Calculating Output Impedance
Output impedance is easy to calculate. Let’s look at three types of amplifiers, single-end tubes amplifiers, push-pull tube amplifiers, and OTL amplifiers. Solid-state amplifiers are similar to OTL’s.
Single-Ended
The first step is to calculate the impedances of the output devices. One 300B has a plate impedance of 700 ohms. If there were more than one tube, we simply divide the plate impedance by the number of tubes. Two 300B tubes would then have a net impedance of 350 ohms.
Next we calculate the impedance ratio between the primary and secondary windings of the output transformer. If the primary were 3000 ohms and the secondary were 8 ohms, the ratio is then 3000 ÷ 8 = 375. The output impedance is then the tube plate impedance divided by this number or 700 ÷ 375 = 2.13 ohms. That’s it! Negative feedback can be applied to reduce the impedance further.
Push-Pull
Let’s use a pair of 6550’s with a transformer with a 5000 ohm primary. Two 6550’s in push-pull have a combined plate impedance of about 10,000 ohms in pentode mode. The transformer has an impedance ratio of 5000 ÷ 8 = 625. The output impedance is then 10,000 ÷ 625 = 16 ohms. In this case it is absolutely essential to employ negative feedback to get the output impedance down. Amplifiers of this nature typically require about 25 dB of negative feedback to get the output impedance down to 0.8 ohms. (25 dB of feedback reduces output impedance 18 times)
OTL
Let’s look at the Transcendent T8 as an example. It uses 8, EL509 tubes in push-pull. Each 509 has a plate impedance of about 150 ohms. 150 ÷8 = 18.75 ohms. This is unacceptable. Negative feedback is employed to achieve proper performance. The amplifier uses 33 dB of negative feedback which reduces the output impedance to 0.4 ohm thereby achieving outstanding woofer control and the ability to drive 4 ohm speakers. This specification was verified by Stereophile when they reviewed the amplifier.
Different tubes will provide similar results. The configuration of the OTL output stage does not matter whether it is series connected push-pull or balanced. The controlling factors here are the number of output devices and the plate impedance of the devices. A 6AS7G is a dual triode with a plate impedance of 280 ohms. An amplifier that uses 8 such tubes will have an output impedance of 280 ÷ 16 = 17.5 ohms. A fourteen tube amplifier will have an output impedance of 10 ohms.
So it is absolutely essential that negative feedback be employed in the design of OTL amplifiers and tube amplifiers in general. There is simply no other way to reduce output impedance to acceptable levels.
