02/14/2020 at 14:55 •
RTL versus DTL
Both RTL (Resistor Transistor Logic) and DTL (Diode Transistor Logic) were common logic families in the early days of transistors. The image above shows inverters in both logic families.
RTL is the simpler of the two, but it suffers from many issues: The L->H threshold is defined by the forward voltage of the base-emitter junction of the transistor and is hence rather low, around 600mV for a typical silicon transistor. Furthermore, if the input is at high level it will sink current which is supplied by the collector resistor of the preceding gate. To maintain consistent logic levels it is therefore necessary to adjust all resistors according to fan-out. Besides that, there is also a lot of nastiness in dynamic operation.
DTL addresses these shortcoming by introducing additional diodes: When the input is high, all the base current will be supplied by the base resistor (R5) and there is no current flowing into the gate. When the input is low, current is sourced from the gate, which is sunk into the transistor of the preceding gate. Since the transistor is fairly low-ohmic when it is turned on, there is much less limitation in fan-out. Furthermore, it is not necessary to adjust gate resistors depending on fan-out. This allows using the same resistor values throughout the entire circuit.
A second improvment in DTL is to lift the L->H threshold to a higher voltage. It is now defined by Vbe+Vd2+Vd1-Vd3, which is roughly 1.3V depending on the compenents used.
From DTL to LTL
The image above shows the circuit of an LTL inverter. At the first glance it looks very straightforward: We replace the two silicon diodes with a LED. Since the LED has a much higher forward voltage (depending on LED type), only a single diode is sufficient. This is nice, because it saves one component, but is it actually a good idea?
02/15/2020 at 10:42 •
Replacing the base diodes in an DTL gate with an LED saves one component. One very interesting side effect is that the LED also emits light. Modern LEDs are already quite bright at around 1mA of current, so the normal base current will be sufficient to turn it on.
But what is the impact on the circuit behavior? Usually we would like to use fast switching diodes for any logic circuit. Switching diodes are optimized for low capacitance and low recovery time to be able to switch very fast between forward and reverse operation. Here I am using a BAW56 dual diode, which has a capacitance of 2pF and 6ns reverse recovery time, as the input diode. LEDs are not optimized for switching operation. They typically have a fairly high capacitance of around ~40pF and take long time to be switched off. Therefore, using an LED in place of D2, the input diode, would slow down the gate significantly.
The base diode is, however, never in reverse operation. Therefore the bad switching properties of the LED are not an issue. In addition, the higher capacitance helps to pull down the base potential quicker if the transistor is to be turned off. You sometimes see intentional reach-through capacitors in parallel to the base diode in DTL gates.
Some attention has to be paid to the terminal between D1 and Q1 base. If the transistor is turned off, this terminal is pulled to negative voltage and is basically floating, since the base-emitter diode is reverse biased. I found that this can lead to a shift of switching voltage depending on duty cycle and frequency of the incoming signal. It may be advised to use a bleeder resistor to conntect this node to the ground. Due to simplicity, I omitted this and made sure to design glitch free logic instead...
I spent quite some time optimizing the basic gate in LTspice. To measure switching speed, I simulated a 5 stage ring oscillator. One crucial choice was to pick the right transistor, as I also outlined in greater detail here.
You can see simulation results for several different configurations above. I also tried various configurations with reach through caps and baker clamps but found that chosing the right transistor, the PMBT2369, yielded much better results that all other options. The PMBT2369 is available in a SOT23 SMD package for around $0.02, so there is really no reason to use the BC847 or MMBT3904 over it.
Final parameters of the simulated inverter are shown above. The relatively high L->H delay is owed to the use of a relatively large collector resistor. Note that the threshold voltages are almost centered between the 5V supply and ground, maximizing noise marging and making the gate compatible to CMOS logic levels.
02/15/2020 at 16:03 •
I designed a neat breadboardable LTL-NAND2 gate to test the design in hardware. You can find the PCB layout and a photo of the finished product above. I use a BAW56 dual-diode in a SOT23 package for the input diode. This form factor is much easier to handle than single diode SMD packages and there is no cost disadvantage. You can see the LED in the center of the PCB. I made a few variation with different LEDs: green (high Vf) and red (lower Vf) and different collector resistors.
