Radio Broadcast (May 1929-Apr 1930)

Formulas and General Theory CALCULATING DETECTOR OUTPUT When reduced to its simplest form the detector action of a vacuum tube should be as readily understood as the generally accepted relations for the amplifying properties of a tube. When considering amplification, the tube may be replaced by a generator whose voltage is (xeg, whose internal resistance is rp, and whose external load impedance is Zp. The useful part of this voltage, that impressed across the load, is the voltage pt,eg multiplied by the ratio between the load impedance to the total impedance in the plate circuit. In an amplifier tube, plate and grid voltages are chosen which will insure operation over a nearly straight portion of the characteristic. For detection voltages are chosen which place operation on a curved portion of the characteristic. For example, if the bias on an amplifying tube is increased until operation takes place about a point near plate current cut-off, then, in addition to the voltage y.eg appearing in the plate circuit, there will be a rectified voltage, E, due to the curved characteristic. This voltage, E, may be expressed as, E = A ^')((AEo)2 volts D. C. (1) Where, EQ (peak) is applied to the grid, for instance a carrier wave, and rP' is the derivative of rP with respect to Ep. Taking small intervals along the characteristic Ep — Ip curve and dividing the EP intervals by the IP intervals, we obtain rP. Plotting rP against EP and taking intervals of rP and Ep, the quotient is rP'. Knowing these characteristics of the tube, the rectified voltage is readily calculated. The voltage E is the total internally generated, rectified voltage and is analogous to the voltage fj.eg in an amplifier. The portion of this voltage appearing across the load ZP is, This is the d.c. voltage appearing across Zp (where Zp is the impedance to d.c, i.e., resistance) when a carrier wave of E0 peak volts is applied to the grid. If the carrier (2) ..2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 GRID VOLTAGE=Ec By J. M. STINCHFIELD Engineering Dept., E. T. Cunningham Inc. 3.5 £ 3.0 UJ Q_ I 2.5 o en o E 2.0 oo ~ 1.5 i UJ £ 1.0 3 O 9 0.5 1 1 1 1 J Grid Current vs Grid Voltage! Static Characteristic / C-327 Tube No. 2 Ef- 2.5 Volts _. Ek=45 Volts To" To — cm. 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 GRID VOLTAGE Ec Fig. 1 wave is then modulated M X 100 per cent., the d.c. voltage will be increased by the factor A voltage of modula tion frequency resulting from the variation in amplitude of the rectified voltage will also appear. Its amplitude will be 2M TABLE I A. F. Modulation (M) = 0.20 at 60 cycles Zp = 50,000-ohm power factor unity Ec = —4.5 volts Ep = 45 volts Carrier A.F. D.C. Plate Measured Equivalent Volts Volts Current /\^ Ip a.f. from r.m.s. r.m.s. Change /\ Ip Microamp. Meas. (ed-i-y~}t) Microamp. /\Ip 0.100 0.200 0.354 0.707 1.000 1.500 0 . 0027 0.0107 0.034 0 . 134 0.269 0.605 0.8 3.3 10.4 41.7 83.4 187. 3.3 10.5 42.00 0.0107 0.034 0.136 times the internally generated voltage of rectification due to the carrier alone. See equation (1). The internally generated audio voltage analogous to (jt,eg is then: [(>?) p.* Eo! M (3) The useful audio output voltage depends upon the impedance of the load ZP to audio frequencies. The basic relation for plate current detection, when it is entirely due to the curvature of the characteristic and the amplitude of the signal is small, is: 6d [0 r7> (rpT^) 2 ME°2] P6ak V°ltS (4) A brief explanation of the expression for the interally generated voltage, should clear away any vagueness of the physical interpretation. The term OS) E is the typical ex Fig. 2 pression for the internally generated voltage of rectification due to the curvature of an E-I static characteristic. The same expression is valid whether it is for a plate current-voltage characteristic, or for the grid current-voltage characteristic, or for the current-voltage characteristic of say a crystal when a small voltage, E sin tot, is applied to its terminals. The r is the slope of the E-I characteristic. The r' is the slope of the E-r characteristic. The term [xE0 represents the amplitude of the carrier in the plate circuit. If a radiofrequency by-pass condenser is connected between the plate-filament terminals the entire amplitude, ixE0, will be effective on the internal resistance of the tube. The factor 2M is equal to the ratio of the amplitudes of the audio or modulation frequency to the rectified d.c. of the unmodulated carrier. In many tubes a considerable decrease in mu occurs as the plate current approaches cut-off. With plate current rectification, the point of operation is usually in this region. The mu variation increases the rectified output. Adding a term to the term will rather closely account for the detection resulting from the variation of mu. Here \x! is the slope of the lx-Ep curve at the point of operation. The basic principles of grid-leak detection are similar to those outlined above. The grid is connected through a highresistance grid leak to some point having a small positive voltage with respect to the negative filament terminal. The small positive voltage brings the grid circuit to a point of operation on the lower bend of the grid current curve. If a small sine wave of radio-frequency voltage is applied through a grid condenser to the grid-filament terminals, a rectified voltage due to the curvature of the Eg-Ig curve will appear in the grid circuit. The portion amplified by the tube appears as: b Orf )E°2(r^)] VOltS ^ iDthe plate circuit (5) When the radio-frequency carrier is modulated M X 100 per cent., the amplitude of the internally generated audio voltage is 2M times the internally generated d.c. voltage. The portion developed across the plate load, Zp, depends upon the ratio between Zp and Zp + rP. The detected audio voltage across the load, Zp, due to the curvature of the grid-current characteristic is " [(,rr)Kr7fK)(^fr,)2MH peak volts (6) O Q I — o o < LL. z 2 t— < o E 2 hO Ixl 1.5 Grid Rectification Factor vs Grid Voltage C -327 Tube No. 2 Ef = 2.5 Volts Eb*4.5 Volts 1.2 1.1 1.0 0.9 0.8 GRID VOLTAGE Fig. 3 0.7 0.6 AUGUST 1929 • • 239