grundig: 1055W/3D- Additive or Multiplicative?
I have a minor question about the designation of the mixing process in the MW and LW bands of the Grundig 1055. The RF signal is applied to the control grid of EF89 pentode mixer, and the local oscillator voltage from the EC92 Local Oscillator triode drives the cathode of the EF89 pentode mixer.
This process was described as additive mixing in this thread.
This thread is in German, I used Google-Translate to read it.
My informal understanding of additive mixing means that the RF signal and local oscillator are linearly added together before being applied to the non-linear mixing device. This is the case in this radio in the FM band, with the self-oscillating EC92 triode converter.
It seems to me that this Radio uses multiplicative mixing in the MW and LW bands, but I am not sure about my understanding of the additive-vs.-multiplicative nomenclature.
In my opinion, multiplicative mixing is a process where the local oscillator signal is supplied to a different electrode in the mixing device, which causes a multiplying (gain varying) action on the RF signal. The most common case is of course a hexode or heptode mixer where the RF signal is supplied to the #1 grid and the local oscillator signal to the #3 grid. American pentagrid converters work roughly the same way, and likewise semiconductor devices like dual-gate mosfets.
But when using a triode or pentode as a mixer valve, it does not matter whether both RF and local oscillator signals are supplied to the control grid or if one of them is instead supplied to the cathode. In both cases, it is an additive mixing. From the valve's viewpoint, both methods of injecting the local oscillator signal causes a voltage between the control grid and cathode. Additive mixing using a pentode is very common in VHF television tuners but there, one can't find any obvious signal path for injection of the local oscillator signal, this is simply done by stray capacitances in the valve (a triode-pentode where the triode is used as oscillator) or in the wiring.
Apart from this Grundig radio, additive mixing using a triode was used in several swedish AM radios during a few years in the late forties and early fifties. Supposedly, this gave lower noise than the pentagrid or hexode mixers of that time but instead, the triode mixer had lower gain so those radios usually needed an extra IF stage. The AGC action of a such mixer can not have been very good as there were no double triodes with remote-cutoff characteristics. Typical double triodes that were used in such circuits were 7F8, ECC40, 12AT7 (notably in Kungs models 751V, 752V and 753V) and 6J6 (in various Luxor models and Sound Radio SR133 (a car radio)).
Maybe Mr. Rudolph can give more an better Solutions?
For mixing purposes, ideally, the received (and modulated) RF signal uRF(t) and the local RF signal from the oscillator uOsz(t) have to be multiplicated, giving uRF(t)*uOsz(t).
uRF(t)*uOsz(t) = ÛRF[1 + m*uAF(t)]cos(ΩCt)*ÛOszcos(ΩOt)
The IF frequency then becomes ΩO - ΩC = ΩIF .
If an ideal multiplicator (now availabls e.g. as IC 1595 or as a switching multiplier 1596) is used, 2 (independent) input ports for uRF(t) and uOsz(t) are available. The same holds for Heptodes, Hexodes, Pentagrid Converters, where the anode current is mainly the product of the voltages at the two input grids.
For Diodes, Triodes, Pentodes, Transistors there are no independent input ports available. The necessary multiplication is done approximately due to the nonlinear characteristic of the device.
vout(t) = a1vin(t) + a2vin(t)2 + a3vin(t)3 + ... Here the quadratic term is used, and the others were suppressed by filtering.
The quadratic term gives the well known relation (a + b)2 = a2 + 2ab + b2 and the term 2ab is the desired product.
In this case, vin(t) = uRF(t) + uOsz(t) = a + b, and this is an additition of the RF and the Oscillator voltages. Therefore this mixing process is called "additive" in contrast to the above mentioned "multiplicative" mixing, where two voltages are multiplicated.
As is often the case in this forum, a narrow scope question returns a rich array of answers. Thank you all for taking the time to contribute.
My first superficial assessment of the pentode mixer with LO injection into the cathode was far too narrow, looking just for separate wire inputs. The mathematical definition clearly outlined by Prof. Rudolph demands a more complete assesment of the topology.
In the Pentode mixer case I asked about, it is very clear that the local oscillator signal, the RF signal and the grid-cathode port are all in series as shown in the solid state examples illustrated by Mr. Knoll, so the mathematical model closest to this topology is certainly the additive mixing case.
In the case where the RF is applied to the control grid, and the local oscillator is applied to the screen grid of a pentode, or to the plate of a triode, the mathematical model fit is less clear. The control-grid/cathode port, is separate from the screen-grid/cathode port or plate/cathode port. The LO signal is not in series or parallel with the RF signal for addition, so this must be multiplicative mixing. But if we consider that the gm for the control grid or screen grid or the plate conductance of a triode, all of these have a strong square law characteristic. The square terms of additive mixing make for a better model fit.
In the case of LO injection into the suppressor grid, the multiplcative model may be a better fit for pentodes where the supressor grid transfer function is quite linear, and works essentially as steering mechanism for current from the plate to the screen grid. This current steering is present in hexodes and heptodes and in solid state multipliers based on differential transistor pairs, like the LM1596. The very small RF signal and the large LO signal do not produce significant individual square law terms. The RF term because it is too small, and the LO because of the linear suppressor grid characteristic. So this case appears to be Multiplicative.
When the local oscillator signal is very large, it's effect is more like multiplying the RF with a square wave. The behaviour is more like a chopping effect. In this case, the harmonic outputs of an additive mixer or a multiplicative mixer are very similar.
Perhaps the most important difference in mixer modes in tubes is wether there is screen grid partition noise or not. Multiplicative tube mixers usually have partition noise, where additive mixers with triodes or diodes do not.
Torbjörn Forsman mentioned additive mixing in Luxor radios. I found this example in the archives: the Luxor 355w. Thanks for the reference to these models, I had never seen triode AM front ends in post war radios aside from the AM/FM three tube Grundig sets, many of which were designed by Hans Knoll.