Transfer characteristics were measured by using the DAC and ADC of an ATtiny416. You can see that different LEDs can be used to adjust the threshold levels of the NAND2 gate. Red with a low forward voltage leads to a L->H threshold around 1.65 V while green as it 2.24/2.33V depending on collector resistor.
To build up more complex circuits it is also important to study the effect of output loading. The figure above shows the NAND2 gate with floating output and with another NAND2 gate connected to it. The threshold is slightly shifted for the loaded output, but not to a level of concern.
The scope picture above shows the transient switching behavior of a loaded NAND2 output with green LED and 8.2k collector resistor. One can see that there are actually two elements to the rising edge. Initially, the voltage rises quickly and is then followed be a slower slope. During the initial part, the 3.4k base resistor of the connected gate helps pulling up the output. However, after the threshold voltage is reached, the current from the base transistor flows into the base of the transistor and the output is only pulled up by the 8.2k collector resistor.
The behavior of the NAND2 gate with 1.8k collector resistor, as shown above, is more consistent and shows a fast rising edge up to Vhigh. I therefore decided to focus on using 1.8k as a collector resistor.
02/15/2020 at 17:33 •
After characterizing a basic NAND2 gate, the next step is to measure the timing properties of the LTL gate. For this purpose I built a ring oscillator based on five gates. The PCB design is shown above. I added one additional inverter as an output buffer to avoid loading of the oscillator while measuring its frequency.
I built two versions of the ring oscillator: One with red LED and one with green LED, both using 1.8k collector resistors.
The scope screenshot shows the input (yellow) and output (turquoise) waveform of one inverter in the ring oscillator (green led). The falling edge is steep since it is actively pulled down by the transistor. The rising edge is, again, separated into two regions depending on wether only collector resistor or base and collector resistor are involved in pulling up the node.
The diagram above shows measurements of ring oscillator frequencies versus supply voltages. The blue line corresponds to the inverter with green LED, the orange line to a red LED. There is a clear trend towards higher frequency for higher supply, which can be explained by the availability of more switching current. The red LED LTL gate has a lower threshold voltage and does therefore switch earlier and faster. Since this design is based on the PMBT2369 switching transistors, no dominant influence of base saturation is observered. LTL gates with normal small signal transistores should exhibit a speed-supply relationship similar to what I observed with RTL.
The supply current shows a linear relationship with supply voltage, as expected for a resistor-loaded gate.
02/16/2020 at 19:09 •
After successful validation of the LTL concept in real hardware I started to build up a library of common gates in LTspice as a foundation for the design of a CPU.
The basic gate of LTL is the NAND2 gate. Symbol and circuit shown above. In my final design I used gates with different threshold level so I added a "G" to a high threshold device with a green LED.
Every gate was tested in a simple testbench in LTspice. I arbitrarily chose a fan out (FO) of 7 for the test case, although this does not occur in the real design.
Test waveforms for the NAND2 gate are shown above - nothing peculiar. There is a little crosstalk between the inputs of the gates if one input is high and the other one is pulled low. This is due to the extremely high slew-rate of the falling edge on the output. In a physical implementation this will hopefully be reduced a bit by additional parasitic capacitances to the power plane.
Next is the NOR2 gate. This can be easily realized by a wired AND of two LTL inverters. A minor but very important detail: If a gate uses a wired AND at the output, neither of the LEDs will be representative of the output signal. In practice this means that additonal indicator-LEDs may have to be added to monitor certain nodes.
Last one is the AOI2 gate (AND OR INVERT). You may not be familiar with this kind of gate, but it is a very useful building block due to it's simple implementation. For example, it can be used as a multiplexer or as part of an ALU.
Finally, a list of part counts for each gate. Since my intention is to build a CPU with a minimal amount of discretes, it is important to keep track of this.
Not too exciting, so let's get to the more special building blocks next...
02/18/2020 at 21:07 •
As a next step we will look into options to design XOR2 gates in LTL.
Another option is to use an AOI2 gate and two inverters. The number of components is almost the same as the NAND2 implementation, but now the propagation delay is only two gates. Furthermore, often inverted signals are alrady available as output from a previous stage. In that case, the inverters can be omitted.
