Temperature Stabilizer Based on a Self-Oscillating Circuit
Abstract Generated abstract
This paper proposes a compact temperature stabilizer for precision measuring equipment that replaces the relay used in earlier thermistor thermostat circuits with a self-oscillating amplifier and bridge feedback arrangement. The authors describe the operating principle: bridge unbalance caused by a temperature drop initiates oscillations that power a heater, while temperatures above the set point produce negative feedback conditions that prevent oscillation. A quantitative analysis relates chamber temperature deviation and instability to thermistor coefficient, bridge sensitivity, amplifier gain, heat loss, and maximum amplifier output power. The results indicate that increasing amplifier gain can improve stabilization accuracy, with an illustrative calculation giving about 0.1 degrees Celsius instability under specified parameter values.
Full Text
TEMPERATURE STABILIZER BASED ON A SELF-OSCILLATING CIRCUIT
V. K. Zhukov, A. B. Buchelnikov
(Presented by the scientific seminar of the Department of Electrical Measuring Engineering)
In the development of precision measuring equipment, it is sometimes necessary to maintain a constant temperature around the most critical components of a device, for example, parts of an oscillator tank circuit, a reference-voltage source of a stabilizer, and so on. For this purpose, small-size thermostats are used. A number of circuits and designs of such thermostats are known. Among them is the thermostat described in [1], in which a thermistor is used as the sensing element, a relay is the actuating element, and the amplifying section is built according to a self-oscillating circuit. The use of a relay worsens the performance of the stabilizer: it makes it less reliable and accurate, and, in the case of temperature stabilization in small volumes, also more bulky and expensive.
Fig. 1. Circuit of a temperature stabilizer
The performance of the stabilizer can be improved if the relay is eliminated from it and it is built according to the circuit shown in Fig. 1.
The thermistor \(R_t\) and the heater \(R_{\mathrm{h}}\) are placed in the volume in which the temperature must be stabilized. The bridge, one arm of which is the thermistor, is balanced at the specified temperature by appropriate selection of the resistors \(R_1\), \(R_2\), and \(R_3\). One diagonal of the bridge is connected to the input of the amplifier, and the other, through a matching transformer, to its output. The heater \(R_{\mathrm{h}}\) is also connected to the output winding of the transformer. The entire system is an amplifier with feedback. The feedback circuit is formed by the bridge. If the temperature in the chamber is equal to the specified value, the bridge is balanced and its transmission coefficient is zero. A decrease in the temperature in the chamber leads to unbalance of the bridge and to an increase in its transmission coefficient. At some temperature, the loop gain \(k \cdot \beta\) of the system becomes greater than 1 and self-oscillations arise in it. The frequency of the self-oscillations is determined by the quasi-resonance frequency of the amplifier. As a result of the onset of oscillation, the heater \(R_{\mathrm{h}}\) is under the voltage \(U_{\mathrm{m}}\), and the power dissipated in it will be
\[ P_{\mathrm{h}} = U_{\mathrm{m}}^{2}/R_{\mathrm{h}}. \tag{1} \]
The temperature in the chamber will begin to rise and will continue to rise until the loop gain \(\kappa \cdot \beta\) becomes less than 1.
If the temperature in the chamber becomes higher than the specified value, the bridge becomes unbalanced; however, self-oscillations do not arise in the circuit, since now the transfer coefficient of the bridge is negative (the phase of \(\Delta U_{\mathrm{m}}\) changes by \(180^\circ\)) and, consequently,
\[ \kappa \cdot \beta < 0 . \tag{2} \]
Thus, the stabilizer will maintain in the chamber such a temperature at which the bridge is close to equilibrium.
Let us establish quantitative relationships between the temperature in the chamber and its instability, on the one hand, and the parameters of the circuit and the chamber, on the other.
The power dissipated by the chamber is proportional to the temperature difference \(\Delta t\) between the ambient medium \(t_{\mathrm{v}}\) and the air in the chamber \(t_{\mathrm{k}}\); therefore it can be represented in the form
\[ P_{\mathrm{k}} = P_{\mathrm{ud}} \cdot \Delta t, \tag{3} \]
where \(P_{\mathrm{ud}}\) is the dissipated power per degree.
The temperature in the chamber will always be lower than the temperature \(t_0\) at which the bridge is balanced by a certain amount
\[ \delta t = t_0 - t_{\mathrm{k}} . \tag{4} \]
Since the temperature in the chamber \(t_{\mathrm{k}}\) is not equal to \(t_0\), the resistance of the thermistor will differ from \(R_{t.0}\) by the amount
\[ \Delta R_t = \alpha_t \cdot R_{t.0} \cdot \delta t, \tag{5} \]
determined by the temperature coefficient \(\alpha_t\) of the thermistor and by the magnitude of its resistance \(R_{t.0}\) at temperature \(t_0\).
