
2022-04-24.


For trying to measure battery impedance directly, but quickly and using immediately available equipment:

A series loop was made of a HP33120A signal generator (ground-referenced), with the middle of its BNC going to a (3300 nF + 220 nF) capacitor, then to the '+' terminal of the 'battery under test' (100V alkaline or lithium-ion), then a 10 ohm resistor completing the circuit to the sig-gen ground. 

An Agilent  DSO-X 2014A oscilloscope (also ground-referenced) measured the voltage across the resistor, connected straight into Ch2, and on Ch1 it measured the voltage from ground to the far end of the battery (i.e. voltage over the battery and resistor) but measured through a big capacitance to block the DC voltage without much phase shift down to hertz) into Ch1. Preferable would have been to measure each voltage separately (the resistor for the current, and across the battery for the voltage), and perhaps to measure well enough to be able to handle the sought AC voltage against the big DC level. 

The restriction of both instruments having ground-referenced BNC sockets was part of the limitation. We don't mind lifting protective-earths now and again, but the result will likely be a mess due to all the couplings and noise; better avoided in quick measurements where there's not time to extra-check everything for lack of disturbance. 

The oscilloscope had its 'Measurement' feature used, to determine AC N-cycle RMS on each of the two channels, and the phase angle between the channels.  It was very unstable on phase measurement until using the averaging or high-res setting for acquisition mode. 

The sig-gen was adjusted and the oscilloscope rms voltages and phase-difference were read and recorded (all manually). 


---- Initial try 

All with sig-gen on max, '10V pp' (expect 10 V peak if it's as usual assuming 50ohm load and so doubling its emf).   
Initially just normal acquisition mode, so very jumpy measurement of phase. 
Also, in this initial try, the capacitor in series with the signal generator was just the 0.22 uF, not the combined 3.3+2.2 uF. 

f[Hz]  Ch1(rms)[V]  Ch2(rms)[V]  phase(1->2)[deg]
20000	1.80	0.875	-7 
15000   1.70	0.808	-6.5  [i.e. -5.x to -7.5 but usually 6.x looking around the middle]
10000	1.48	0.680	-9.6  [often in 10.x]
 9000	1.41    0.642   -8
 8000	1.33	0.600	-8.5
 7000	1.24	0.550	-10.3
 6000	1.13	0.490	-10.8
 5000	1.00	0.427	-11.9
 4000	0.85	0.355	-14
 3000	0.685	0.275	-16
 2000	0.491	0.188	-18
 1000	0.287	0.096	-28
  900	0.266	0.087	-30
  800	0.246	0.078	-31
  700	0.225	0.068	-33
  600	0.205	0.058	-37
  500	0.186	0.049	-42
  400	0.168	0.039	-44
  300	0.150	0.029	-47
  200	0.133	0.019	-51
  100	0.111	0.098	-?? [really dancing around] 

[ now improved by 'averaging' acquisition mode, #8 averages ]
  100   0.111   0.098   -51
   90	0.108	0.088	-50
   80	0.104	0.0078	-49
   70	0.099	0.0069	-47
   60	
getting too tiny and jumpy !


---- Proper tests 

Kept the averaging (higher frequencies) or high-res setting for all these. 

Used a bigger series capacitor, 3.3 uF + 0.22 uF, for the signal generator.  
(The 3.3 calls itself 3.3MF [& 160V], which is puzzling as it's far too small an object to be plausible for 3.3 mF, but the same manufacturer did use a micro symbol for the 0.22uF capacitor of similar design, so why not write 3.3uF or 3300nF? The newer LCR meter says this capacitor is -j48 ohm at 1 kHz, so it's clearly 3.3 uF.)

Checked also the parallel bundle of three even bigger capacitors used as dc block for oscilloscope Ch1 input: LCR meter says -j2.52 ohm at 1 kHz, so 63 uF, so 22 uF each.  Time-constant > 1 minute!  Good down to e.g. 0.5 Hz with decentish phase response.  In order not to waste time waiting, the oscilloscope input was shorted at turn-on to get this capacitor charged in a second or two. 

Now try again, going up, with the bigger capacitance and the averaging. 
This time, keep current more stable by reducing voltage as frequency increases. 
At the weakest currents, with high gain needed [10 Hz] the 'high res' acquisition mode ended up better than the averaging - it presumably is averaging of adjacent higher-sampled sample points, instead of the averaging of multiple periods.  (The plain averaging wiggled in amplitude even though not overloaded on either channel as checked against the non-averaged view.)


Hz	mV,ch1	mV,ch2	deg,1->2 
10	465	15.4	-16   # at 10V 
20	785	29.8	-25
30	996	43	-32
40	1132	56.2	-37
50	632	33.9	-43   # to 5V for 50Hz
60	668	39.8	312
70	695	45.8	-50
80	717	51.8	-52
90	734	57.7	-54
100	747	63.6	-55
200	826	119	-55   
300	881	170	-50   # switched from high-res to averaging from here on
400	929	214	315
500	972	251	-41
600	1008	282	320
700	412	124	-35   # to 2V for 700Hz
800	422	132	-32
900	430	139	-30
1000	436	145	-28
2000	455	173	-19
3000	453	181	-15
4000	448	185	-13
5000	444	187	-12
6000	440	190	-11
7000	435	191	-11
8000	432	192	-10
9000	429	193	-9
10000	427	193	-9
11000	424	194	-8
12000	422	194.5	-8
15000	417	195	-8
20000	410	197	-7
30000	402	199	-5

Now the lithium battery.
Same sequence. 

10 	39.6	15.8	-3
20	78	31.5	-2
30	116	47.3	-2
40	153	63	-2
50	190	78.6	-1
50	94.7	39.2	-2  # with 5V
50	95.5	39.2	-2  # 5V and changed scope gain to match [note, scope is frequently adjusted in gain and timebase] 
60	113	47.0	-2
70	131	54	-2
80	150	62.5	-2
90	168	70.1	-2
100	186	77.6	-2
200	354	148	-2
300	500	209	-3
400	616	260	-3
500	707	300	-3
600	777	331	-4
700	831	356	-4  # still 5V
700	331	142	-5  # now 2V
700	329.7	142.3	-4  # adjusted scope 
800	346	150	-5
900	358	156.5	-5
1000	368	162	-5
2000	398	184	-6
3000	398	192	-6
4000	395	196	-6
5000	391	198	-6
6000	389	199	-5
7000	387	200	-5
8000	385	201	-4
9000	383	201	-3
10000	382	202	-3
11000	382	202	-3
12000	380	202	-3
15000	379	203	-3
20000	377	203	-2
30000	375	203	-1