An LTL version of a XOR2 gate based on a cross coupled transistor pair is shown above. First, this device has an output inverter to restore the low level. An input diode and resistor is added to avoid current sinking during high. To fix the threshold levels, two additional diodes were added (D1, D3). LEDs cannot be used in this place, because there are other elements in the current path (D1,D2, output transistor from preceding gate) that add to threshold voltage. The threshold level is still defined by the differential voltage between two inputs. This is still of concern, but a little less relevant now since the output levels have been restored. Assuming the input low level is 1xVCEsat, the threshold level is equal to VD1-VD3+VBE+D2+VCESat: 0.7+0.7+0.2 ~ 1.6V. This is much higher than the 0.7V of the bare transistor, however still not the same as the LTL threshold levels.
02/19/2020 at 20:23 •
Now to the last category of building blocks: Flip Flips.
If you grew up learning about digital electronics in the advanced CMOS era, like me, you will most likely be accustomed to using edge triggered flip flops for everything. Unfortunately, it turns out that proper edge triggered flip flop require at least 6 NAND gate equivalents, unless you have dynamic CMOS logic at your disposal.
For those of us who were suddenly beamed into the discrete LTL age, latches are a much more part count efficient solution, as they only consume about half as many components as a static edge triggered flip flop.
A commonly known minimal representation of a gated D-latch in NAND2 is shown above. See also Wikipedia article. A nice propery of this design is that it only requires a single clock input and has both inverted and non-inverted data outputs. Data from Din is forwarded to the output while Clk is high. The state of the latch is frozen on the high->low transition of the clk and held while clk is low.
When using this design in high speed circuits it becomes apparent that it has a nasty habit of generating glitches. The origin of this effect is the NAND2 gate in the lower left. The clock signal arrives on one input directly and on the other it is delayed through the NAND2 gate in the top left.
This effect can be somewhat reduced by tweaking the propagation delay of the logic gates. In LTL this is easily possible by changing the LED color to change threshold voltage. In this case I introduced a faster "red" (hence the R) gate with lower threshold as the top left gate.
There is also a way to reduce gate count to three by replacing one of the NAND2 gates with a wired AND. This is described in a now expired patent. (A similar design is described in this patent)
The patent also describes to work around the aforementioned glitch by introducing one faster gate. A disadvantage of this design is that it is only has an inverted output. The clock input is also inverted compared to the previous design: Data will be forwarded for clk='0' and held for clk='1'.
02/22/2020 at 00:17 •
The original MCPU architecture is shown above. There are separate flows for the address and data-path. The state machine is not shown. Since this design is catered for a CPLD, it assumes edge triggered flip-flops for all registers.
The MCPU programmers model is based on two registers: Accumulator and PC. The ISA consists of four instructions in a fixed encoding that is based on a two bit opcode and a six bit memory address. This ISA can be directly mapped to the datapath shown above with minimal control overhead. See MCPU link for more information including assembler, emulator and example code.
02/22/2020 at 10:29 •
Implementation of the address path is straightforward based on the previously designed gates.
The first design of the adress path is shown above. A half adder is needed to increment the PC. Since the gates are relatevely fast, I used a ripple carry adder. There are two latches for address and PC respectively. An AOI2 gate is used as multiplexer between PC and external address. The address latch can be loaded with zeros by pulling both control inputs of the MUX to low. This can be used to reset the PC.
Six of the bit slices were combined in a testbench to test the design of the full width datapath. A two phase clock is needed to alternatingly clock both latches. In this setting the circuit is configured to reset the PC and then increment it with each clock cycle.
Output traces of clock, reset and the first two output bits are shown above. Everything works nicely.
02/22/2020 at 11:25 •
Designing PCBs with regular structures using free tools turned out to be surprisingly tedious. In the end I used the free version of Eagle due to it's block feature which allowed replicating of circuit and layout units. The other options I looked at were EasyEDA and KiCad.
Unfortunately, the free version of Eagle is limited to a single sheet, so I ended up transferring my nice hierachical LTspice implementation into a single paged mess of a schematic. The image above shows a one bit slice.
Curiously enough, none of the many LEDs in the LTL gates represented the actual state of the address output pins. Therefore I introduced two additional indicator LEDs.
The final PCB layout is shown above. I managed to fit a four bit wide slice of the adress path into one 8,5x7cm² PCB.