The change in \(R_t\) leads to unbalance of the bridge and to an increase in its transfer coefficient
\[ \beta = \frac{\Delta U_{\mathrm{m}}}{U_{\mathrm{m}}} = \frac{\Delta R}{R_{t.0}} \cdot m \]
to the value
\[ \beta = \alpha_t \cdot m \cdot \delta t . \tag{6} \]
In the last expression, \(m\) denotes the proportionality coefficient between the relative change in resistance of the bridge arm \(\Delta R_t / R_{t.0}\) and the bridge unbalance caused by it, \(\Delta U_{\mathrm{m}} / U_{\mathrm{m}}\). The largest value of \(m\), equal to 0.25, is obtained for an equal-arm bridge.
Because of the nonlinearity of its amplitude characteristic, the amplifier transfer coefficient depends on the magnitude of the input voltage, in this case on the magnitude of the bridge unbalance voltage. In order not to complicate the problem, we shall represent this dependence in the form of a linear function
\[ \kappa = \kappa_0 (1 - n \Delta U_{\mathrm{m}}). \tag{7} \]
In the steady-state operating regime, the power dissipated by the chamber must be equal to the power released in the heater. Equating on this basis the right-hand sides of expressions (1) and (3), we find
\[ \Delta U_{\mathrm{m}} = \frac{\sqrt{P_{\mathrm{ud}} \cdot \Delta t \cdot R_{\mathrm{n}}}}{\kappa}, \]
whence, after substituting \(\kappa\) from (7), we obtain
\[ \Delta U_{\mathrm{m}} = \frac{\kappa_0 + \sqrt{\kappa_0^2 - 4 \kappa_0 \cdot n \sqrt{P_{\mathrm{ud}} \cdot \Delta t \cdot R_{\mathrm{n}}}}} {2 n \kappa_0}. \tag{8} \]
From another relation,
\[ \kappa \cdot \beta = 1, \tag{9} \]
which is also valid in the steady-state regime, taking (6), (7), and (8) into account, we find the amount by which the temperature in the chamber differs from the bridge-equilibrium temperature:
\[ \delta t = \frac{2}{ m a_t \cdot \kappa_0 \left( 1 + \sqrt{1 - \frac{4n}{\kappa_0}\sqrt{P_{\mathrm{ud}}\cdot \Delta t \cdot R_{\mathrm{n}}}} \right) }. \tag{10} \]
It can be shown that
\[ \frac{4n}{\kappa_0}\sqrt{P_{\mathrm{ud}}\cdot \Delta t \cdot R_{\mathrm{n}}} = \sqrt{\frac{P_{\mathrm{ud}}\cdot \Delta t}{P_{\mathrm{n.max}}}} = \sqrt{\frac{P_k}{P_{\mathrm{n.max}}}}, \tag{11} \]
and, consequently,
\[ \delta t = \frac{2}{ m a_t \cdot \kappa_0 \left( 1 + \sqrt{1 - \sqrt{\frac{P_{\mathrm{ud}}\cdot \Delta t}{P_{\mathrm{n.max}}}}} \right) }. \tag{12} \]
Here \(P_{\mathrm{n.max}}\) denotes the maximum power that the amplifier can deliver to the load \(R_{\mathrm{n}}\).
If the temperature in the chamber is the same as in the environment and is equal to \(t_0\), i.e., \(\Delta t = 0\), then oscillations cannot arise in the circuit. They will arise only when the temperature in the chamber has decreased by the amount
\[ \delta t = \delta t_0 = \frac{1}{m a_t \cdot \kappa_0}. \tag{13} \]
Taking (13) into account, expression (12) can be written in the following form:
\[ \delta t = \frac{2\delta t_0}{ 1 + \sqrt{1 - \sqrt{\frac{P_{\mathrm{ud}}\cdot \Delta t}{P_{\mathrm{n.max}}}}} }. \tag{14} \]
As the ambient temperature decreases, \(\Delta t\) will begin to increase, and with it the power dissipated by the chamber will also increase. At a certain value \(\Delta t = \Delta t_{\max}\), the power dissipated by the chamber becomes equal to the amplifier power. The temperature in the chamber will differ from the bridge-equilibrium temperature, as follows from (14), by the amount
\[ \delta t_{\max} = 2\delta t_0. \tag{15} \]
A further decrease in the ambient temperature will cause a proportional change in the temperature in the chamber, i.e., the stabilizer will cease to function normally.
Thus, a change in the ambient temperature from \(t_{\mathrm{v}} = t_0\) to the value \(t_{\mathrm{v}} = t_0 - \Delta t_{\max}\), at which \(P_{\mathrm{n.max}} = P_{\mathrm{ud}}\cdot \Delta t_{\max}\), leads to a change in the temperature in the chamber by the amount
\[ \delta t_{\max} - \delta t_0 = \delta t_0 = \frac{1}{m\cdot a_t \cdot \kappa_0}. \]
By increasing \(\kappa_0\), one can achieve high accuracy in maintaining the specified temperature in the chamber. For example, at \(m = 1/4\), \(a_t = 0.01\), and \(\kappa_0 = 1000\), the temperature instability will be \(0.1^\circ\mathrm{C}\).
References
- E. A. Promlet. Transistor Thermostat. Instrument Engineering, 1966, February.