40x Gain with BC547: Achieve 10,000+ Amplification

Description

For a collector follower with emitter resistor, the gain per stage is frequently between 10 and 50 times. The gain increases when the emitter resistor is omitted. However, distortion also increases. With a typical transistor like the BC547B, the transistor's gain is approximately 40 times the collector current (Ic), provided the collector current remains below a few milliamps. This value theoretically corresponds to the expression q/KT, where q represents the charge of the electron, K is Boltzmann’s constant, and T is the temperature in Kelvin.

For simplicity, assuming room temperature, this value is rounded to 40. For a single-stage amplifier circuit with a grounded emitter, the AC voltage gain (Uout /Uin) is theoretically equal to SRc. As observed previously, the slope S is approximately 40Ic. Consequently, the gain is approximately equal to 40IcRc. This provides a practical rule of thumb: the gain of a grounded emitter circuit amounts to 40·Ic·Rc, which is equal to 40 times the voltage across the collector resistor.

If Ub is, for example, equal to 12 V and the collector is set to 5V, it is known, irrespective of the resistor values, that the gain will be about 40(12–5) = 280. It is notable that in this way, the gain can be very high theoretically, by selecting a high power supply voltage. Such a voltage could be obtained from an isolating transformer from the mains. An isolating transformer can be constructed by connecting the secondaries of two transformers together, resulting in a galvanically isolated mains voltage.

Circuit diagram:

This signifies that, with a mains voltage of 240 Veff, approximately 340 V DC will be produced after rectification and filtering. If the amplifier circuit utilizes a power supply voltage of 340 V and sets the collector voltage to 2 V, then the gain is theoretically equal to 40 x (340–2). This exceeds 13,500 times! Nevertheless, there are practical drawbacks. This relates to the output characteristic of the transistor. In practice, the transistor actually possesses an output resistor between the collector and emitter.

This output resistance exists as a transistor parameter and is termed ‘hoe’. In typical designs, this parameter is of little consequence because it has no noticeable effect when the collector resistor is not large. When powering the amplifier from 340 V and setting the collector current to 1 mA, the collector resistor will have a value of 338 k. The influence of the ‘hoe’ parameter depends on the type of transistor. It is also noted that with such high gains, the base-collector capacitance, in particular, will begin to play a role.

Consequently, the input frequency may not be too high. To achieve a higher bandwidth, a transistor with a small Cbc, such as a BF494 or perhaps even an SHF transistor like a BFR91A, will be required. The value of the base resistor will then need adjustment to reflect the new hfe. The author performed measurements with a BC547B at a power supply voltage of 30 V. A collector voltage of 2 V was selected. Measurements confirmed the rule of thumb. The gain exceeded 1,000 times, and the effects of ‘hoe’ and the base-collector capacitance were not noticeable because of the now much smaller collector resistor.