm{e}}\cdot R_{\mathrm{dyn}}}. \tag{2} \]
The parameters marked with primes refer to transistor \(T_1\). Assuming that transistors \(T_1\) and \(T_2\) are identical, expression (2) can be simplified. It takes the form
\[ K_u \simeq \frac{h_{21.\mathrm{e}}}{D_{h.\mathrm{e}}}\cdot \frac{a_1}{1+a_1}. \]
The input and output resistances of the amplifier are determined by the formulas:
\[ R_{\mathrm{in}}= \frac{h'_{11.\mathrm{e}}+D'_{h.\mathrm{e}}\cdot R_{\mathrm{dyn}}} {1+h'_{22.\mathrm{e}}\cdot R_{\mathrm{dyn}}}, \tag{3} \]
\[ R_{\mathrm{out}}= \frac{R_{\mathrm{out.tr.}}\cdot R_{\mathrm{dyn}}} {R_{\mathrm{out.tr.}}+R_{\mathrm{dyn}}}. \tag{4} \]
Here \(R_{\mathrm{out.tr.}}\) is the output resistance of semiconductor triode \(T_1\) in the common-emitter circuit.
If both triodes are identical, then expressions (3, 4) take the form:
\[ R_{\mathrm{in}}= \frac{h_{11.\mathrm{e}}(1+a_1)} {1+a_1\dfrac{h_{22.\mathrm{e}}\cdot h_{11.\mathrm{e}}}{D_{h.\mathrm{e}}}}, \tag{5} \]
\[ R_{\mathrm{out}}= \frac{h_{11.\mathrm{e}}+R_{\Gamma}} {D_{h.\mathrm{e}}+h_{22.\mathrm{e}}R_{\Gamma}} \cdot \frac{1} { 1+ \dfrac{1+R_{\Gamma}/h_{11.\mathrm{e}}} { \left(1+\dfrac{h_{22.\mathrm{e}}\cdot R_{\Gamma}}{D_{h.\mathrm{e}}}\right)\cdot a_1 } }. \tag{6} \]
To make the amplifier more versatile, it is advisable to reduce its output resistance by connecting an emitter follower at the output, acting as an impedance transformer. The resulting circuit may be regarded as a single functional system, which we shall hereafter call an amplifier module (AM) (Fig. 7).
Fig. 7. Circuit of an amplifier module.
Figure 8 shows the phase-frequency characteristics of the amplifier module and, for comparison, the phase-frequency characteristic of a rheostat amplifier stage using a transistor. The comparison shows that they are practically identical.
Consequently, the restrictions imposed on the permissible value of the depth of negative feedback by the stability requirement, when using an AM, will be no more stringent than when using an ordinary rheostat amplifier stage.
If the permissible depth of negative feedback is limited only by the required value of the gain, then the use of an AM instead of a rheostat amplifier stage makes it possible to introduce deeper negative feedbacks.
Fig. 8. Phase-frequency characteristics of the amplifier module (upper curve) and of the rheostat amplifier stage (lower curve).
The results obtained were used in designing measuring amplifiers for alternating voltage. We have developed two versions of measuring amplifiers. Both amplifiers are structurally made in the form of modules and possess considerable versatility with respect to their possible applications.
REFERENCES
- Ya. Budinskii. Low-Frequency Transistor Amplifiers, Svyazizdat, 1963.
- N. S. Bertoya. High resistance transistor circuits, Radio and Electron. Engr. 26, No. 1, 1963.