Amplification

Introduction

When I-V conversion is established by means of a small resistor, an amplification stage will be needed to obtain a sufficient large output voltage. The driver stage should satisfy the following requirements, it should provide a low output impedance, i t must have low distortion, and it should be very linear.

The active elements that can be used inside a driver stage are FETs, transistors, opamps and tubes. We've experimented with several amplification stages, but in general we like the results obtained by tube amplification. This chapter will describe some of our experiences with tube amplification.

Theory

In Figure 1 a common anode follower using a triode can be found. In [Vall48] the design principles of such a anode follower are explained thoroughly. The operating point can be determined by drawing a load-line (determined by Rp and Rk) in the Ip - Vp plate characteristics. Instead of using a fixed cathode potential, a negative voltage between grid and cathode can be obtained by a cathode resistor Rc . The advantages of a circuit with a cathode resistor w.r.t. a circuit with a fixed negative bias are the common ground terminal between input and output, and only one DC supply is needed. The cathode resistor can be considered as a local feedback from cathode to grid. A cathode capacitor is often used to remove the local feedback caused by Rc for audio frequencies. Capacitor Cp decouples the DC component from the signal on the plate, and an amplified output signal free of DC components is obtained (Vout). Cp and Ck should be chosen such that they have no impact on the audio frequence range. A -3dB point can be determined by the reactance Xc = 1 / (2 π f0 C) . The frequency at which Xc equals Rc , represents the -3dB point. A value of f0 = 10Hz should suffice in practice, and with this assumption a value of C can be determined as C = 1 / (63 . Rc ).

Figure 1: Anode follower

The usual way of designing an anode follower is as follows. First an operating point ( Vpc and Ic ) must be chosen from the Vpc - Ip characteristics. It is hard to tell which operation point will lead to better sound. but it seems to be safe to choose average values as mentioned by several text-books.

After an operation point has been chosen, the corresponding Vgc can be derived from the Vpc - Ic characteristics. If for example an operating point of Vpc = 90 V, and Ip = 6 mA is chosen for an E88CC (6922, 6DJ8), we can derive that Vgc must be approximately -2 Volt. This leads to a cathode resistor Rc of 333 Ω . When the operating point of a tube is determined, one can derive the amplification μ and the internal resistance Ri from the data sheets. In case of an E88CC we find that μ = 32 and Ri = 3.8 k Ω .

The choice of the plate resistor Rp can be determined in two ways. If the power voltage Vbb is known, Rp = ( Vbb - Vpc - (- Vgc )) / Ic . A large plate resistor imposes a small load on the tube, and also imposes a small load of the power supply. If for instance Rp in the example is taken 22k Ω , then Vbb = 22 . 6 + 90 + 2 = 224 V.

The formulas for the amplification and output impedance are [Vall48]:

and

For the example we can derive that Av = 19.1 and Z = 8k8.

If a sufficient large cathode capacitor is used, Rc can be taken 0 in the formulas for Av and Z . In this case we find for the example a value of at least 50 μ F for Ck , and Av = 27.3 and Z = 3k2.

Another circuit which is very popular nowadays is the so called SRPP (Series Regulated Push Pull), which can also be found in [Vall48]. The main advantages of an SRPP are a high amplification, low output impedance and high linearity.

Figure 2: SRPP

Dimensioning an SRPP is similar to dimensioning an anode follower. First an operation point is chosen, which gives us Vpc , Ip and Vgc . From this we can derive Rp and Rc (= - Vgc / Ic ). The power supply voltage equals 2 . Vpc + 2 . - Vgc . If we would take an ECC88 in the same conditions as in the anode follower example ( Vpc = 90 Volt, Ic = 6mA), we would get Rp = Rc = 333 Ω , and Vbb = 184 V.

The formulas for the amplification and output impedance are [Vall48]:

and

Without a cathode capacitor we would get Av = 5.6 and Z = 1k9. Without cathode capacitor we would get Av = 24.9 and Z = 845 Ω .

In Table 1 an overview of values can be found for a SRPP with different kind of tubes.

Table 1: SRPP dimensions
Tube	Vpc in Volt	Ip in mA	Vgc in Volt	Rp, Rc in ohm	Vbb in Volt	Av	Z in ohm	Rd in ohm
ECC81	200	5	-3	600	406	46.5	3k2	22
ECC82	200	5	-8	1k6	416	12.6	2k7	80
ECC83	240	2	-1.5	750	483	72.8	14k3	14
ECC83	150	1.3	-1	770	302	69	16k2	14
ECC85	200	5	-2.5	500	405	36.5	3k8	27
ECC88	90	6	-2	333	184	24.9	845	40

Observations

We've chosen for an E88CC (6DJ8 or 6922) triode, because the relative low internal resistance (Ri = 2.64 k Ω ) and the moderate amplification factor ( μ = 32) lead to good values for Av and Z . Another argument concerns the availability of good quality brands of the E88CC (Golden Dragon, Sovtek, Mullard, Tesla, General Electric et.al.).

We did some experiments with different values for Ic using an ECC88. We thought that `average values' (3~6mA) sounded better than low values (1mA), but weren't quite sure whether we could perceive any difference in sound using those different values. According to [Tent95] the plate resistor Rp should be magnitudes larger than the internal resistance Ri of the tube (e.g. > 10 . Ri ), because this will have a positive effect on the sound of such a circuit.

Some technical and listening experiments gave us the following results: