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miniature double voltage transformer (for low voltages) in market?

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Greetings,
I developed an experimental circuit (see attachment)



The battery and resistor simulates a typical power source that I have (that is 1.4V or 4.5V typically at 4mA at maximum). Switches represent relays controlled externally. Capacitor C1 acts as energy collector when sw1 and sw2 are on. Furthermore, sw3 and sw4 is temporarily off from generator and capacitor C1 to isolate load from power source. When switches status reverse, C1 acts a source for the remaining circuit. My goal is to convert typical pulse to a higher voltage (4V or 11V) at the price of reducing current to 2mA minimum. The transformer in this schematic is not an accurate representation of dual voltage transformer. (the editor does not support it) In this case, the cores of two transformers should be connected. On other circuit simulator, I was able to achieve voltage spike or oscillations decaying exponentially and rapidly. The voltage spike was greater that 10V. Later I will attempt to develop circuit (using passive zero resistance) to turn decaying oscillation into a narrow pulse which I believe it can be done. My question is, can I find miniature dual voltage transformer for this typical low voltage and current inputs with very little losses in conversion process (converting input to output? I was looking in alternative circuits such as dc to dc converters or using microamps powered amplifiers and I could not find a circuit to convert input source from capacitor (C1) to a pulse of higher voltage...

thank you for your time
 

Maybe you could elaborate on your objective? The exact pulse (width, voltage, current).

I have two options,
if input voltage is 1.4V pulse of 5mA current with duration of , let say, 5ms. Then the output desired is a pulse 5V 1.5mA with duration of 1ms. Another options is, if input voltage is 4.5V pulse of 5mA current with duration of , let say, 5ms. Then the output desired is a pulse 12V 1.5mA with duration of 1ms. I thing I should solve it mathematically by describing the input in form of a function f(x) and output with a function of g(x) and consider a circuit of function of h(x). Then convolution of input with system circuit yields an output or f(x)*h(x) -> g(x) . To find a circuit I have to deconvolve output signal with input signal or g(x)*f(x) (-1) -> h(x). This is an analytical approach. That is the only way to get rid of transformer unless I find one. The above circuit I used is by trial and error without analytical method. Of course, I will appreciate suggestions on transformers as well. Thanks js on the component suggestion, I am looking into that.
Thanks
 

a transformer can change the voltage [and impedance] but not the pulse width
 

a transformer can change the voltage [and impedance] but not the pulse width

Thats okay with me. Also the size does not matter. Just a function. All I need is a pulse with higher voltage with current more than 1.5 mA. My original question is ' is there a transformer dual voltage that can function under low power ratings.?' Or should I make it myself?
 

yes there are such transformers but they will, of course, simply multiply the voltage

but there is no pulse width change, nor assurance of a current minimum
 

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