H bridge complimentary transistors must be a matched pairs.
Oh, I did not mean both sides ACTIVE, that would be dumb thing to do obviously, I meant that current draw is there for either when active only L side or only R side of the bridge. Also such dead short would most likely produce more then 300mA, the first h-bridge went up to 3A then power supply went to overcurrent mode.
So far only thing that is about to smoke are those PNP base resistors which are now actualy brown in middle 
I'll try to swap them for bigger values and see.
Indeed, but current is not the issue, its the high voltages you get (known as "inductive kick back"), you need those diodes in an H-bridge driving anything inductive such as a motor / electromagnet / relay. Even small inductors can generate 100's of volts and zap your semiconductors instantly.
No, no need for this whatsoever, they are used in saturation and cutoff, so there's nothing to match anyway.
Its complementary, not complimentary (which means a freebie).
The speed of switching must be match to achieve cool operation.
Vbe and HFE matching is also needed for cool operation as the transistors do not immediately go into cutoff or saturation do to input capacitance effects.
Normally you'd make the deadtime large enough to match the datasheet's worse-case switching times for the device across full temperature range.
Note that switching speed changes with temperature and load current, so unless you can predict these accurately there's no way to take advantage of any device matching. (Minimizing deadtime reduces losses in the diodes).
When you have parallel banks of MOSFETs making a single switch then you have to match within each bank so that you get equal current sharing during the switching transient (if one device hogs all the current it can be a problem). Perhaps that's what you are thinking of?
YES, Definitely then.
(Using BJTs) You can prove what I’ve mentioned by purposely having widely varying characteristics between the NPN and PNP.
You will find, as the differences widen, the hotter the transistors will be.
As a side note (a slightly different application) when the 4 legs are separately controlled by say 4 outputs on an Arduino, placing a small delay between switching one leg to the other, can completely remove any chance of shoot through.
The delay of course gives time for a transistor to turn off before the next turns on.
Example:
An H-Bridge is only necessary when changing directions is a requirement.
This is for a "clock" - generally, they go in one direction.
Here is the simulation with the left hand side active and 1k resistors for the PNP bases. I've used a 470R resistor to simulate the load. Currents in the pA and fA range you can ignore. Only the mA is significant. I don't have models for your transistors so I have used general purpose ones.
It looks OK:
EDIT
Here is the LTspice model incase someone want to play with it:
H-Bridge-Full-Transistor_V0_02.zip (807 Bytes)
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An H-Bridge is only necessary when changing directions is a requirement.
That is exactly the point. The clock go in one direction, yes, but to do so, they require pulses that change polarity for each pulse.
Here is the simulation with the left hand side active and 1k resistors for the PNP bases.
Thanks, I will try it tomorow. My soldering iron is cold and I am tired today already
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Why don't you use a 50cent L293D chip (post#4).
Is this a school assignment?
Leo..
No wonder, calculate yourself: 24V/220R is a base current of about 100mA and 2.4W resistor power!
But this base current is required to safely drive 1A of output current. You may try 470R for half the current and 1/4 of the power.
Using TIP... darlingtons would allow for much lower base currents.
You haven't looked at clock motors then. 
They go backwards then do they?
NO! These clocks need pulses of opposite polarity to the previous pulse in order to run. The small electric pointer clockworks, which run with 1.5V, also work in this way, there is an IC inside that generates these impulses controlled by quartz, only they need one impulse every second, but here too the polarity is changed after every impulse.
Reverse engineer any dollar store 1.5V clock mechanism. They work the same way, except its every second not every minute.
Am I totally out of it? Where's all that at?
The dollar store? Maybe it's just too boring and technical for a YouTube blast. I found out by scoping it.
So relays would be inappropriate?
They'd go "tick-tock".
Hey, there's a project!
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